Constructive Adpositional Grammars: Foundations of Constructive Linguistics

&RQVWUXFWLYH $GSRVLWLRQDO *UDPPDUV

&RQVWUXFWLYH $GSRVLWLRQDO *UDPPDUV )RXQGDWLRQV RI &RQVWUXFWLYH /LQJXLVWLFV

%\

)HGHULFR *REER DQG 0DUFR %HQLQL

&RQVWUXFWLYH $GSRVLWLRQDO *UDPPDUV )RXQGDWLRQV RI &RQVWUXFWLYH /LQJXLVWLFV E\ )HGHULFR *REER DQG 0DUFR %HQLQL 7KLV ERRN ILUVW SXEOLVKHG  &DPEULGJH 6FKRODUV 3XEOLVKLQJ  %DFN &KDSPDQ 6WUHHW 1HZFDVWOH XSRQ 7\QH 1( ;; 8. %ULWLVK /LEUDU\ &DWDORJXLQJ LQ 3XEOLFDWLRQ 'DWD $ FDWDORJXH UHFRUG IRU WKLV ERRN LV DYDLODEOH IURP WKH %ULWLVK /LEUDU\ &RS\ULJKW ‹  E\ )HGHULFR *REER DQG 0DUFR %HQLQL $OO ULJKWV IRU WKLV ERRN UHVHUYHG 1R SDUW RI WKLV ERRN PD\ EH UHSURGXFHG VWRUHG LQ D UHWULHYDO V\VWHP RU WUDQVPLWWHG LQ DQ\ IRUP RU E\ DQ\ PHDQV HOHFWURQLF PHFKDQLFDO SKRWRFRS\LQJ UHFRUGLQJ RU RWKHUZLVH ZLWKRXW WKH SULRU SHUPLVVLRQ RI WKH FRS\ULJKW RZQHU ,6%1    ,6%1   

Table of Contents

/LVW RI )LJXUHV                                                        L[ /LVW RI 7DEOHV                                                         [LLL /HJHQGD                                                              [Y &KDSWHU  ,QWURGXFWLRQ                                                           7KH DGSRVLWLRQDO SDUDGLJP                                          7KH IRUPDO PRGHO                                                  :KDW LV LQ WKLV ERRN"                                                &KDSWHU  6\QWD[                                                               *RYHUQPHQW                                                      'HSHQGHQF\                                                      9DOHQF\                                                          7UDQVIRUPDWLRQ                                                   

    

&KDSWHU  &RQVWUXFWLRQV                                                         *UDPPDU FKDUDFWHUV                                               7KH VWDWLYHYHUEDQW UHODWLRQV                                        7KH DGMXQFWLYHVWDWLYH UHODWLRQV                                     7KH FLUFXPVWDQWLDOYHUEDQW UHODWLRQV                                 7KH FLUFXPVWDQWLDODGMXQFWLYH UHODWLRQV                              :KDW LV ODQJXDJH VWUXFWXUH"                                        

      

&KDSWHU  7UDQVIRUPDWLRQV                                                      7KH HSVLORQ WUDQVIRUPDWLRQ                                         7KH PHFKDQLFV RI WUHH WUDQVIRUPDWLRQV                               +RZ UHGXQGDQF\ ZRUNV                                            7R EH DQG WR KDYH WKDW LV WKH TXHVWLRQ                               +LGGHQ SUHGLFDWLRQV                                              

     

YL

7DEOH RI &RQWHQWV

7KH ZKLFK KXQW                                                     &DXVDWLYHV DQG IDFWLWLYHV                                            &KDSWHU  &RQVWUXFWLYH GLFWLRQDULHV                                                7UDQVIHUHQFH                                                       6WUDWHJLHV RI JUDPPDU FKDUDFWHU FKDQJH                               7RZDUG FRQVWUXFWLYH GLFWLRQDULHV                                     &KDSWHU  'LVFRXUVH DQG EH\RQG                                                  +RZ WR GHDO ZLWK LOORFXWLRQ FRQVWUXFWLYHO\                            3UDJPDWLF DGSRVLWLRQDO WUHHV                                         $ WD[RQRP\ RI SUDJPDWLF FKDUDFWHUV                                  &RQVWUXFWLYH LQGLUHFW VSHHFK DFWV                                     &RQVWUXFWLYH &RQYHUVDWLRQDO $QDO\VLV                                &KDSWHU  &RQFOXVLRQ                                                            $SSHQGL[ $ ([DPSOHV                                                             ,QWURGXFWLRQ                                                        6\QWD[                                                             &RQVWUXFWLRQV                                                      7UDQVIRUPDWLRQV                                                    &RQVWUXFWLYH GLFWLRQDULHV                                            'LVFRXUVH DQG EH\RQG                                               $SSHQGL[ % 7KH )RUPDO 0RGHO                                                     *UDPPDU FDWHJRULHV                                                $GWUHHV                                                            7UDQVIRUPDWLRQV                                                    $Q DEVWUDFW YLHZ                                                   /LQNV ZLWK RWKHU IRUPDO PRGHOV                                      1RWHV                                                                

7DEOH RI &RQWHQWV

YLL

%LEOLRJUDSK\                                                          ,QGH[                                                                

List of Figures 7KH WZR LQWHUSUHWDWLRQV RI OD YHFFKLD SRUWD OD VEDUUD            7KH DGSRVLWLRQDO WUHH RI Ê OD URVVD GL 0DUDQHOOR             

 

7KH DEVWUDFW DGSRVLWLRQDO WUHH VWUXFWXUH                ([DPSOH RI UHFXUVLYH DGSRVLWLRQDO WUHH                ([DPSOH RI DQ H[WHQGHG DGSRVLWLRQDO WUHH               ([DPSOH RI SDUWLDO FRQVWUXFWLRQ                    7KH DEVWUDFW JRYHUQPHQW UHODWLRQ                   7KH SDFNHG WUHH RI ,¶YH QRW VHHQ /L]D 6KH ZDV QRW ZLWK 3DXO    7KH SDFNHG WUHH RI ,¶YH QRW VHHQ /L]D 6KH ZDV QRW ZLWK 3DXO    7KH DEVWUDFW GHSHQGHQF\ UHODWLRQ                   7KH SDFNHG WUHH RI ,¶YH QRW VHHQ /L]D 6KH ZDV QRW ZLWK 3DXO    7KH FROODSVHG WUHH RI
                     

                     

                     

                     

$EVWUDFW WUHHV DQG JUDPPDU FKDUDFWHUV      $EVWUDFW YHUEDQW UHODWLRQV             $EVWUDFW DGMXQFWLYH UHODWLRQV            $EVWUDFW LGHQWLW\ UHODWLRQV UHGXQGDQF\      7KH FROODSVHG WUHH RI $K             7KH H[SOLFLW DQG UHGXFHG WUHH RI 'HDU PH     7KH WUHHV RI 3DXO DSRORJLVHV WR /L]D       7KH WUHHV RI 3DXO EURNH WKH YDVH  7KH YDVH EURNH 7KH WUHHV RI 1JDUUNXQWX DULOL NDQ\LUUNX   7KH WUHHV RI ,Q~ ^JD_ZD` KDVtWWH LPDVX     

         

         

         

         

         

         

         

         

         

         

         

         

         

         

[

/LVW RI )LJXUHV

7KH WUHHV RI ZDEDVHG -DSDQHVH SKUDVHV ZLWK LDGMHFWLYHV HI  7UHHV RI 6DODNVKD DQG LR KR VXGDWR               7KH XQGHUO\LQJ WUHH RI WKH EDOO LV RQ WKH WDEOH         7KH ILQDO WUHH RI FKLOGUHQ¶V VSHHFK EDOO WDEOH           7KH WUHHV RI , ZDQW PRUH PLON                  7KH WUHHV RI WKH MXLFH LV JRQH                  7UHHV RI R QRIR LD SHSH                      0LQLPDO VWUXFWXUDO SDLU IRUWHV YHQWRV DQG YHQWRV IRUWHV      7KH WZR SRVVLEOH LQWHUSUHWDWLRQV RI DPRU SDWULV          7UHHV RI WKH HOHSKDQW DQG WKDW HOHSKDQW              7UHHV RI WKDW RQH DQG WKDW                     7KH FLUFXPVWDQWLDO RI J LQ HYLGHQFH              0DQ\ FLUFXPVWDQWLDOV DW ZRUN LQ K              $EVWUDFW WUHH RI FLUFXPVWDQWLDOYHUEDQW UHODWLRQV JK      7UHH RI 'RPDQL YHQJR DQG 9HQJR GRPDQL             7UHH RI 4XDQGR YHUUDL"                      7UHHV RI WKDW KLJKO\ VHQVLWLYH WRSLF H[SOLFLW DQG ǫ WUDQVIRUPHG 7UHHV RI XQ YUDLPHQW EHDX SD\VDJH H[SOLFLW DQG ǫ UHGXFHG  

                 

                 

                 

                 

                 

                 

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` SUHSDUHG^  `              7KH DGWUHH RI ZHUH VOHSW                      7KH DGWUHH RI ZDV VWHSSHG                     7UHHV RI 6KDK¶V VOHHSLQJ DQG 7KH PHOWLQJ RI WKH LFH FXEH       $GWUHHV RI 7KHUH DUH P\ VKRHV DQG 3DXO LV KHUH            $GWUHH RI 7XUNLVK NHGLP YDU                      7KH DGWUHHV RI 3DXO KDV JRW D %HQWOH\ DQG 3DXO KDV ZDVKHG KLV FDU 7KH DGWUHH RI 3DROD KD FRUVR OD PDUDWRQD HQWUR TXDWWUR RUH     7KH DGWUHH RI 3DROD q FRUVD D FDVD                 

                    

                    

                    

                    

/LVW RI )LJXUHV

[L

7KH DGWUHHV RI 3DROR KD ^ODYDWR OD FDPLFLD  OD FDPLFLD ODYDWD`   7KH DGWUHH RI 0HHWLQJ SHRSOH LV HDV\                 7KH DGWUHH RI 7KH PDFKLQH QHHGV IL[LQJ                7KH DGWUHH RI D ZRUNLQJ FODVV KHUR                 7KH DGWUHH RI D GHDG PDQ ZDONLQJ                 7KH DGWUHH RI ZLWKRXW WHOOLQJ KLP                  7KH DGWUHH RI $YHQGR WHOHIRQDWR                   7KH DGWUHH RI (VVHQGR SDUWLWD                    7KH DGWUHH RI $ /LVD SLDFH EDOODUH                   7KH DGWUHH RI 3 YXROH SURYDUH DG DQGDUH D IDUH XQD YDFDQ]D     7KH DGWUHH RI /DPHQWR HOHV WHUHP SHUGLGR R FRPERLR         7KH DGWUHH RI 0DULR KD XQD FDPLFLD ODYDELOH D VHFFR         $GWUHHV RI )UHQFK GH JRYHUQHG E\ VWDWLYHV               $GWUHHV RI )UHQFK GH JRYHUQHG E\ YHUEDQWV              7KH DGWUHH RI /L]D ZLSHG WKH WDEOH FOHDQ               7KH DGWUHH RI $OIUHG FDQ SD\ EHFDXVH                7KH DGWUHH RI $OIUHG FDQ SD\ KHQFH                 7KH DGWUHH RI WKH PDQ ZKR ERXJKW WKH ERRN IRU WKH JLUO        7KH DGWUHH RI WKH ERRN ZKLFK WKH PDQ ERXJKW IRU WKH JLUO       7KH DGWUHH RI WKH JLUO IRU ZKRP WKH PDQ ERXJKW WKH ERRN       7KH DGWUHH RI WKH ER\ ZKRVH ERRN WKH PDQ ERXJKW IRU WKH JLUO    7KH DGWUHH RI :KHQ 3DXO ZLOO FRPH EDFN /L]D ZLOO VPLOH       7KH DGWUHH RI , ZRQGHU KRZ PDQ\ HUURUV , GLG            7KH DGWUHH RI :KDW WLPH LV LW"                     7KH DGWUHH RI ,FK ODVVH .DUO GLH %OXPHQ JLH‰HQ            7KH DGWUHH RI 3DXO PDNHV /L]D EX\ D FDU E\ 5RQ¶V IRU  SRXQGV 7KH DGWUHH RI OHW KHU GR LW                      

                          

                          

                          

                          

7KH SODFH RI OH[HPHV LQ WKH DEVWUDFW DGSRVLWLRQDO WUHH VWUXFWXUH        7KH FRQVWUXFWLRQ RI WKH DGMHFWLYHWRVWDWLYH WUDQVIHU L ULFFKL          5HSUHVHQWLQJ WUHH WUDQVIRUPDWLRQV                       +RZ HPSKDVLV LV PDSSHG LQWR LQIRUPDWLRQ SURPLQHQFH 3UDJPDWLF DEVWUDFW DGWUHH DW WXUQ             3UDJPDWLF DEVWUDFW DGWUHH DW WXUQ             +RZ WXUQV DUH UHSUHVHQWHG                $EVWUDFW SUDJPDWLF DGWUHH IRU DVVHUWLYHV         3UDJPDWLF DGWUHH RI WKH DVVHUWLYH , ZRQ WKH UDFH     $EVWUDFW SUDJPDWLF DGWUHH IRU GLUHFWLYHV         3UDJPDWLF DGWUHH RI WKH GLUHFWLYH :LQ WKH UDFH    

       

       

       

       

       

       

       

       

       

       

       

[LL

/LVW RI )LJXUHV

3UDJPDWLF DGWUHH RI WKH GLUHFWLYH /L]D RUGHUHG 3DXO WR OHDYH    $EVWUDFW SUDJPDWLF DGWUHH IRU FRPPLVVLYHV             3UDJPDWLF DGWUHH RI WKH FRPPLVVLYH ,¶OO ZLQ WKH UDFH        $EVWUDFW SUDJPDWLF DGWUHH IRU H[SUHVVLYHV              3UDJPDWLF DGWUHH RI WKH H[SUHVVLYH , WKDQN P\ WHDP IRU WKHLU KHOS  $EVWUDFW SUDJPDWLF DGWUHH IRU 'HFODUDWLRQV             3UDJPDWLF DGWUHH RI «EODFN VKHHS«                $GWUHHV RI WKH LQGLUHFW GLUHFWLYH , SURPLVH \RX¶OO GR LW        $GWUHHV RI WKH LQGLUHFW FRPPLVVLYH , UHTXHVW P\VHOI WR EH EUDYH  7ZR H[DPSOHV RI LQGLUHFW DFWV HQFDSVXODWLQJ H[SUHVVLYHV     

         

         

         

         

         

List of Tables ,QGLFDWRUV RI JRYHUQPHQW DQG GHSHQGHQF\                 



7KH PRUSKRORJLF JUDPPDU FKDUDFWHUV                    7KH XQHUJDWLYHXQDFFXVDWLYH K\SRWKHVLV                  

 

6RPH (QJOLVK FRQMXQFWLRQV DQG WKHLU WUDMHFWRU\                $ W\SRORJLFDO FRPSDULVRQ RI WKH PDLQ FRUUHODWLYHV              &RQVWUXFWLYH H[LVWHQWLDO FRUUHODWLYH DQVZHUV LQ YDULRXV ODQJXDJHV       *HUPDQLF YHUEDQW FRQVWUXFWLRQ LQ (QJOLVK SHUIRUPHG E\ DEODXW        6WDWLYH HH DQG YHUEDQW —D WUDQVIHUV LQ +HEUHZ H[DPSOH         5HSUHVHQWDWLRQ RI DQ DGSRVLWLRQDO JUDPPDU                  6HDUOH¶V GLUHFWLRQV RI ILW                            7KH SUDJPDWLF FKDUDFWHUV                           7KH &RQVWUXFWLYH &RQYHUVDWLRQDO $QDO\VLV RI )LQQ          

Legenda $EEUHYLDWLRQV DGWUHH         VKRUWFXW IRU µDGSRVLWLRQDO WUHH¶

ad j            JHQHULF DGMHFWLWYH ad p           JHQHULF DGSRVLWLRQ dep           GHSHQGHQW JURXS gc             JHQHULF JUDPPDU FKDUDFWHU gov            JRYHUQRU JURXS "WKH /DG\      H[DPSOH RI GRXEWIXO H[SUHVVLRQ V\QWDFWLFDOO\ RU VHPDQWLFDOO\

JRRG KHUH     H[DPSOH RI XQJUDPPDWLFDO H[SUHVVLRQ V\QWDFWLFDOO\            H[DPSOH RI H[SUHVVLRQ FDQFHOHG E\ D WUDQVIRUPDWLRQ  ZLWK

Abs           DEVROXWLYH FDVH PRUSKRV\QWDFWLFDOO\ PDUNHG Acc           DFFXVDWLYH FDVH PRUSKRV\QWDFWLFDOO\ PDUNHG Gen           JHQLWLYH FDVH PRUSKRV\QWDFWLFDOO\ PDUNHG Dat           GDWLYH FDVH PRUSKRV\QWDFWLFDOO\ PDUNHG Erg           HUJDWLYH FDVH PRUSKRV\QWDFWLFDOO\ PDUNHG Nom           QRPLQDWLYH FDVH PRUSKRV\QWDFWLFDOO\ PDUNHG Opener        VHPDQWLF UROH FDVH RU FRQFHSW LQ D VHPDQWLF IUDPH H[DPSOH

6\PEROV ←             LQGLFDWRU RI GHSHQGHQF\ →             LQGLFDWRU RI JRYHUQHPHQW ↔             XQGHUVSHFLILHG LQGLFDWLRQ JRYHUQHPHQWGHSHQGHQF\ >             VKRUWFXW IRU WUDQVIHUHQFH {             DGSRVLWLRQDO WUHH WUDQVIRUPDWLRQ △             VKRUWFXW IRU D KLGGHQ DGSRVLWLRQDO WUHH

[YL

/HJHQGD

/HWWHUV ↓ A           DVVHUWLYH SUDJPDWLF FKDUDFWHU A             DGMXQFWLYH JUDPPDU FKDUDFWHU ↑ C            FRPPLVVLYH SUDJPDWLF FKDUDFWHU D             JHQHULF JUDPPDU FKDUDFWHU RI WKH GHSHQGHQW l D           'HFODUDWLRQ SUDJPDWLF FKDUDFWHU ↑ D           GLUHFWLYH SUDJPDWLF FKDUDFWHU E              FLUFXPVWDQWLDO JUDPPDU FKDUDFWHU = E           H[SUHVVLYH SUDJPDWLF FKDUDFWHU ǫ              ]HURPDUNHG DGSRVLWLRQ F              DGSRVLWLRQ JUDPPDU FKDUDFWHU LPSRVHG E\ WKH DGSRVLWLRQ G             JHQHULF JUDPPDU FKDUDFWHU RI WKH JRYHUQRU I              XQGHUVSHFLILHG RU JHQHULF YHUEDQW JUDPPDU FKDUDFWHU Ivx             YHUEDQW JUDPPDU FKDUDFWHU v LQGLFDWHV YDOHQF\ x VDWXUDWLRQ ← − I             XQDFFXVDWLYH YHUEDQW DOZD\V PRQRYDOHQW → − I             XQHUJDWLYH YHUEDQW DOZD\V PRQRYDOHQW I2             ELYDOHQW YHUEDQW JUDPPDU FKDUDFWHU I3             WULYDOHQW YHUEDQW JUDPPDU FKDUDFWHU I4             WHWUDYDOHQW YHUEDQW JUDPPDU FKDUDFWHU I5             SHQWDYDOHQW YHUEDQW JUDPPDU FKDUDFWHU L              OLVWHQHU W\SH RI DFWDQW λ              JHQHULF SUDJPDWLF FKDUDFWHU O             VWDWLYH JUDPPDU FKDUDFWHU H[WUDYDOHQF\ RU JHQHULF Ox            VWDWLYH JUDPPDU FKDUDFWHU  x LQGLFDWHV WKH DFWDQW YDOXH O1            VWDWLYH JUDPPDU FKDUDFWHU ILUVW YDOHQF\ O2            VWDWLYH JUDPPDU FKDUDFWHU VHFRQG YDOHQF\ O3            VWDWLYH JUDPPDU FKDUDFWHU WKLUG YDOHQF\ O4            VWDWLYH JUDPPDU FKDUDFWHU IRXUWK YDOHQF\ Ox            VWDWLYH JUDPPDU FKDUDFWHU H[WUD YDOHQF\ Q             H[WUD LQYDOHQW DFWDQW LQ WKH FRQVWUXFWLRQ DV Ox R             UHFHLYHU D W\SH RI DFWDQW S              VSHDNHU D W\SH RI DFWDQW W             IRXUWK LQYDOHQW DFWDQW LQ WKH FRQVWUXFWLRQ DV O4 X             ILUVW LQYDOHQW DFWDQW LQ WKH FRQVWUXFWLRQ DV O1 ← − ← − X             XQDFFXVDWLYH DFWDQW DOZD\V IRU I → − → − X             XQHUJDWLYH DFWDQW DOZD\V IRU I Y             VHFRQG LQYDOHQW DFWDQW LQ WKH FRQVWUXFWLRQ DV O2 ← − Y             QRQSURPLQHQW VHFRQG LQYDOHQW DFWDQW LQ JRYHUQPHQW → − Y             SURPLQHQW VHFRQG LQYDOHQW DFWDQW LQ GHSHQGHQF\ Z              WKLUG LQYDOHQW DFWDQW LQ WKH FRQVWUXFWLRQ DV O3

Chapter One Introduction 7KLV ERRN SUHVHQWV D IUDPHZRUN WR XQGHUVWDQG KRZ ODQJXDJH LV VWUXFWXUHG²LQ SDUWLFXODU DW D PRUSKRORJLFDO DQG V\QWDFWLF OHYHO²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µODQJXDJH¶ WR UHIHU WR QDWXUDO ODQJXDJHV²VXFK DV (QJOLVK &KLQHVH RU 8UGX²LQ JHQHUDO WHUPV LI WKH FRQWH[W LV FOHDU HQRXJK WR DYRLG DPELJXLW\ 2WKHUZLVH ZH ZLOO VSHFLI\ LI ZH DUH WDONLQJ DERXW QDWXUDO RU IRUPDO DUWLILFLDO ODQJXDJHV $QDORJRXVO\ WKLV NLQG RI FRQYHQWLRQ ZLOO EH IROORZHG IRU RWKHU FRPPRQ WHUPV ZKLFK DUH XVHG ERWK E\ OLQJXLVWV DQG PDWKHPDWLFLDQV LQ YHU\ GLIIHUHQW ZD\V VXFK DV µJUDPPDU¶ µV\QWD[¶ RU µVHPDQWLFV¶  7KLV FODULILFDWLRQ LV QHHGHG EHFDXVH WKLV ERRN LV DGGUHVVHG ERWK WR SHRSOH EHORQJLQJ WR WKH KXPDQLWLHV²VXFK DV PRVW OLQJXLVWV DUH EXW DOVR SHGDJRJLVWV LQYROYHG LQ ODQJXDJH OHDUQLQJ LVVXHV²DQG SHRSOH EHORQJLQJ WR KDUG VFLHQFHV DERYH DOO PDWKHPDWLFLDQV EXW DOVR ORJLFLDQV FRPSXWHU VFLHQWLVWV DQG QDWXUDO ODQJXDJH HQJLQHHUV :H EHOLHYH WKDW WKH VRFDOOHG µWZR FXOWXUHV¶²HYHQ WKUHH DV UHFHQWO\ SRVHG E\ .DJDQ  ²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



&KDSWHU 2QH

2I FRXUVH ZH GR QRW SUHWHQG WR UHLQYHQW WKH ZKHHO RXU ZRUN LV ZHOO URRWHG ERWK LQ WKH OLQJXLVWLF DQG PDWKHPDWLFDO WUDGLWLRQV RI WKHLU RZQ 7KH VHTXHO RI WKLV FKDSWHU LV GHYRWHG WR FODULI\ ZKDW DUH RXU VWDUW SRLQWV DQG KRZ WKH\ DUH UHODWHG RU QRW ZLWK RWKHU ZRUNV LQ WKH ILHOGV

 7KH DGSRVLWLRQDO SDUDGLJP ,W LV ZRUWK QRWLFLQJ WKDW WKH WHUP µFRQVWUXFWLYH¶ LV XVHG LQ GLIIHUHQW DQG FRPSOH PHQWDU\ ZD\V ZLWKLQ WKH ERRN ,Q WKLV VHFWLRQ ZH H[SODLQ µFRQVWUXFWLYH¶ UHIHU ULQJ WR FRQVWUXFWLYH PDWKHPDWLFV 7KH IXQGDPHQWDO FRQFHSW RI WKLV ERRN LV WKH DGSRVLWLRQ ZKLFK LV OLQJXLVWLFDOO\ D JHQHUDOLVDWLRQ RI FRQMXQFWLRQV SUHSRVLWLRQV SRVWSRVLWLRQV DQG VR RQ²EURDGO\ VSHDNLQJ OLQNLQJ ZRUGV 7KH DGSRVLWLRQDO SDUDGLJP ZDV WKH PDLQ UHVXOW RI WKH 3K' GLVVHUWDWLRQ E\ *REER   6LQFH WKHQ ZH SXW RXU ZRUN D VWHS IRUZDUG DQG WKLV ERRN LV WKH SUHVHQWD WLRQ RI WKH UHVXOWV RI WKDW HIIRUW ,Q IDFW QRZ DGSRVLWLRQV²WKH FRUQHUVWRQHV RI WKH DGSRVLWLRQDO SDUDGLJP²DUH GHVFULEHG LQ WKH VSLULW RI FRQVWUXFWLYH PDWKHPDW LFV DQG WKDW¶V ZK\ WKH IUDPHZRUN LV FDOOHG µFRQVWUXFWLYH DGSRVLWLRQDO JUDPPDUV¶ &RQVWUXFWLYH $G*UDPV IRU VKRUW  &RQVWUXFWLYH PDWKHPDWLFV %ULGJHV DQG 5LFKPDQ  LV V\QWKHWLFDOO\ D ZD\ WR GHYHORS WKH PDWKHPDWLFDO WKRXJKW WKDW VWULFWO\ SUHVHUYHV WKH LQIRUPDWLRQ FRQWHQW RI DQ\ VWDWHPHQW 3UHFLVHO\ GLVMXQFWLYH DQG H[LVWHQWLDO VWDWHPHQWV DUH UHTXLUHG WR LQGLFDWH ZLWQHVVHV IRU WKHLU WUXWK IRU H[DPSOH ∃x.P(x) FDQ EH SURYHG LQ VRPH WKHRU\ T LI DQG RQO\ LI ZH FDQ H[KLELW VRPH YDOXH v VXFK WKDW P(v) KROGV LH LW ORJLFDOO\ GHVFHQGV IURP T  6R VRPH IRUPV RI ORJLFDO WKLQNLQJ DUH QRW DFFHSWHG HJ WKH /DZ RI ([FOXGHG 0LGGOH VLQFH WKH\ LQWURGXFH XQMXVWLILHG LQIRUPDWLRQ LQ IDFW LI P ∨ ¬P LV DQ D[LRP LW GRHV QRW LQGLFDWH ZKHWKHU WKH ILUVW RU WKH VHFRQG GLVMXQFW KROGV DQG WKHUH LV QR JXDUDQWHH WKDW VXFK DQ LQIRUPDWLRQ FDQ EH UHFRYHUHG IURP WKH WKHRU\ T  DQG LQ JHQHUDO LW FDQQRW 7URHOVWUD DQG 6FKZLFKWHQEHUJ  7URHOVWUD   7KH WHUP µJUDPPDUV¶ UHIHUV WR WKH IDFW WKDW WKH PDWKHPDWLFDO VWUXFWXUH LV RQH ZKLOH WKH LQVWDQWLDWLRQV DUH PDQ\ DV QDWXUDO ODQJXDJHV DUH :H ORRN DW GLIIHUHQW VKDGRZV LH QDWXUDO ODQJXDJHV  HDFK RQH ZLWK LWV GLIIHUHQW VKDSH ZKLOH WKH VXQ LV DOZD\V WKH VDPH WKH VWUXFWXUH ²VHH &KDSWHUV  DQG  IRU GHWDLOV %HIRUH SURFHHGLQJ LW LV LPSRUWDQW WR H[SODLQ KRZ ZH GHDO ZLWK WKH µVKDG RZV¶ LH WKH GLYHUVLW\ RI QDWXUDO ODQJXDJHV²LQ RWKHU ZRUGV WKH SUREOHP RI OLQJXLVWLF XQLYHUVDOV DQG W\SRORJ\ )URP D SK\ORJHQLF SRLQW RI YLHZ ZKLOH HY HU\ VSHFLHV VHHPV WR XQGHUVWDQG WKHLU PHPEHUV RQO\ KXPDQV GHYHORSHG GLIIHUHQW

,QWURGXFWLRQ



ODQJXDJHV²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²V\QWKHWLFDOO\ SDWWHUQV RI XVDJH RI IRUPPHDQLQJ FRUUH VSRQGHQFHV WKDW FDUU\ WKH PHVVDJHV EH\RQG WKH JLVW RI WKH ZRUGV WKDW WRRN SDUW LQ WKH FRQVWUXFWLRQ LWVHOI 7KLV IDFW OHDGV XV WR DQRWKHU XVH RI WKH WHUP µFRQVWUXFWLYH¶ ZLWKLQ WKLV ERRN /LQJXLVWLF FRPPXQLFDWLRQ LV V\PEROLF DQG V\PEROV DUH ³VRFLDO FRQYHQWLRQV E\ PHDQV RI ZKLFK RQH LQGLYLGXDO DWWHPSWV WR VKDUH DWWHQWLRQ RU PHQWDO VWDWH WR VRPHWKLQJ LQ WKH RXWVLGH ZRUOG´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¶V ZK\ KLJKO\ IUHTXHQW ZRUGV DUH XVXDOO\ VKRUW LQ WHUPV RI V\OODEOHV (DFK JUDPPDU LV PDGH RI FRQVWUXFWLRQV SURYLGLQJ XV WKH OLQJXLVWLF GDWD WR EH DQDO\VHG &RQVWUXFWLRQV EHLQJ FHQWUDO RXU ZRUN FDQ EH SXW LQWR UHODWLRQ ZLWK WKH HDUO\ VWDJHV RI WUDQVIRUPDWLRQDO JUDPPDU &KRPVN\   DQG WR WKH ZRUNV RI FRJQLWLYH OLQJXLVWV SURSRVLQJ FRQVWUXFWLRQDO DQDO\VHV VXFK DV 7RPDVHOOR   *ROGEHUJ    DQG &URIW   0RVW RI RXU OLQJXLVWLF REVHUYDWLRQV GHULYH IURP WKH ZRUNV E\ FRJQLWLYH OLQ



&KDSWHU 2QH

JXLVWV 7KH PDLQ OLPLW RI WKHVH DQDO\VHV OLHV LQ WKH IDFW WKDW WKH\ DUH FRQVWUXF WLRQDO LQVWHDG RI FRQVWUXFWLYH 7KDW LV WKH\ WDNH FRQVWUXFWLRQV DV SULPLWLYHV UH MHFWLQJ LQ WRWR DQ\ IRUPDOLVP ZKLFK LV VHHQ DV LQHYLWDEO\ µ&KRPVN\DQ¶ LQ QDWXUH 0DWWKHZV  DOUHDG\ REVHUYHG >«@ IRU PRUH RI WKH SDVW ILIWHHQ \HDUV GHVSLWH RFFDVLRQDO GLVSDUDJHPHQW IURP RQH VLGH RU DQRWKHU HDFK VFKRRO KDV LQ SUDFWLFH KDG OLWWOH UHDVRQ WR UHIHU WR WKH RWKHU ,W LV ZRUWK QRWLQJ IRU H[DPSOH WKDW &URIW¶V UHFHQW LQ WURGXFWLRQ WR 7\SRORJ\ DQG 8QLYHUVDOV  FLWHV QR ZRUN E\ &KRPVN\ 0DWWKHZV  

7KH VLWXDWLRQ LV HYHQ JHWWLQJ ZRUVH DV H[HPSOLILHG E\ WKH PRVW UDGLFDO FRQ VWUXFWLRQDO DSSURDFK ZKLFK VWDWHV WKDW WKHUH LV QR OLQJXLVWLF FDWHJRU\ WKDW LV ERWK IRUPDO DQG XQLYHUVDO DV DVVHUWHG E\ &URIW    2I FRXUVH DEDQGRQLQJ XQLYHUVDO FDWHJRULHV DQG UHODWLRQV OHDGV WR D YHU\ GLIIHUHQW YLHZ RI 8QLYHUVDO *UDPPDU 8QGHU WKH DOWHUQDWLYH YLHZ 8QLYHU VDO *UDPPDU GRHV QRW FRQVLVW RI DQ LQYHQWRU\ RI XQLYHUVDO FDWHJRULHV DQG UHODWLRQV DYDLODEOH WR DOO VSHDNHUV >«@ 7KH IRUPDO VWUXFWXUHV LQ JUDPPDUV DUH ODQJXDJHSDUWLFXODU DQG XQLYHUVDOV RI ODQJXDJH PXVW EH VRXJKW HOVH ZKHUH >«@ ,Q SULQFLSOH WKDW DSSHDUV WR EH WKH GLUHFWLRQ WKDW &KRPVN\DQ JHQHUDWLYH JUDPPDU KDV KHDGHG JHQHUDO FRQVWUDLQWV RQ V\QWDFWLF VWUXFWXUH EXW D SUROLIHUDWLRQ RI V\QWDFWLF FDWHJRULHV ,Q SUDFWLFH KRZHYHU WKH V\Q WDFWLF FDWHJRULHV DUH DVVXPHG WR EH FURVVOLQJXLVWLFDOO\ YDOLG DQG WKH VDPH FDWHJRULHV RU D VXEVHW WKHUHRI DUH SRVLWHG RI HYHU\ ODQJXDJH 7KLV SUDFWLFH DOVR KROGV IRU RWKHU IRUPDO V\QWDFWLF WKHRULHV

:H FODLP WKDW D IRUPDOLVP LV SRVVLEOH ZLWKRXW QHJOHFWLQJ WKH XVDJHEDVHG UHVXOWV RI FRJQLWLYH OLQJXLVWV 7KH SUREOHP LV LQ WKH JHQHUDO SHUVSHFWLYH 0RVW FRJQLWLYH OLQJXLVWV DUH µPD[LPDOLVWV¶ LH WKH\ FRQVLGHU VHPDQWLFV DQG V\QWD[ LQGLVVRFLDEOH DQG WKHUHIRUH VHPDQWLFV LV SXW DW WKH FHQWUH RI DQDO\VLV ZKLOH V\Q WD[ LV SXW DW WKH SHULSKHU\²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

,QWURGXFWLRQ



FRQVWUXFWLRQV LV QRW RQO\ SRVVLEOH EXW DOVR IHDVLEOH *ROGEHUJ    $IWHU DOO &KRPVN\ LV D OHDGLQJ ILJXUH LQ WKH &RJQLWLYH 5HYROXWLRQ DORQJ ZLWK *HRUJH 0LOOHU 0DUYLQ 0LQVN\ $OOHQ 1HZHOO DQG +HUEHUW 6LPRQ   ZH FODLP WKDW DW OHDVW SDUW RI &KRPVN\¶V ZRUN FDQ EH SXW LQ WKH VWUHDP RI FRJQLWLYH OLQJXLVWLFV LI ZH GR QRW UHMHFW IRUPDOLVDWLRQ DV D ZKROH $W WKH VDPH WLPH ZH EHOLHYH WKDW DQRWKHU ZD\²QRW EDVHG RQ FRQVWLWXHQWV²WR IRUPDOLVH JUDPPDUV LV SRVVLEOH DQG ZRUWK DWWHQWLRQ SDUWLFXODUO\ IRU FRJQLWLYH OLQJXLVWLFV  ,Q VXP LW¶V QR PRUH WKH WLPH RI WKH ³OLQJXLVWLF ZDUV´ +DUULV   ZH FODLP WKDW ERWK DSSURDFKHV DUH YDOLG DV WKH\ WDON DERXW GLIIHUHQW DVSHFWV RI WKH VDPH SKHQRPHQRQ LH QDWXUDO ODQJXDJH JUDPPDUV WKH &KRPVN\DQ DSSURDFK LV WRSGRZQ GHGXFWLYH EHFDXVH LW ORRNV IRU UHJXODULWLHV EH\RQG WKH YDULHW\ RI ODQJXDJHV ZKLOH FRJQLWLYH OLQJXLVWV WU\ WR H[SODLQ YDULHW\ RQ D XVDJHEDVHG SHU VSHFWLYH IROORZLQJ D GDWDGULYHQ LQGXFWLYH DSSURDFK 2XU DLP LV WR WDNH WKH EHVW SUDFWLFHV IURP ERWK DSSURDFKHV ZLWKRXW DGKHULQJ WR DQ\ µ&KXUFK¶ +HUH ZH RIIHU D VWURQJ JHQHUDO H[SOLFDWLYH IRUPDOLVP ZLWK D ORW RI H[DPSOHV WDNHQ IURP GLIIHUHQW ODQJXDJHV RI WKH ZRUOG ZLWK D VSHFLDO UHJDUG WR (QJOLVK 2XU IRUPDOLVP WDNHV LQWR DFFRXQW WKH UHVXOWV RI OLQJXLVWLF W\SRORJ\ $UH WKHUH DQ\ ODQJXDJH XQLYHUVDOV" 7KH FURVVDQDO\VHV RI JUDPPDUV PDGH E\ W\SRORJLVWV VKRZHG XV WKDW JUDPPDU FDWHJRULHV DULVHQ LQ *UHHN DQG 5RPDQ FRQWH[W IRU HGX FDWLRQDO SXUSRVHV²LH WHDFKLQJ DQG OHDUQLQJ RI *UHHN DQG /DWLQ DV ZULWWHQ ODQ JXDJHV²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²DQG *UHHQ EHUJ¶V UHVXOWV LQ V\QWDFWLF W\SRORJ\ FDQQRW EH GLVUHJDUGHG VR HDVLO\ 7RPDVHOOR FODLPV WKDW WKH RQO\ ODQJXDJH XQLYHUVDOV WKDW H[LVW DUH WKH RQHV RI FRPPXQLFDWLRQ DQG FRJQLWLRQ EHLQJ LQ SDUWLFXODU WKH SUHVHQFH RI H[SUHVVLRQV RI UHIHUHQFH DQG WKH SUHVHQFH RI SUHGLFDWLRQ 0RUHRYHU WKH\ KDYH QR FRXQWHUSDUW LQ WHUPV RI OLQJXLV WLF XQLYHUVDOV RI IRUP :H FODLP H[DFWO\ WKH RSSRVLWH WKH PHFKDQLVPV XQGHU O\LQJ WKH FRQVWUXFWLRQV DUH WKH OLQJXLVWLF FRXQWHUSDUWV RI WKH FRJQLWLYH DELOLW\ RI SDWWHUQILQGLQJ DQG LQWHQWLRQUHDGLQJ ZKLFK OHW WKH VSHDNHU DQG WKH OLVWHQHU²LQ WKH VLPSOHU GHIDXOW FDVH²WR EXLOG XS WKH OLQJXLVWLF UHSUHVHQWDWLRQ ZLWKLQ WKHLU MRLQW DWWHQWLRQDO IUDPH 7KH EHVW DFFRXQW RI WKH DWWHQWLRQ IRFXV DV D FRJQLWLYH OLQ JXLVWLF DELOLW\ ZH KDYH IRXQG LQ OLWHUDWXUH LV WKH WUDMHFWRU\ODQGPDUN DV\PPHWU\



&KDSWHU 2QH

E\ /DQJDFNHU     RI ZKLFK ZH ZLOO JLYH D IRUPDO LQWHUSUHWDWLRQ LQ WHUPV RI LQIRUPDWLRQ SURPLQHQFH²VHH &KDSWHU  $WWHQWLRQ VKRXOG EH GLUHFWHG VRPHZKHUH LQ RUGHU WR IXQFWLRQ SURSHUO\ ZH FODLP WKDW IRXU JUDPPDU FKDUDFWHUV DUH XQLYHUVDO EHLQJ WKH H[SUHVVLRQV RI UHI HUHQFH SUHGLFDWLRQ DQG WKHLU UHVSHFWLYH PRGLILHUV²UHVSHFWLYHO\ DGMXQFWV DQG FLUFXPVWDQWLDOV :KRUI  DQG 7HVQLqUH  GLG FRPH WR WKH VDPH FRQ FOXVLRQ HYHQ LI VWDUWLQJ IURP GLIIHUHQW EDVHV ,Q SDUWLFXODU WKH ZRUN E\ 7HVQLqUH  ZDV WKH VWDUW RI WKH VRFDOOHG 'HSHQGHQF\ *UDPPDUV ZKLFK ZDV UDUHO\ SXW LQWR UHODWLRQ ZLWK FRJQLWLYH OLQJXLVWLFV  :H GHHSO\ DQDO\VHG WKDW FODVVLF ZRUN WKURXJK WKH OHQV RI PRGHUQ IRUPDOLVPV DQG ZH KDYH IRXQG WKDW PRVW LI QRW DOO GHULYHG ZRUNV KDYH WDNHQ WKH FRQFHSWV RI GHSHQGHQF\ DQG YHUEDO YD OHQF\ IURP 7qVQLHUH EXW DW WKH VDPH WLPH FRPSOHWHO\ GLVUHJDUGLQJ KLV XVH RI JUDPPDU FKDUDFWHUV  0RUHRYHU ZH UHWDLQ WKH FRQFHSW RI µSUHSRVLWLRQDO V\VWHP¶ ERUURZHG IURP 3HQQDFFKLHWWL¶V DQDO\VLV RI %U¡QGDO   HDFK QDWXUDO ODQJXDJH JUDPPDU KDV D UHODWLYHO\ VPDOO VHW RI SUHSRVLWLRQV RU RWKHU NLQG RI DGSRVLWLRQV ZKRVH IXQFWLRQ LV GHWHUPLQHG E\ WKH UHVXOW RI WKH RSSRVLWLRQ ZLWK WKH RWKHU SUHSRVLWLRQV LQ WKH JUDPPDU LWVHOI ,Q IDFW HYHQ JHQHWLFDOO\ FORVH ODQJXDJHV²VXFK DV )UHQFK DQG ,WDOLDQ²VKRZ D FRQVLGHUDEOH GLIIHUHQFH LQ WKH XVH RI WKHLU SUHSRVLWLRQV EHFDXVH WKH\ EHORQJ WR GLIIHUHQW SUHSRVLWLRQDO V\VWHPV 3HQQDFFKLHWWL    7KH FHQWUDO UROH JLYHQ WR DGSRVLWLRQV²EURDGO\ SUHSRVLWLRQV SRVWSRVLWLRQV RU LQSRVLWLRQV GHSHQGLQJ RQ WKH VSHFLILF ODQJXDJH²OHDG WR DQRWKHU IXQGDPHQWDO JUDPPDU FKDUDFWHU DGSRVLWLRQV 7KLV JUDPPDU FKDUDFWHU FROOHFWV WKH µVWUXFWXUDO PRUSKHPHV¶ RI D ODQJXDJH %HFDXVH RI LWV VRPHZKDW WHFKQLFDO QDWXUH LW KDV EHHQ QHJOHFWHG IRU D ORQJ WLPH 7KH QDPH µDGSRVLWLRQDO SDUDGLJP¶ IROORZHG QDWXUDOO\ 7KH DGSRVLWLRQDO SDUDGLJP ZDV ILUVW GHYHORSHG LQ *REER   ZKLFK H[ WHQGV 3HQQDFFKLHWWL¶V ZRUN LQ DQ RULJLQDO ZD\ $GSRVLWLRQV EHFRPH D PRUH DE VWUDFW JHQHUDO HOHPHQW LQ RUGHU WR XQGHUVWDQG JUDPPDU VWUXFWXUHV ,Q SDUWLFXODU ]HURPDUNHG DGSRVLWLRQV²VLJQHG WKURXJK DQ HSVLORQ ǫ ²SXW ZRUG RUGHU SKH QRPHQD LQ WKH VDPH UHDOP RI PRUSKRORJ\ 7KXV PRUSKRORJ\ DQG V\QWD[ DUH FODULILHG WKURXJK D XQLILHG PRGHO DQG D XQLTXH PHFKDQLVP²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

,QWURGXFWLRQ



DEVROXWLYH JUDPPDUV 2XU UHIHUHQFH IRU HUJDWLYLW\ XQGHU D WKHRUHWLFDO SRLQW RI YLHZ LV WKH ZRUN E\ 'L[RQ   ZKR QRWHV LQ WKH DSSHQGL[ WKDW VXUSULVLQJO\ WKHUH DUH IHZ WKHRUHWLFDO PRGHOV ZKLFK JLYHV DQ H[SODQDWLRQ RI HUJDWLYLW\ EH FDXVH WKH WKHRU\ ³ZRXOG KDYH WR UHFRJQLVH WKDW WKHUH DUH WKUHH EDVLF V\QWDFWLF VHPDQWLF SULPLWLYHV $ 6 DQG 2 UDWKHU WKDQ MXVW WZR µVXEMHFW¶ DQG µREMHFW¶ KRZHYHU WKHVH DUH GHILQHG´ VHH 'L[RQ    &RQVWUXFWLYH DGSRVLWLRQDO JUDPPDUV VROYH WKLV SUREOHP LQ WHUPV RI LQIRUPD WLRQ SURPLQHQFH DV H[SODLQHG LQ WKH QH[W FKDSWHUV )XUWKHUPRUH ZH DGKHUH WR WKH XQDFFXVDWLYH K\SRWKHVLV RULJLQDOO\ SURSRVHG E\ 3HUOPXWWHU   ZKLFK JLYHV D FOHDU DQG FRQYLQFLQJ OLQJXLVWLF DFFRXQW RI WKH SUREOHP HYHQ LI WKH 5HODWLRQDO *UDPPDU SVHXGR IRUPDOLVP LV QRW FRQYLQFLQJ  )LQDOO\ QR DJUHHPHQW LV SRVVLEOH RQ D ILQLWH IL[HG OLVW RI WKH XQLYHUVDO W\SHV RI VHPDQWLF UROHV²FDOOHG LQ D &KRPVN\DQ SHUVSHFWLYH µWKHWDUROHV¶²VLPSO\ EH FDXVH WKH\ GHSHQG RQ WKH FRQVWUXFWLRQV WKH\ EHORQJ WR ,Q RWKHU ZRUGV VHPDQWLF UROHV DUH FRQVWUXFWLRQGHSHQGHQW DQG KHQFH ODQJXDJHGHILQHG DQG VR WKHLU OLVW LV RSHQ DQG XQGHILQHG DW OHDVW IRU WKH SXUSRVHV RI WKH SUHVHQW ERRN  )RU H[DPSOH LI D FRQVWUXFWLRQ GHDOV ZLWK IRRG VXFK DV ; HDW < LW KDV PXFK PRUH VHQVH WR FDOO ; Eater LQVWHDG RI Agent IROORZLQJ WKH WHQHWV RI FRJQLWLYH OLQJXLVWLFV DV WKH VHPDQWLF UROHV EHORQJLQJ WR WKH VHPDQWLF IUDPH RI food DFWL YDWHG E\ D FRQVWUXFWLRQV VXFK DV ; HDW < VKRZ GLVWLQFWLYH FKDUDFWHULVWLFV LQ WKH GLVWULEXWLRQDO DQDO\VLV RI WKH FRUSXV LQ GLIIHUHQW ODQJXDJHV²HJ (QJOLVK *HU PDQ DQG %HQJDOL &URIW  ² ZKLFK FDQQRW EH H[SODLQHG ZLWK D VXLWDEOH GHJUHH RI SUHFLVLRQ E\ WKH PRUH XVHG GLFKRWRP\ Agent YV Patient )RU H[DPSOH WKH (QJOLVK FRQVWUXFWLRQ <HDWLQJ ; H[HPSOLILHG E\ RLOHDWLQJ PLFUREHV VWDWHV WKDW < LV WKH Food DQG ; LV WKH Non-human eater SURWRW\SLFDOO\ KDYLQJ WKH VHPHPH animal VR RLOHDWLQJ URERW LV DOVR DFFHSWDEOH ZKLOH ILVK HDWLQJ FKLOG LV QRW VLQFH FKLOG LV QRW D Non-human eater  :KDW LW LV LPSRUWDQW WR XQGHUOLQH KHUH LV WKDW WKH SURGXFWLYLW\ RI FRQVWUXF WLRQV²LH KRZ PXFK ; V DQG < V FDQ YDU\ ZLWKLQ WKH VFRSH RI WKDW SDUWLFXODU FRQVWUXFWLRQ²LV ERXQG WR WKH FRQVWUXFWLRQ LWVHOI 7KH DLP RI VHPDQWLF UROHV LV H[DFWO\ WR UHSUHVHQW WKLV GHJUHH RI IUHHGRP ZKLFK FDQ EH ]HUR DW WKH OLPLW DV LQ WKH FDVH RI FRPSOHWHO\ JUDPPDWLFDOL]HG LG LRPDWLF H[SUHVVLRQV²VXFK DV NLFN WKH EXFNHW ZKHUH HDFK OH[LFDO LWHP FDQQRW EH PRYHG SDUDGLJPDWLFDOO\²RU YHU\ KLJK VXFK DV /HW¶V ; ZKHUH WKH RQO\ FRQ VWUDLQW DSSOLHG WR ; LV LWV JUDPPDU FKDUDFWHU LQ SDUWLFXODU WKH QHHG WR EHORQJ WR WKH FODVV RI (QJOLVK YHUEV



&KDSWHU 2QH

 7KH IRUPDO PRGHO ,Q WKH ILHOGV RI PDWKHPDWLFDO DQG FRPSXWDWLRQDO OLQJXLVWLFV WKHUH DUH PDQ\ QDWXUDO ODQJXDJH JUDPPDU IRUPDOLVPV FXUUHQWO\ XQGHU LQYHVWLJDWLRQ ,Q SDUWLFXODU RXU IRUPDOLVP FDQ EH SXW LQWR WKH UHDOP RI WKH VRFDOOHG µFDWHJRULDO JUDPPDUV¶²LH UHSUHVHQWDWLRQV RI QDWXUDO ODQJXDJH JUDPPDUV LQ WHUPV RI FDWHJRULHV 7KLV OLQH RI UHVHDUFK LV IDU IURP EHLQJ QHZ EHLQJ URRWHG LQ WKH ZRUNV E\ $MGXNLHZLF]   &KXUFK   %DU+LOOHO   DQG /DPEHN    2XU IRUPDO PRGHO LV LQWHQGHG DV D JXLGLQJ UHIHUHQFH IRU WKH GHYHORSPHQW RI OLQJXLVWLF FRQFHSWV ,Q WKLV VHQVH LW VKRXOG EH XQGHUVWRRG DV D µZHDN¶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µXQLTXH LQWHUSUHWDWLRQ¶ RI WKH FRUUHVSRQGLQJ WH[W LH D XQLTXH ZD\ WR XQGHUVWDQG WKH JUDPPDU FKDUDFWHUV RI HDFK HOHPHQW LQ WKH WH[W WKH FRQFHSW RI µJUDPPDU FKDUDFWHU¶ ZLOO EH GLVFXVVHG DQG H[SODLQHG LQ GHWDLO LQ &KDSWHU   )RU H[DPSOH OHW¶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

,QWURGXFWLRQ

q
A
→A
ǫ2 A
I2 A
Aq
A /D YHFFKLD SRUWD
← A
ǫ2 A O1
I1 A A


△



q
A
←A
ǫ2 A
I2 A
Aq
A
→A OD VEDUUD
ǫ2 A O2
I1 A A


△

△

△

△

△

OD

VEDUUD

/D YHFFKLD

SRUWD

O2

I2

O1

I2

)LJXUH  7KH WZR LQWHUSUHWDWLRQV RI OD YHFFKLD SRUWD OD VEDUUD

VWDQGV LQ WKH SDUVHU RI WKH ,WDOLDQ ODQJXDJH ,Q IDFW WZR FKDLQV RI FRQVWUXFWLRQV HTXDOO\ YDOLG DQG VHPDQWLFDOO\ SODXVLEOH FDQ JHQHUDWH WKH UHVSHFWLYH DGSRVLWLRQDO WUHHV $OVR LQ (QJOLVK WKHUH DUH VRPH NQRZQ H[DPSOHV RI VHQWHQFH ZKHUH WKHUH LV PRUH WKDQ RQH YDOLG V\QWDFWLF UHODWLRQVKLS IRU H[DPSOH  7LPH IOLHV OLNH DQ DUURZ DQG IUXLW IOLHV OLNH D EDQDQD ZKHUH µIOLHV¶ FRXQWV DV D YHUE LQ WKH ILUVW RFFXUUHQFH DQG DV SDUW RI WKH QRXQ LQ WKH VHFRQG RQH %\ FRQWUDVW WKHUH DUH FDVHV ZKHUH WKHUH LV RQO\ RQH DGSRVLWLRQDO WUHH EXW WKHUH LV PRUH WKDQ RQH VHPDQWLF LQWHUSUHWDWLRQ  Ê OD URVVD GL 0DUDQHOOR ([DPSOH  FDQ EH LQWHUSUHWHG DV 6KH¶V WKH UHGKDLUHG JLUO FRPLQJ IURP 0DUDQHOOR DQ ,WDOLDQ WRZQ LQ WKH (PLOLD5RPDJQD UHJLRQ DV ZHOO DV LW¶V WKH )HUUDUL FDU PHDQLQJ WKH IDPRXV VSRUW FDU SURGXFHG LQ 0DUDQHOOR ,Q WKLV FDVH ZH KDYH WZR GLIIHUHQW PHDQLQJV IRU WKH VDPH WH[W XQGHU WKH VDPH V\QWDFWLF LQWHUSUHWDWLRQ WKH DGWUHH ZLOO EH WKH VDPH )LJXUH   $GWUHHV DUH EXLOW IURP VRPH EDVLF EULFNV YLD D IHZ VWDQGDUG FRQVWUXFWLRQV &RUUHFWO\ LGHQWLI\LQJ WKH EULFNV DQG WKH EDVLF FRQVWUXFWLRQV LV WKH PDLQ REMHFWLYH RI WKLV ERRN %XW OHW¶V VXSSRVH WR KDYH WKHP WKHQ ZH FDQ JHQHUDWH WKH ZKROH ODQJXDJH DQG YLFH YHUVD ZH FDQ FKHFN LI D SLHFH RI WH[W LV V\QWDFWLFDOO\ FRUUHFW E\ DVNLQJ LI WKHUH LV D FRUUHVSRQGLQJ DGWUHH 0RUHRYHU ZH ZRXOG VD\ WKDW D SLHFH RI WH[W LV V\QWDFWLFDOO\ DPELJXRXV LI LW DGPLWV PRUH WKDQ RQH FRUUHFW DGWUHH 



&KDSWHU 2QH

q
A
→ A ǫ
2 A
I2 A
Aq
A

←
A ǫ
2 A

I1 A
q

A
A  Ë
←A 2 GL O I 1
A A > O 2
A
Aq
A 0DUDQHOOR
← A ǫ O2
A > O A 2
A
Aq
A OD A
← ǫ A
A > O A 2 A
A
 URVVD O2 A>A

△

)LJXUH  7KH DGSRVLWLRQDO WUHH RI Ê OD URVVD GL 0DUDQHOOR

,Q PDWKHPDWLFDO WHUPV DGWUHHV DQG FRQVWUXFWLRQV EHWZHHQ WKHP IRUP D VWUXF WXUH $G7UHH ZKLFK LV D FDWHJRU\   VHH 0DF /DQH  DQG %RUFHX[   $ PDWKHPDWLFDO FDWHJRU\ LV DQ DOJHEUDLF VWUXFWXUH FRPSRVHG E\ WZR FODVVHV WKH REMHFWV DQG WKH DUURZV DUURZV OLH EHWZHHQ WZR REMHFWV WKH VRXUFH RU GRPDLQ DQG WKH WDUJHW RU FRGRPDLQ $OVR D FDWHJRU\ VWDWHV WKDW WKHUH DUH GLVWLQFW DUURZV WKH LGHQWLWLHV RQH IRU HYHU\ REMHFW A DQG VXFK WKDW WKH VRXUFH DQG WKH WDUJHW DUH A 0RUHRYHU D FDWHJRU\ LV HTXLSSHG ZLWK D SDUWLDO RSHUDWLRQ DOORZLQJ WR FRPSRVH WZR DUURZV ZKHQHYHU RQH KDV WKH GRPDLQ ZKLFK LV WKH WDUJHW RI WKH RWKHU RQH &RPSRVLWLRQ LV UHTXLUHG WR EH DVVRFLDWLYH DQG LGHQWLWLHV DFW DV RQH H[SHFWV ZLWK UHVSHFW WR FRPSRVLWLRQ ,QWXLWLYHO\ WKHUH LV DQ DUURZ f IURP A WR B ZKHQHYHU ZH FDQ FRQVWUXFW WKH B WUHH VWDUWLQJ IURP WKH A WUHH DSSO\LQJ WKH FRQVWUXFWLRQ f  :H GR DOORZ FRPSOH[ FRQVWUXFWLRQV REWDLQHG E\ VHTXHQWLDOO\ FRPSRVLQJ VLPSOHU RQHV LI f DQG g DUH FRQVWUXFWLRQV VXFK WKDW f (A) = B DQG g(B) = C  WKDW LV LI f PDSV A LQWR B DQG

,QWURGXFWLRQ



g FRQVWUXFWV C IURP B WKHQ g ◦ f LV WKH FRQVWUXFWLRQ ZKLFK PDSV A LQWR C E\ GRLQJ g DIWHU f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²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



&KDSWHU 2QH

SKUDVH $Q LPSRUWDQW UHVXOW DERXW SXUH FDWHJRULDO JUDPPDUV LV 3HQWXV  WKDW VKRZV KRZ WKHLU JHQHUDWLYH SRZHU LV WKDW RI FRQWH[WIUHH JUDPPDUV DQG WKXV LQDGHTXDWH IRU WKHRULHV RI QDWXUDO ODQJXDJH V\QWD[ WKLV UHVXOW DSSOLHV RQO\ WR FDWHJRULDO JUDPPDUV ZKLFK KDYH D QDWXUDO FRPSXWDWLRQDO FRXQWHUSDUW GHILQHG DV DQ H[WHQVLRQ RI WKH λFDOFXOXV LH ZKHUH FRPSRVLWLRQ UXOHV DUH IXQFWLRQDO DS SOLFDWLRQV 8QIRUWXQDWHO\ OHDYLQJ WKH VLPSOH DQG VDIH ZRUOG RI λ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¶W XVH &&*V DV VXFK 8QGHU D PDWKHPDWLFDO SRLQW RI YLHZ D JUDPPDU LV D VHW RI LQIHUHQFH UXOHV FRQWUROOHG E\ WKH OLQJXLVWLF FDWHJRULHV LQWHUSUHWHG DV IXQFWLRQDO VSDFHV VHH YDQ %HQWKHP   VXFK UXOHV FDQ EH LQIHUUHG E\ VXLWDEOH WHFKQLTXHV IURP PDFKLQH OHDUQLQJ 0DQQLQJ DQG 6FKW]H   HVVHQWLDOO\ XV LQJ VWDWLVWLFDO PHDVXUHV $OVR WKH SUREDELOLVWLF DSSURDFK LV XVHG WR FRSH ZLWK WKH IDFW WKDW QRQGHWHUPLQLVWLF SRO\QRPLDO SUREOHPV FDQQRW EH HIILFLHQWO\ VROYHG DV IDU DV PRGHUQ PDWKHPDWLFV NQRZV  5DQWD  SURSRVHV D IRUPDO IUDPHZRUN IRU ZULWLQJ JUDPPDUV DQG OLQ JXLVWLF WKHRULHV²IROORZLQJ WKH PRWWR VHQWHQFHVDVSURRIV )URP D PDWKHPDWL FDO SRLQW RI YLHZ LW LV EDVHG RQ 0DUWLQ /|I 7\SH 7KHRU\ VHH 0DUWLQ /|I   XVLQJ WKH &RTXDQG¶V DOJRULWKP IRU W\SH FRQVWUXFWLRQSDUWLDO SURRI GHULYDWLRQ &R TXDQG   6R LW LV XOWLPDWHO\ EDVHG RQ D GHSHQGHQWW\SH SUHGLFDWLYH YDULDQW RI WKH λ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

,QWURGXFWLRQ



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²WKLV LV WKH VHQWHQFH¶V µG\QDPLFV¶ $V LW ZLOO EH FOHDU LQ WKH VHTXHO RI WKLV ERRN ZH IROORZ WKH K\SRWKHVLV SRVHG E\ '\QDPLF 6\Q WD[ WKDW PRUSKR V\QWD[ LV WKH PHFKDQLVP IRU FRQVWUXFWLQJ UHSUHVHQWDWLRQV RI FRQWHQW +RZHYHU WKHUH DUH LPSRUWDQW GLIIHUHQFHV QDPHO\ WKH XVH RI OLQJXLVWLF FRQVWUXFWLRQV²EDVHG RQ FRJQLWLYH OLQJXLVWLFV UHVXOWV²LV IRUPDOO\ UHVROYHG LQ D WRWDOO\ GLIIHUHQW ZD\ 0RUHRYHU ZKLOH '\QDPLF 6\QWD[ PDNHV XVH RI +LOEHUW¶V HSVLORQ FDOFXOXV LQ RUGHU WR VROYH TXDQWLILHG QRXQ SKUDVHV RXU IRUPDO EDVHV DUH FRPSOHWHO\ GLIIHUHQW

 :KDW LV LQ WKLV ERRN" 7KH DLP RI WKH SUHVHQW ZRUN LV IRXQGDWLRQDO ,Q SDUWLFXODU ZH ZDQW WR JLYH WKH ULJKW KLQWV WR XQGHUVWDQG QDWXUDO ODQJXDJH JUDPPDUV ZLWKLQ WKH DGSRVLWLRQDO SDUDGLJP )RU XV µXQGHUVWDQGLQJ¶ PHDQV ERWK KDYLQJ LQVLJKWV DERXW WKH IXQF WLRQLQJ RI UHDOZRUOG XVDJH RI D JLYHQ QDWXUDO ODQJXDJH²LQ WHUPV WKDW DUH FRPSD UDEOH ZLWK RWKHU ODQJXDJHV DV ZHOO²DQG KDYLQJ LQVLJKWV DERXW ZKDW LV VWUXFWXUDO LQ D JLYHQ QDWXUDO ODQJXDJH LQ FRQVWUXFWLYH PDWKHPDWLFDO WHUPV ,Q SUDFWLFH WKHUH DUH QR GLVWLQFW ³OLQJXLVWLF YV PDWKHPDWLFDO´ LQVLJKWV UDWKHU WKH MRLQW OLQ JXLVWLF DQG PDWKHPDWLFDO DSSDUDWXV VKRXOG EH UHJDUGHG DV WKH WZR VLGHV RI WKH VDPH FRLQ 8QGHU D GLIIHUHQW SHUVSHFWLYH WKLV ERRN LV IRXQGDWLRQDO DV KHUH WKH UHDGHU FDQ DFTXLUH DOO WKH LQVWUXPHQWV QHFHVVDU\ IRU WKH IRXQGLQJ RI &RQVWUXFWLYH /LQ JXLVWLFV LH DQ DSSOLFDWLRQ RI FRQVWUXFWLYH PDWKHPDWLFV WR WKH UHDOP RI OLQJXLV WLFV²EURDGO\ WKH VWXG\ RI QDWXUDO ODQJXDJHV :KHQ IRXQGDWLRQV DUH SRVHG PDQ\ EXLOGLQJ GHWDLOV DUH VWLOO WR EH GHILQHG ,Q WKLV ERRN ZH LQGLFDWH ZKLFK GHWDLOV LQVWDQWLDWLRQV VSHFLILF SKHQRPHQD DUH QRW FRYHUHG LQ RUGHU WR KHOS WKH UHDGHU VHH SRVVLEOH IXUWKHU GLUHFWLRQV RI WKLV ZRUN VWDQGLQJ RQ WKH VROLGLW\ RI WKH IRXQ GDWLRQV SRVHG KHUH $ FUXFLDO SDUW RI WKH IRXQGDWLRQV DUH WKH LQVWUXPHQWV IURP &DWHJRU\ 7KHRU\ LQ SDUWLFXODU WKH LQWXLWLRQV DERXW VKHDYHV DQG *URWKHQGLHFN WRSRORJLHV²WKH LP



&KDSWHU 2QH

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²DIWHU WKH UHDGLQJ DQG XQGHUVWDQGLQJ RI WKH PDLQ WH[W²WKH $SSHQGL[ ZLOO EH UHDGDEOH ZLWK SURILW DQG LQWHUHVW WR DOO UHDGHUV

Chapter Two Syntax +RZ LV D OLQJXLVWLF FRQVWUXFWLRQ PDGH" 7KH FRQVWUXFWLYH DGSRVLWLRQDO JUDPPDU DSSURDFK JLYHV DQ DQVZHU DW PRUH WKDQ RQH OHYHO ,Q WKLV FKDSWHU ZH ZLOO UHDG WKH DQVZHU DW WKH V\QWDFWLF OHYHO :LWK µV\QWD[¶ ZH PHDQ WKH FRYHUW VWUXFWXUH RI D FRQVWUXFWLRQ LH WKH UHODWLRQ EHWZHHQ VHPDQWLFV DQG WKH RYHUW V\QWDFWLF VWUDWXP ZKLFK LV UHIOHFWHG LQ WKH ZRUG RUGHU DQG FROORFDWLRQ SKHQRPHQD  ,Q RWKHU WHUPV RXU V\QWD[ PRGHO ZLOO FODULI\ WKH DVVRFLDWLRQ EHWZHHQ PHDQLQJ DQG JUDPPDU ZLWKLQ WKH PRGHO

p
↔A
adpA

gc AA

△

△

dep gc

gov gc

)LJXUH  7KH DEVWUDFW DGSRVLWLRQDO WUHH VWUXFWXUH

7KH IXQGDPHQWDO WHQHW RI WKH DGSRVLWLRQDO SDUDGLJP LV WKDW JUDPPDU FDQ EH DQDO\VHG LQWR UHODWLRQV EHWZHHQ HDFK SDLU RI OLQJXLVWLF HOHPHQWV ZKLFK DUH UHFXUVLYHO\ GHILQHG )LJXUH  VKRZV WKH JHQHULF DGSRVLWLRQDO WUHH²E\ QRZ DGWUHH²ZKHUH WKLV WHQHW LV PDGH H[SOLFLW /LQJXLVWLFDOO\ WKH JRYHUQRU gov LV WKH HOHPHQW RI WKH WULSOH²IRUPHG E\ JRYHUQRU DGSRVLWLRQ GHSHQGHQW²WKDW FDQ µVWDQG DORQH¶ LH ZLWKRXW WKH GHSHQ GHQW 7KH PHWKRG ZH IROORZ LQ RUGHU WR DQDO\VH WKH GDWD LV FROORFDWLRQ :LWKLQ WKH FRJQLWLYH SHUVSHFWLYH ODQJXDJHV DUH H[SUHVVLRQV RI KXPDQ FRJ QLWLRQ WKHUHIRUH JUDPPDU LV D FRQFHSWXDOLVDWLRQ SULQFLSOH LH LW LV GULYHQ E\ WKH JHQHUDO UXOHV RI KXPDQ FRJQLWLRQ²LQ DOO LWV SDUWV LH SKRQRORJ\ PRUSKRORJ\ V\QWD[ VHPDQWLFV DQG SUDJPDWLFV :KDW IROORZV LV WKDW WKH FROORFDWLRQ RI ZRUGV LQ WKH V\QWDJPDWLF D[LV LV ZKDW ZH VKRXOG DQDO\VH WR XQGHUVWDQG ZKLFK FRQVWUXF WLRQ LV LQ DFWLRQ 8VLQJ WKH ZRUGV RI 7D\ORU    ³WKH YHU\ ZRUGLQJ WKDW ZH FKRRVH LQ RUGHU WR OLQJXLVWLFDOO\ HQFRGH D VLWXDWLRQ UHVWV RQ WKH PDQQHU LQ ZKLFK WKH VLWXDWLRQ KDV EHHQ PHQWDOO\ FRQVWUXHG´



&KDSWHU 7ZR

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µKRRN¶ LH WKH DGSRVLWLRQ adp SXW ULJKWO\ XQGHU WKH URRW RI WKH WUHH 7KH DGSRVLWLRQ PDUNV WKH PRUSKHPH ZKRVH IXQFWLRQ LV WR JRYHUQ WKH VXERUGLQDWH DGWUHH ZKLFK VWDQGV RQ WKH OHIW EUDQFK E\ FRQYHQWLRQ²LI WKHUH LV QR DGSRVLWLRQ LH WKH UHODWLRQ LV V\QWDFWLF LQ QDWXUH DQ HSVLORQ ǫ ZLOO EH SXW WKHUH )XUWKHUPRUH WKH DGSRVLWLRQ JLYHV WKH ILQDO JUDPPDU FKDUDFWHU gc RI LWV VXERUGLQDWH DGWUHH VHH QH[W FKDSWHU IRU GHWDLOV  $QRWKHU FRQYHQWLRQ ZH DGRSW LV WKDW WKH JRYHUQRU gov DOZD\V VWDQGV RQ WKH ULJKW EUDQFK RI WKH FXUUHQW DGWUHH ZKLOH WKH GHSHQGHQW dep DOZD\V VWDQGV RQ WKH OHIW RQH VHH QH[W VHFWLRQV IRU GHWDLOV   7KLV VWUXFWXUH LV UHFXUVLYH LH dep DQG gov FDQ EH DGWUHHV ,I HPSW\ WKH\ DUH VLJQHG E\ D ER[   3OHDVH QRWH WKDW adp FDQQRW EH DQ DGWUHH LH LW LV DOZD\V D PRUSKHPH SRVVLEO\ HPSW\ ǫ  7KH WULDQJOH △ VLJQV WKDW WKHUH LV DQ DGWUHH µSDFNHG¶ LQ WKH OLQJXLVWLF H[SUHVVLRQ ,Q RWKHU WHUPV WKH OHDI HLWKHU JRYHUQRU gov RU GHSHQGHQW dep  EULQJV LPSOLFLW LQIRUPDWLRQ WKDW ZDV KLG GHQ²HVVHQWLDOO\ IRU UHDGLQJ 7KLV QRWDWLRQDO FRQYHQWLRQ IROORZV WKH FRQVWUXF WLYH GLNWDW RI µKLGLQJ LQIRUPDWLRQ¶ LQ D ZD\ WKDW FDQ EH UHFRYHUHG RQ QHHG ,Q WKLV UHVSHFW ZH IROORZ 6DPELQ DQG 9DOHQWLQL  DQG WKH WUDGLWLRQ RI FRQVWUXFWLYH DQG SUHGLFDWLYH PDWKHPDWLFV

6\QWD[



p
↔A
adpA

gc AAp

↔A

adpA

gc AA p


↔A depR govR
adpA gc

gc AA gc depL govL gc gc )LJXUH  ([DPSOH RI UHFXUVLYH DGSRVLWLRQDO WUHH

)LJXUH  VKRZV H[DFWO\ ZKDW MXVW GHFODUHG WKH DGWUHHV XQGHU WKH WULDQJOHV RI )LJXUH  KDYH EHHQ PDGH H[SOLFLW depL DQG govL VWDQGLQJ VLPSO\ IRU µOHIW GHSHQGHQW¶ DQG µOHIW JRYHUQRU¶ ZKLOH depR DQG govR VWDQG IRU WKH ULJKW RQHV  7R DYRLG WUHH EUDQFK FODVKLQJ ZH FDQ OHQJWKHQ WKH EUDQFKHV DFFRUGLQJO\ SOHDVH QRWH WKDW WKLV IDFW LV RQO\ IRU GUDZLQJ QHHGV LH LW LV QRW D IRUPDO IDFW %\ FRQYHQWLRQ ZKHQ PRUH WKDQ D JRYHUQRU gov LV SUHVHQW DV LQ )LJXUH  WKH OHQJWKHQHG EUDQFK ZLOO EH WKH OHIW RQH 2WKHUZLVH WKH OHQJWKHQHG EUDQFK ZLOO EH WKH RQH RQ WKH ULJKW  ,W LV ZRUWK QRWLFLQJ WKDW WKH WZR EUDQFKHV DUH DV\PPHWULFDO WKLV LV QRW RQO\ D FRQYHQWLRQ EXW LW KDV SUHFLVH WKHRUHWLFDO UHDVRQ 7KDW LV D JRYHUQRU gov FDQ KDYH PRUH WKDQ RQH GHSHQGHQW dep ZKLOH WKH RSSRVLWH LV QRW SRVVLEOH 7KLV LV YHU\ LPSRUWDQW ZKHQ GHDOLQJ ZLWK YHUEDOEDVHG FRQVWUXFWLRQV 6HFWLRQ   7KH FRQVHTXHQFH LV TXLWH REYLRXV WKH RQO\ SRVVLEOH H[WHQGHG DGWUHHV DUH VLPLODU WR WKH RQH VKRZQ LQ )LJXUH  ZKHUH WKH ULJKW EUDQFK JRYHUQRU govR UXOHV RYHU WZR GHSHQGHQWV depR1  depR2  )URP D VWULFWO\ IRUPDO SRLQW RI YLHZ WKH DV\PPHWU\ FDQ EH LQWHUSUHWHG DV WKH IDFW WKDW DOWKRXJK WKH LQYROYHG DGWUHHV depR1  depR2 DQG govR DUH FRQVWUXFWHG LQGHSHQGHQWO\ IURP HDFK RWKHU WKH µUXOH LQ WKH JUDPPDU¶ ZKLFK DOORZV WKH IRU PDWLRQ RI WKH FRPSRVHG DGWUHH LV VWULFWO\ UHODWHG WR WKH JRYHUQRU DQG WDNHV LQWR DFFRXQW RQO\ WKH JUDPPDU FKDUDFWHUV RI WKH GHSHQGHQWV ,Q IDFW LQ WKH IRUPDO PRGHO ZH FRXOG VD\ WKDW WKHUH LV DQ DUURZ IURP WKH REMHFW govR WR WKH REMHFW GHSLFWHG LQ )LJXUH  ZKLOH WKHUH LV QR DUURZ IURP depR1 RU depR2 WR WKH VDPH REMHFW²DQG WKLV LV REYLRXV VLQFH depR1 DQG depr2 DUH LQGH[HV LQ IDPLOLHV RI DU URZV 7KH UHDGHU LV LQYLWHG WR QRWLFH WKDW SDUWLDO FRQVWUXFWLRQV DUH DGPLWWHG DV LQ



&KDSWHU 7ZR

p
↔A
adpA

gc AAp

↔A

adpA

gc AAp p


↔A
↔A depR2
adpA
adpA

gc AA gc

gc AA depL gc

govL gc

depR1 gc

govR gc

)LJXUH  ([DPSOH RI DQ H[WHQGHG DGSRVLWLRQDO WUHH

)LJXUH  LI WKHUH LV D FRQVWUXFWLRQ OHDGLQJ IURP WKH OHIWPRVW DGWUHH WR WKH ULJKW PRVW RQH WKHQ WKHUH DUH WZR SDUWLDO FRQVWUXFWLRQV ZKLFK DUH WKH RQHV GHVFULEHG E\ WKH { DUURZV p
A ↔ p
adp A
A
A ↔
gc Ap A
adp
A A
govR { ↔ { depR2
gc A A
adp gc gc
gc A govR depR1 A
gc gc govR depR1 gc gc )LJXUH  ([DPSOH RI SDUWLDO FRQVWUXFWLRQ

 *RYHUQPHQW :LWKLQ WKH DGSRVLWLRQDO SDUDGLJP WKH UHODWLRQ EHWZHHQ WKH JRYHUQRU DQG WKH GH SHQGHQW LV XVHG WR FDWHJRULVH WKH OLQJXLVWLF GDWD ,Q IDFW D VSHDNHU PD\ FKRRVH HLWKHU WKH JRYHUQRU RU WKH GHSHQGHQW WR EH SURPLQHQW KRZHYHU VRPHWLPHV KH FDQQRW RU GR QRW ZDQW WR  7KH WUDMHFWRU\ LV WKH GLUHFWLRQ RI WKH LQIRUPDWLRQ SURPLQHQFH DQG LW LV LQ GLFDWHG E\ WKH DGSRVLWLRQ adp  %\ FRQYHQWLRQ LWV VWDUW SRLQW LQGLFDWHV ZKHUH

6\QWD[



7DEOH  ,QGLFDWRUV RI JRYHUQPHQW DQG GHSHQGHQF\

W\SH RI UHODWLRQ JRYHUQPHQW GHSHQGHQF\ JHQHULF

GLUHFWLRQ JRYWRGHS GHSWRJRY ERWK LUUHOHYDQW RU XQNQRZQ

LQGLFDWRU ← → ↔

WKH LQIRUPDWLRQ SURPLQHQFH VWDQGV LQ WKDW SDUWLFXODU DGWUHH DQG LW FDQ EH HLWKHU WKH JRYHUQRU gov RU WKH GHSHQGHQW dep  7KXV WKH WUDMHFWRU\ FDQ LQGLFDWH WZR SRVVLEOH GLUHFWLRQV WKH RQH EHLQJ WKH UHYHUVH RI WKH RWKHU IURP WKH JRYHUQRU WR WKH GHSHQGHQW DQG IURP WKH GHSHQGHQW WR WKH JRYHUQRU :H ZLOO UHIHU WR WKLV NLQG RI DUURZ²SODFHG ULJKWO\ DERYH WKH DGSRVLWLRQ² ZLWK WKH WHUP LQGLFDWRU LQ RUGHU WR DYRLG QDPH FODVKLQJ ZLWK RWKHU WHUPV DOUHDG\ IDPLOLDU WR WKH UHDGHUV EHORQJLQJ WR WKH PDWKHPDWLFDO FRPPXQLWLHV 7KH ELGLUHFWLRQDO LQGLFDWRU ↔ LV XVHG IRU JHQHUDO XQGHUVSHFLILHG SXUSRVHV LH ZKHQ WKH GLUHFWLRQ LV HLWKHU VWLOO XQGHFLGHG XQNQRZQ RU QRW LPSRUWDQW ,Q VXP WKH SRVVLEOH LQGLFDWRUV DUH WKUHH HLWKHU WKH WUDMHFWRU\ JRHV LQ WKH ULJKWOHIW GLUHFWLRQ ← JRYHUQPHQW  RU LQ D OHIWULJKW RQH → GHSHQGHQF\  RU ELGLUHFWLRQDO ↔  DV VKRZQ LQ 7DEOH  :H KDYH D UHODWLRQ RI JRYHUQPHQW ZKHQ WKH JRYHUQRU UXOHV RYHU WKH GHSHQ GHQW EHFDXVH WKH JRYHUQRU LV WKH PRVW SURPLQHQW HOHPHQW LQ WKH FRXSOH ,W LV WKH VLPSOHVW FDVH W\SLFDOO\ XQPDUNHG OLQJXLVWLF SKHQRPHQD VKRZ JRYHUQPHQW q
A
←A
adp A gc AA

dep JRY gc gc )LJXUH  7KH DEVWUDFW JRYHUQPHQW UHODWLRQ )LJXUH  VKRZV WKH DEVWUDFW JRYHUQPHQW UHODWLRQ WKH WUDMHFWRU\ VWDUWV IURP WKH JRYHUQRU gov KHUH LQ EROG IRU HPSKDVLV  E\ FRQYHQWLRQ DOZD\V SXW DW WKH ULJKW EUDQFK²DQG HQGV LQWR WKH GHSHQGHQW dep  $GWUHHV DUH UHFXUVLYHO\ GHILQHG DQG VR WUDMHFWRULHV²D VWUXFWXUDO SDUW RI DQ\ DGWUHH 7KLV IRUPDO IDFW KDV DQ H[DFW OLQJXLVWLF FRXQWHUSDUW ZH FDQ VKRZ WKH W\SH



&KDSWHU 7ZR

RI UHODWLRQ DW GLIIHUHQW ODQJXDJH OHYHOV IURP SKRQRORJ\ XS WR GLVFRXUVH SUDJ PDWLFV FRYHULQJ DOO WKH OLQJXLVWLF VSHFWUXP²PRUSKRORJ\ V\QWD[ DQG VHPDQWLFV LQFOXGHG $Q DLP RI WKLV ERRN LV WR VKRZ FRQFUHWHO\ KRZ WKLV IDFW RSHUDWHV )RU WKH PRPHQW OHW XV VKRZ VRPH H[DPSOHV WR FODULI\ WKLV FUXFLDO SRLQW D

gov ↔ dep ,¶YH QRW VHHQ /L]D ǫ 6KH ZDV QRW ZLWK 3DXO

E

gov → dep { GRQ¶W DVN ,¶YH QRW VHHQ /L]D ǫ VKH ZDV QRW ZLWK 3DXO

([DPSOHV DE SHUWDLQ WR WKH VDPH VFHQH )RU µVFHQH¶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q
A
↔ ǫA
I A AA



△

△

6KH ZDV ,·YH QRW

I

I

)LJXUH  7KH SDFNHG WUHH RI ,¶YH QRW VHHQ /L]D 6KH ZDV QRW ZLWK 3DXO )LJXUH  JLYHV WKH UHSUHVHQWDWLRQ RI D DV DQ DGWUHH ZKHUH HDFK OHDI LV D FRPSOHWH SKUDVH I DV ZH ZLOO VHH LQ GHWDLOV LQ WKH QH[W FKDSWHUV DQG WKHUHIRUH LW LV VWLOO QRW H[SOLFLW KHUH²WKLV LV ZK\ WKH WULDQJOHV △  ([DPSOH E VKRZV D FRPSOHPHQWDU\ FDVH LQ SDUWLFXODU D UHODWLRQ RI JRY HUQPHQW RFFXUULQJ ZLWKLQ WZR GLVWLQFW SKUDVHV  7KH VSHDNHU KDV SXW WKH PDLQ VWUHVV RQ WKH ZRUG QRW LQ EROG WR VKRZ WKH SUDJPDWLF HPSKDVLV  ZKLFK JLYHV D FXH RI WKH QRQORFXWLRQDU\ DVSHFW RI WKH OLQJXLVWLF DFW SXW H[SOLFLWO\ ZLWK WKH

6\QWD[



q
A
← ǫA
I A AA



△

△

6KH ZDV ,·YH QRW

I

I

)LJXUH  7KH SDFNHG WUHH RI ,¶YH QRW VHHQ /L]D 6KH ZDV QRW ZLWK 3DXO

GLUHFWLYH GRQ¶W DVN VHH &KDSWHU  IRU PRUH GHWDLOV  )LJXUH  VKRZV WKH FRUUH VSRQGLQJ DGSRVLWLRQDO WUHH

 'HSHQGHQF\ 7KH WUDMHFWRU\ RI WKH LQIRUPDWLRQ SURPLQHQFH FDQ EH UHYHUVHG FRPSDUHG WR JRY HUQPHQW LH WKH LQIRUPDWLRQ SURPLQHQFH EHORQJLQJ WR WKH GHSHQGHQW 7KLV LV WKH FRPSOHPHQWDU\ FDVH RI JRYHUQPHQW DQG LWV QDPH LV GHSHQGHQF\ 

q
A
→A
adp A gc AA

gov GHS gc gc )LJXUH  7KH DEVWUDFW GHSHQGHQF\ UHODWLRQ )LJXUH  VKRZV WKH DEVWUDFW GHSHQGHQF\ UHODWLRQ WKH GHSHQGHQW ZDV SXW LQ EROG IRU HPSKDVLV  1RWH WKDW WKHUH LV QR RWKHU SRVVLELOLW\ RI FKRLFH HLWKHU WKH WUDMHFWRU\ FRUUHVSRQGV WR WKH JRYHUQRU RU WR WKH GHSHQGHQW RU OHW XQGHUVSHFLILHG OHDGLQJ WR WKH ELGLUHFWLRQDO UHODWLRQ DV VKRZQ LQ 7DEOH   7KH IROORZLQJ H[DPSOH SHUWDLQ WR WKH VDPH VFHQH VHHQ DERYH LQ DE  ZKHUH E\ FRQWUDVW WKH LQIRUPDWLRQ SURPLQHQFH LV FRPSOHWHO\ UHYHUVHG F

gov ← dep { \RX NQRZ ,¶YH QRW VHHQ /L]D VKH ZDV QRW ZLWK 3DXO ZKDW , PHDQ



&KDSWHU 7ZR

([DPSOH F VKRZV WKDW WKH VHFRQG RFFXUUHQFH RI WKH ZRUG QRW LQ EROG ZDV VWUHVVHG DQG KHQFH WKH QRQORFXWLRQDU\ LQIRUPDWLRQ SURYLGHG E\ WKH VSHDNHU LV FRPSOHWHO\ GLIIHUHQW LH WKH IDFW WKDW /L]D ZDV QRW ZLWK 3DXO HYHQ LI VKH ZDV H[SHFWHG WR EH SXW H[SOLFLWO\ ZLWK \RX NQRZ ZKDW , PHDQ 

q
A
→A
ǫI A A
A


△

△

6KH ZDV QRW

,·YH

I

I

)LJXUH  7KH SDFNHG WUHH RI ,¶YH QRW VHHQ /L]D 6KH ZDV QRW ZLWK 3DXO )LJXUH  VKRZV WKH FRUUHVSRQGHQW DGWUHH ,W LV ZRUWK QRWLFLQJ WKDW WKH OLQ JXLVWLF HOHPHQW ZKLFK LV GLIIHUHQW LV RQO\ DQ HPSKDVLV QRW HYHQ D PRUSKHPH ,Q IDFW LQ DOO RWKHU DVSHFWV WKH ZRUGLQJ RI DEF DUH SHUIHFWO\ LGHQWLFDO 7KLV LV LQ SDUWLDO FRQWUDVW WR WKH TXRWDWLRQ E\ 7D\ORU   SXW DERYH KLV SULQFLSOH LV ILQH EXW LW LV QRW HQRXJK WR JLYH DQ DFFRXQW RI WKH FRPSOH[LW\ RI OLQJXLVWLF SKH QRPHQD DW D FRJQLWLYH OHYHO 7KHVH PLQLPDO SDLUV VKRZ WKH H[SUHVVLYH SRZHU²LQ OLQJXLVWLF WHUPV²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

 9DOHQF\ ,Q DQ DGSRVLWLRQDO WUHH WKH OHIW DQG ULJKW EUDQFKHV IROORZ GLIIHUHQW UXOHV RI FRQ VWUXFWLRQ ,Q SDUWLFXODU JRYHUQRUV DQG GHSHQGHQWV VKRZ DQ DV\PPHWULFDO EH KDYLRXU D JRYHUQRU FDQ KDYH PRUH GHSHQGHQWV ZKLOH HDFK GHSHQGHQW FDQ KDYH RQO\ RQH JRYHUQRU

6\QWD[



7KH QXPEHU RI GHSHQGHQWV UXOHG E\ D JRYHUQRU LV DQ LPSRUWDQW YDOXH EHFDXVH LW JLYHV WKH IXQGDPHQWDO VWUXFWXUH RI WKH DGWUHH  :H FDOO WKLV YDOXH YDOHQF\ )ROORZLQJ WKH GHILQLWLRQ E\ 7HVQLqUH ZKR ILUVW LQWURGXFHG LW LQ OLQJXLVWLFV IURP FKHPLVWU\  YDOHQF\ LV D IHDWXUH RI WKH YHUE DQG ZH ZLOO DOVR XVH LW PRVWO\ LQ UHODWLRQ ZLWK YHUEV 2Q SHXW DLQVL FRPSDUHU OH YHUEH j XQH VRUWH G¶DWRPH FURFKX VXVFHSWLEOH G¶H[HUFHU VRQ DWWUDFWLRQ VXU XQ QRPEUH SOXV RX PRLQV pOHYp G¶DFWDQWV VHORQ TX¶LO FRPSRUWH XQ QRPEUH SOXV RX PRLQV pOHYp GH FURFKHWV SRXU OHV PDLQ WHQLU GDQV VD GpSHQGDQFH 7HVQLqUH  SDJH  &KDSWHU  SDU  EROG LQ WKH RULJLQDO  

(YHQ LI ZH UHSUHVHQW YDOHQF\ LQ D GLIIHUHQW ZD\ IURP WKH 7HVQHULDQ RQH ZH VWLOO UHWDLQ WKH XVH RI WKH WHUP DFWDQW WR LQGLFDWH WKH GHSHQGHQWV EHORQJLQJ WR D VLQJOH JRYHUQRU +HQFH ZH ZLOO VSHDN RI ILUVW VHFRQG WKLUG DFWDQW DQG VR RQ dep1  dep2  dep3  HWF  %\ WKH ZD\ LW LV ZRUWK UHPDUNLQJ WKDW LQ FRQVWUXFWLYH DGSR VLWLRQDO JUDPPDUV YDOHQF\ LV D IHDWXUH RI WKH JRYHUQRU gov ²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µSUHVHQW¶ LQ WKH FRQVWUXFWLRQ VLOHQWO\ SOD\LQJ LWV UROH ,Q UDUH FDVHV D JRYHUQRU FDQ KDYH IRXU GHSHQGHQWV DW WKH VDPH WLPH TXDGULYD OHQF\ DGMHFWLYH µWHWUDYDOHQW¶  DQG LQ H[FHSWLRQDOO\ UDUH FDVHV ILYH TXLQYDOHQF\ DGMHFWLYH µSHQWDYDOHQW¶  $ YDOXH RI ]HUR DYDOHQF\ RU DOVR ]HURYDOHQF\ LV DOVR SRVVLEOH DQG QRW VR UDUH LQGHHG LQ WKLV ODVW FDVH WKH DGWUHH FROODSVHV DQG UHGXFHV WR D VLPSOH OHDIURRW
I )LJXUH  7KH FROODSVHG WUHH RI


&KDSWHU 7ZR

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

q
A
→A
WR2 A
I2 A Aq

A .LP
←A O2
ǫ2 A
I1 A A


△

△

7KH ELF\FOH

EHORQJV

O1

I2

q
A
←A
ǫ2 A
I2 A Aq

A
→A WKH ELF\FOH
ǫ2 A O2
I1 A A


△

.LP

O1

△

RZQV

I2

)LJXUH  7ZR GLIIHUHQW ELYDOHQW WUHHV

,Q WKH FRQVWUXFWLRQ DFWLYDWHG E\ WKH VWHP EHORQJ )LJXUH  OHIW  WKH ILUVW DFWDQW O1 LV SURWRW\SLFDOO\ LQDQLPDWH 7KH ELF\FOH  :H VD\ WKDW WKH ILUVW DFWDQW KDV VDWXUDWHG WKH ILUVW YDOHQF\ RI WKH ELYDOHQW YHUE EHORQJV I21  0RUHRYHU WKH UHODWLRQ DFWLYDWHG E\ WKH ILUVW DFWDQW LQ WKLV SDUWLFXODU FRQVWUXFWLRQ LV RI GHSHQ GHQF\ ←  DV WKLV DFWDQW UHFHLYHV µSDVVLYHO\¶ WKH DFW RI EHORQJLQJ  2Q WKH FRQWUDU\ WKH VHFRQG DFWDQW O2 ZKLFK VDWXUDWHV WKH VHFRQG YDOHQF\ I22 LV SULPDU\ UHVSRQVLEOH RI WKH DFW RI EHORQJLQJ KHQFH WKH UHODWLRQ ZLOO EH RI JRYHUQPHQW →  6LPLODUO\ WKH FRQVWUXFWLRQ DFWLYDWHG E\ RZQV VKRZV D FRP SOHPHQWDU\ DUUDQJHPHQW RI LQIRUPDWLRQ SURPLQHQFH )LJXUH  ULJKW 

6\QWD[



 7UDQVIRUPDWLRQ 7KH FULWHULD WR GHWHUPLQH WKH W\SH RI WKH JRYHUQRUGHSHQGHQW UHODWLRQ DUH E\ QR PHDQV JHQHUDO EXW RQ WKH FRQWUDU\ ODQJXDJHGHILQHG RU HYHQ PRUH SUHFLVHO\ FRQVWUXFWLRQGULYHQ ,Q RWKHU ZRUGV ZKHQ D FRQVWUXFWLRQ²LH D SDWWHUQ RI XV DJH²HPHUJHV E\ IUHTXHQF\ RI XVH WKH VWUXFWXUH RI WKH FRQVWUXFWLRQ DGWUHH EH FRPHV SDUWLDOO\ IL[HG LQ VRPH OLQJXLVWLF HOHPHQWV 6RPHWLPHV HYHQ OHDYHV FDQ EH IL[HG DV LQ WKH FRQVWUXFWLRQ Y VROG KHUH DOUHDG\ VHHQ DW WKH EHJLQQLQJ RI WKLV FKDSWHU WKURXJK LWV LQVWDQWLDWLRQ JRRG FRUQ VROG KHUH  EXW LQ HYHU\ FDVH WKH VWUXFWXUH RI WKH DGWUHH VKRXOG EH GHWHUPLQHG²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²LH VLPLODU FRQVWUXFWLRQV LQ V\QFKURQLF DQG GLDFKURQLF WHUPV DJDLQ ZH ZLOO DSSO\ WKH PHWKRG RI FROORFDWLRQ H[DPLQLQJ PLQLPDO SDLUV  ,Q IDFW HYHQ LI V\QFKURQLFDOO\ WKH V\VWHP²LH D OLYLQJ ODQJXDJH LQ D JLYHQ PRPHQW²UXQV SHUIHFWO\ DQG KHQFH WKHUH LV QR UHDVRQ WR FKDQJH ODQJXDJHV FKDQJHV FRQVWDQWO\ WKLV µSDUDGR[ RI FKDQJH¶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{ B E\ PRGLI\LQJ WKH WUHH VWUXFWXUH RI A LQ WKH WUHH VWUXFWXUH RI B ,Q RUGHU WR XQGHUVWDQG KRZ WUDQVIRUPDWLRQ ZRUNV OHW XV WDNH D YHU\ IDPRXV H[DPSOH²VOLJKWO\ DGDSWHG²IURP D FODVVLF SDSHU E\ &KDUOHV - )LOOPRUH F  ZKR LQ WKH ODWH V VWDUWHG WR LQYHVWLJDWH WKH OLQJXLVWLF FRQFHSW RI µFDVH¶ DOVR UHIHUULQJ WR 7HVQLqUH    D 7KH MDQLWRU ZLOO RSHQ WKH GRRU ZLWK WKH NH\



&KDSWHU 7ZR

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²KHUH RQO\ D ²FDQ EH DGYDQFHG WR WKH ILUVW SRVLWLRQ LQ D UHGXFHG FRQVWUXFWLRQ F  ,W LV LPSRUWDQW WR QRWH WKDW WKH VFHQH VKRXOG EH WKH VDPH ERWK LQ WKH IXOO\ H[ SOLFLW FRQVWUXFWLRQ D DQG LQ LWV UHGXFWLRQV EI  HYHQ LI WKH LQIRUPDWLRQ SURPLQHQFH LV GLIIHUHQW ,Q RUGHU WR XQGHUVWDQG WKLV FUXFLDO SRLQW ZH SURFHHG E\ FRQWUDGLFWLRQ /HW VXSSRVH WKHUH H[LVWV D IRXUWK DFWDQW W IRU WKH VWHP RSHQ /HW WKLV IRXUWK DFWDQW EULQJ WKH VHPDQWLF UROH RI Benefactive DV LQ WKH IROORZLQJ H[DPSOH J 7KH MDQLWRU ZLOO RSHQ WKH GRRU ZLWK WKLV NH\ IRU WKH /DG\ ,Q RWKHU ZRUGV ZH DUH WU\LQJ WR YHULI\ LI WKH FRQVWUXFWLRQ LV RI WKH WHWUDYDOHQW W\SH X RSHQ Y ZLWK Z IRU W LQVWHDG RI WKH WULYDOHQW W\SH X RSHQ Y ZLWK Z K "7KH /DG\ ZLOO RSHQ WKH GRRU L "7KH GRRU ZLOO RSHQ ZLWK WKH /DG\ M "7KH NH\ ZLOO RSHQ WKH /DG\ ([DPSOHV KM VKRZ WKDW QR DGYDQFHPHQW LV SRVVLEOH WKHUHIRUH WKH VXS SRVHG IRXUWK DFWDQW Benefactive LV H[WUDYDOHQW  2Q WKH FRQWUDU\ WKH Opener X WKH MDQLWRU  WKH Opened Objective Y WKH GRRU DQG WKH Instrument Z WKH NH\ FDQ EH DGYDQFHG KHQFH WKH\ DUH LQYDOHQW DQG VR WKH FRQVWUXFWLRQ ZLOO KDYH WKH IROORZLQJ DEVWUDFW JHQHUDO IRUP ZKLFK LV WULYDOHQW X RSHQ Y ZLWK Z 1RZ LW LV ZRUWK UHFDOOLQJ KHUH WKDW ZH FRQVLGHU VHPDQWLF UROHV DQ RSHQ LQ YHQWRU\ QRW D IL[HG OLVW EHFDXVH VHPDQWLF UROHV EHORQJ WR WKH VHPDQWLF IUDPHV

6\QWD[



ZKLFK DUH ODQJXDJHGHILQHG  ,Q WKLV UHVSHFW ZH FRQVLGHU WKH HPSLULFDO WUHDW PHQW RI OLQJXLVWLF GDWD E\ PRVW FRJQLWLYH OLQJXLVWV FRQYLQFLQJ q
A
→A A
ZLWK I3

3 AAq
A
← WKH NH\ ǫA
I3 A Z 2 AAq


A
→ WKH GRRU ǫA
A Y I31 AA



△

△

△

△

WKH MDQLWRU ZLOO RSHQ

X

I3

)LJXUH  7KH WUHH RI ; RSHQ < ZLWK = )LJXUH  VKRZV D UDWKHU FRPSOH[ DGSRVLWLRQDO WUHH ZKLFK UHSUHVHQWV WKH FRQVWUXFWLRQ RI D  :H FDQ QRWLFH WKDW WKH ILUVW DQG WKLUG DFWDQWV X DQG Z WKH MDQLWRU DQG WKH NH\ UHVSHFWLYHO\ JRYHUQ WKHLU UHODWLRQV DV WKH\ µGR VRPHWKLQJ¶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{ X  ZLWK D IXUWKHU RPLVVLRQ RI WKH SUHSRVLWLRQ PDUNLQJ WKH Instrumental 7KH UHVXOWLQJ WUHH LV VKRZQ LQ )LJXUH  ULJKW  )LQDOO\ H[DPSOHV HI VKRZ WZR SRVVLEOH (QJOLVK SDVVLYH FRQVWUXFWLRQV JHQHUDWHG E\ WKH VWHP RSHQ Y be RSHQHG E\ X H DQG Y be RSHQHG ZLWK Z 



&KDSWHU 7ZR

q
A
→ A ZLWK A
 3
I

3 A Aq

A 
←A WKHNH\ 
ǫ3 A Z 
I2 A
Aq
A
→A WKH GRRU
ǫ3 A Y
I1 A
A

△

△

△

△

WKH MDQLWRU

ZLOO RSHQ

X

I3

)LJXUH  7KH UHGXFHG WUHH RI 7KH MDQLWRU ZLOO RSHQ WKH GRRU

q
A
→A
3ZLWK A3
I3 { I2 A
Aq
A
←A WKH NH\ ǫ
A 3 Z{Y I { I31 A 2
{
Aq
A
→A WKH GRRU

ǫ A Y{X
I

13 A A


△

△

△ ((

△

q
A →A
ZLWK
I3 A
2 Aq
A
← WKH NH\ ǫA
I3 A Y
1 A

△

△

△

WKH GRRU ZLOO RSHQ

X

I3

( WKH(MDQLWRU ZLOO RSHQ ( X I3 )LJXUH  7KH WUHH RI 7KH GRRU ZLOO RSHQ ZLWK WKH NH\

6\QWD[



q
A
← q ǫA
I3 A
A 2 AAq
←

ǫA
I3 A
A 2 →A AAq


WKH GRRU  ZLWK A

A Y I3 { I31 AAq { WKH GRRU
→

3 ǫA A

A Y I31 AA
→A

WKH NH\ ǫ A

Z{X 3

I

1 AA WKH NH\ ZLOO RSHQ X I3 ( ( ( WKH(MDQLWRU ZLOO RSHQ ( X I3

△

△

△

△

△

△

△

)LJXUH  7KH WUHH RI 7KH NH\ ZLOO RSHQ WKH GRRU

I  ZKHUH WKH ILUVW YDOHQF\ LV RFFXSLHG E\ WKH RULJLQDOO\ VHFRQG DFWDQW Y HJ WKH GRRU  ,W LV ZRUWK QRWLFLQJ WKDW HYHU\ (QJOLVK SDVVLYH FRQVWUXFWLRQ WUDQVIRUPV D WULYDOHQW YHUE LQ ELYDOHQW I3{2  EHVLGHV WKH FKDQJLQJ LQ WKH SDWWHUQ RI WKH LQIRUPDWLRQ SURPLQHQFH q q
A
A
←A
←A
3ZLWK A3
E\ A
I3 { I2 A
I31 { I32 A
Aq Aq

A
A
→A
→A WKH NH\ WKH MDQLWRU ǫ A ǫ A

3 3 3 Y{X Y{X { I I { I31 A I 1 2 2 A

A
A




ZLOO EH RSHQHG ZLOO EH RSHQHG

I3{2 I3{2





△

△

△

△

△

△

WKH GRRU

WKH GRRU

Y{X

Y{X )LJXUH  7KH WUHHV RI 7KH GRRU ZLOO EH RSHQHG



&KDSWHU 7ZR

([DPSOH I )LJXUH  ULJKW VKRZV WKH H[WUDFWLRQ RI WKH ILUVW DFWDQW X DV WKH PRVW SURPLQHQW LQIRUPDWLRQ LQ WKH SKUDVH ZKLOH H LV VLPSOHU DV LW VLPSO\ RPLWV WKH ILUVW DFWDQW ZKLOH WKH RWKHUV DUH DGYDQFHG E\ RQH SRVLWLRQ )LJXUH  OHIW WKH OHIW EUDQFK RI WKH DGSRVLWLRQDO WUHH EHORQJLQJ WR WKH GRRU ZDV OHQJWKHQHG RQO\ IRU FODULW\ 

q
A
→A
IRU A I0 A

Aq
A
→A WKH /DG\
ZLWK A O I33 A

Aq
A
← WKH NH\ ǫA A
Z I32 AAq


A
→ WKH GRRU ǫA A
Y I31 AA



△

△

△

△

△

WKH MDQLWRU ZLOO RSHQ

X

I3

)LJXUH  7KH WUHH RI 7KH MDQLWRU ZLOO RSHQ WKH GRRU ZLWK WKH NH\ IRU WKH /DG\

)URP D VWULFWO\ IRUPDO SRLQW RI YLHZ ZH DUH VD\LQJ WKDW DGWUHHV DUH µJHQ HUDWHG¶ E\ WKH YDOHQFH DQG SRVVLEO\ RWKHU FRQVWUXFWLRQ UXOHV  DQG WKHQ WUDQV IRUPHG WR WKHLU ILQDO IRUP 7KLV VHSDUDWLRQ EHWZHHQ JHQHUDWLRQ DQG SUHVHQWDWLRQ RI DQ DGWUHH LV LPSRUWDQW WR VXSSRUW WKH FRQVWUXFWLYH FKDUDFWHU RI RXU DSSURDFK DV WUDQVIRUPDWLRQV DUH UHVSRQVLEOH IRU WKH KLGLQJ RI LQIRUPDWLRQ ZKLFK LV SUHVHQW LQ WKH JHQHUDWLRQ SKDVH  )RU LQVWDQFH )LJXUH  VKRZV WKH JHQHUDWHG DGWUHH IRU H[DPSOH J  (DFK RI WKH H[DPSOHV EI LV REWDLQHG E\ KLGLQJ VRPH SLHFHV RI WKLV DGWUHH ZKLFK DUH EDUUHG LQ WKH GHULYHG DGWUHHV 8VXDOO\ WKH EDUUHG SLHFHV DUH RPLWWHG DV LQ )LJXUH  RU ZULWWHQ DV ǫ  WKH ]HUR PRUSKHPH ZKHQ LQVLGH WKH DGWUHH DV LQ )LJXUH  $OWKRXJK WKLV FRQYHQWLRQ LV XVHIXO LW PD\ EH PLVOHDGLQJ VLQFH WKH SLHFHV DUH QRW DEVHQW EXW UHDOO\ KLGGHQ LH WKH\ SOD\ D UROH ZKHQ ZH ZDQW WR DSSO\ IXUWKHU WUDQVIRUPDWLRQV WR WKH DGWUHH 7KLV IDFW VKRXOG EH HYLGHQW VLQFH WUDQVIRUPDWLRQV DUH ILUVW FRPSRVHG DQG WKHQ DSSOLHG WR

6\QWD[



WKH JHQHUDWHG JHUP

$ FDVH VWXG\ WKH GDWLYH DOWHUQDWLRQ FRQVWUXFWLRQ &RQVWUXFWLYH DGSRVLWLRQDO JUDPPDUV JLYH D VLPSOH DQG HIIHFWLYH H[SODQDWLRQ RI GHEDWHG QXDQFHV LQ QDWXUDO ODQJXDJH JUDPPDUV )RU H[DPSOH OHW XV WDNH WKH (Q JOLVK FRQVWUXFWLRQ NQRZQ DV µGDWLYH DOWHUQDWLRQ¶ RU LQ OHVV UHFHQW WLPHV µGDWLYH PRYHPHQW¶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

p
→A
ǫA 3

I3 AAp
←A WKH FDU
ǫ A Z

I32 AAp
→A .LP
ǫA Y 3

I1 AA

△

p
→A
WR A 3

I3 AAp
←A .LP
ǫA Z 3

I2 AAp
→A WKH FDU
ǫ A Y

I31 AA

△

$QQ

JDYH

$QQ

JDYH

X

I3

X

I3

)LJXUH  7KH WUHHV RI $ JDYH . WKH FDU DQG $ JDYH WKH FDU WR . 7KHVH WZR FRQVWUXFWLRQV )LJXUH  DUH GLIIHUHQW DV LQ ERWK FDVHV LW LV WKH WKLUG DFWDQW WKDW LV SXW LQ HYLGHQFH ,Q IDFW D )LJXUH  OHIW VKRZV WKDW WKH PRVW VDOLHQW LQIRUPDWLRQ²LQ RWKHU ZRUGV WKH SKUDVDO WUDMHFWRU\²LV WKH FDU ZKLOH E\ FRQWUDVW LQ E )LJXUH  ULJKW LW LV .LP WKH PRVW SURPLQHQW HOHPHQW ZLWKLQ WKH SKUDVH



&KDSWHU 7ZR

F $QQ JDYH KLP WKH FDU G $QQ JDYH WKH FDU WR KLP 7KLV DQDO\VLV LV FRQILUPHG E\ WKH IDFW WKDW F  ZKLFK UHVHPEOHV D  LV SHUIHFWO\ JUDPPDWLFDO ZKLOH G LV KDUGO\ DFFHSWDEOH  $FFRUGLQJ WR $EUHX *RPHV   WKH 'DWLYH DOWHUQDWLRQ FRQVWUXFWLRQ LQ %UD]LOLDQ 3RUWXJXHVH LV VLPLODU WR E  D

0DULD GHX R OLYUR SDUDDǫ 3HGUR 0DU\ JDYH WKH ERRN WR 3HWHU

p
→A
DA 3

I3 AAp
←A 3HGUR
ǫA Z 3

I2 AAp
→A R OLYUR
ǫ A Y

I31 AA

△

0DULD

X

△

GHX

I3

)LJXUH  7KH WUHH RI 0DULD GHX R OLYUR D 3HGUR ,Q D  WKH SUHSRVLWLRQ LQWURGXFLQJ WKH H[SOLFLW QRPLQDO Receiver LQ (Q JOLVK LQYDULDEO\ PDUNHG E\ WKH SUHSRVLWLRQ WR FDQ EH UHQGHUHG ZLWK SDUD D RU HYHQ D ]HUR PRUSKHPH ǫ  DFFRUGLQJ WR GLIIHUHQW GHJUHHV RI JUDPPDWLFDOL]DWLRQ ,Q ,WDOLDQ WKH SURQRPLQDOLVDWLRQ RI WKH Receiver LQYRNHV D FRQVWUXFWLRQ VLP LODU WR WKH (QJOLVK RQH ZLWK D ]HUR PDUNHU F  ZKLOH WKH SUHVHQFH RI DQ H[SOLFLW QRPLQDO PDUNHU DFWLYDWHV D FRQVWUXFWLRQ VLPLODU WR WKH (QJOLVK RQH SUHVHQWLQJ WKH SUHSRVLWLRQ WR G  E

0DULD GLHGH LO OLEUR D 3LHWUR 0DU\ JDYH WKH ERRN WR 3HWHU

F

0DULD JOL GLHGH LO OLEUR 0DU\ KLP JDYH WKH ERRN

6\QWD[

p
→A
DA 3

I3 AAp
←A 3LHWUR
ǫA Z 3

I2 AAp
→A LO OLEUR
ǫ A Y

I31 AA

△



p
→A
ǫA 3

I3 AAp
→A LO OLEUR
ǫ A Y

I32 AAp
←A 0DULD
ǫA X 3

I1 AA

△

0DULD

GLHGH

JOL

GLHGH

X

3

Z

I3

I

)LJXUH  7KH WUHHV RI 0 GLHGH LO OLEUR D 3 DQG 0 JOL GLHGH LO OLEUR

)LJXUH  ULJKW VKRZV WKH WUHH GHVFULELQJ E  ZKHUH WKH WKLUG DFWDQW LV DGYDQFHG PHDQLQJ WKH H[DFW VHQVH DOUHDG\ H[SODLQHG QH[W WR WKH YHUE GLHGH JOL EHLQJ D FOLWLF ZKLFK LV DGYDQFHG QH[W WR WKH YHUE   'HWHUPLQLQJ DGYDQFHPHQWV LV PDGH WKURXJK WKH FRPSDULVRQ RI FRQVWUXFWLRQ VLEOLQJV ,W LV REYLRXV WKDW WKH LQVWDQFH LQ E  VKRZLQJ H[SOLFLWO\ WKH Receiver DQG WKH LQVWDQFH LQ F  VKRZLQJ LW LPSOLFLWO\ YLD D FOLWLF DUH VWURQJO\ UHODWHG )XUWKHUPRUH WKH SURQRPLQDO Receiver FDQ EH VDIHO\ RPLWWHG G  ZKLOH WKH VHFRQG DFWDQW WKH Objective LV DOPRVW PDQGDWRU\ H  G

0DULD JOL GLHGH LO OLEUR  JDYH WKH ERRN KLP 0DU\ 

H

 "0DULD JOL GLHGH  LO OLEUR  "0DU\ KLP JDYH  WKHERRN

7KLV PLQLPDO SDLU VKRZV KRZ XVDJHEDVHG ODQJXDJH GDWD LV XVHG WR GHWHUPLQH WKH VWUXFWXUH RI D FRQVWUXFWLRQ LQ WHUPV RI YDOHQF\ DQG LQIRUPDWLRQ SURPLQHQFH ,W LV ZRUWK QRWLFLQJ WKDW WKHUH DUH VRPH ODQJXDJHV WKDW HQFRGH WKH LQIRUPDWLRQ SURPLQHQFH LQWR WKH FRQVWUXFWLRQ ZLWK FDVH PDUNLQJ IRU H[DPSOH *HUPDQ D

'HU 0DQQ JDE GHU )UDX GDV $XWR 7KH PDQNom JDYH WKH /DG\Dat WKH FDUAcc

E

'HU 0DQQ JDE HV GHU )UDX 7KH PDQNom JDYH LWAcc WKH /DG\Dat



&KDSWHU 7ZR

q
A
← ǫA
I3 A 2 Aq
>Acc @
A
→ GDV $XWR ǫA
Y I3 A
3 Aq >Dat@
A
→ GHU )UDX ǫA
Z I3 A
1 A >Nom@

△

△

△

GHU 0DQQ

X

q
A
→ ǫA
I3 A 3 Aq
>Dat @
A
← GHU )UDX ǫA
Z I3 A
2 Aq >Acc@
A HV
→ ǫA Y
I3 A
1 A >Nom@

△

JDE

△

3

GHU 0DQQ

I

X

JDE

I3

)LJXUH  7KH WUHHV RI 'HU 0DQQ JDE

,Q D )LJXUH  OHIW  WKH WKLUG DFWDQW LV QRPLQDO GHU )UDX DQG QH[W WR WKH YHUE JDE  ZKLOH LQ E )LJXUH  ULJKW WKH VHFRQG DFWDQW LV SURQRPLQDO HV DQG LW VKLIWV LQ WKH VHFRQG SRVLWLRQ ,Q WKLV UHVSHFW *HUPDQ EHKDYHV H[DFWO\ WKH RSSRVLWH WR ,WDOLDQ VHH WKH YDULRXV LQVWDQFHV LQ    6RPHWLPHV WKHUH DUH WZR FRPSHWLQJ FRQVWUXFWLRQV ZLWK WKH VDPH PRUSKRORJ\ EXW GLIIHUHQW FROORFDWLRQ DV LQ 7VXQJD²UHSRUWHG E\ $EUHX *RPHV   D

:DNRQJH ZDSHOH PE\LD ZDQDFH :RPDQ JDYH PRQH\ FKLOGUHQ

E

:DNRQJH ZDSHOH ZDQDFH PE\LD :RPDQ JDYH FKLOGUHQ PRQH\

+HUH WKH LQIRUPDWLRQ SURPLQHQFH LV OHIW XQGHUVSHFLILHG ↔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

6\QWD[

p
A
↔ ǫA
I3 A
3 Ap
A ↔ ZDQDFH
ǫ A
3 A Z
I2 Ap
A
↔ PE\LD ǫA
I Y
31 AA

△

△



p
A
↔ ǫA
I3 A
2 Ap
A
↔ PE\LD ǫA
I Y
33 AAp
A ↔ ZDQDFH
ǫ A
3 A Z
I1 A

△

△

△

ZDSHOH

△

:DNRQJH

3

:DNRQJH

X

I

X

ZDSHOH

I3

)LJXUH  7KH WUHHV RI :DNRQJH ZDSHOH

,Q WKH QH[W FKDSWHU WKH SLFWXUH ZLOO EH FRPSOHWHG DW D LQWUDSKUDVDO OHYHO LH KRZ D VLQJOH SKUDVH LV PDGH 7KH NH\ FRQFHSW ZLOO EH WKH JUDPPDU FKDUDF WHU ZKLFK ZLOO KHOS XV WR XQGHUVWDQG WKH LQQHU G\QDPLFV RI PRUSKRV\QWD[ DQG WKH VWUXFWXUH RI WKH OH[LFRQ :H ZLOO UHSULVH DQG GHILQH ZLWK PRUH GHWDLOV HY HU\ FRQFHSW SUHVHQWHG LQ WKLV FKDSWHU ERWK LQ D IRUPDO ZD\ DV ZHOO DV WKURXJK XVDJHEDVHG OLQJXLVWLF H[DPSOHV

Chapter Three Constructions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µPRUSKHPH¶ LQ WKH VWDQGDUG VHQVH PHDQLQJ D ZRUG²RU D ZRUG SDUW²ZKLFK FDQQRW EH IXUWKHU DQDO\VHG )RU LQVWDQFH LQ (Q JOLVK IUHWOHVV LV D ZRUG PDGH E\ WZR PRUSKHPHV LH IUHW DQG OHVV WKH PLQXV LQGLFDWHV WKDW WKH\ DUH ERXQG RQH ZLWK HDFK RWKHU  ZKLOH JLUO LV D ZRUG PDGH E\ RQH PRUSKHPH RQO\  0RUSKHPHV ZRUN WRJHWKHU WR IRUP OLQJXLVWLF FRQVWUXF WLRQV LQ WKH VHQVH SXW E\ FRJQLWLYH OLQJXLVWV²DQ H[DPSOH RI FRQVWUXFWLRQ EHLQJ Y be HDWHQ E\ X &URIW   7KLV SHUVSHFWLYH LV TXLWH XQSRSXODU DPRQJ OLQJXLVWV LQ JHQHUDO DQG FRPSX WDWLRQDO OLQJXLVWV LQ SDUWLFXODU ZKR XVXDOO\ WDNH DV WKH EDVLF XQLW RI WKH DQDO\VLV WKH QRWLRQ RI µZRUG¶  ,Q RXU XQGHUVWDQGLQJ RI WKH OLWHUDWXUH WKLV KDSSHQV EHFDXVH WKH URXJK QR WLRQ RI µZRUG¶ LV D VWULQJ RI FKDUDFWHUV EHORQJLQJ WR WKH DOSKDEHW DOORZHG E\ D SDUWLFXODU ODQJXDJH²ZULWWHQ EHWZHHQ WZR VSDFHV ZLWKLQ D SKUDVH  7KLV URXJK GHILQLWLRQ²VRPHWLPHV UHIHUUHG DV WKH QRWLRQ RI µZRUGVDVVWULQJV¶²VHHPV WR EH LQWXLWLYH WR PRVW VSHDNHUV RI :HVWHUQ ODQJXDJHV DQG FRPIRUWDEOH WR QDWXUDO ODQ JXDJH SURFHVVLQJ WUHDWPHQW 1RQHWKHOHVV WKH DGYDQWDJHV RI WKLV SHUVSHFWLYH ZKLFK DSSHDU FOHDU DW D ILUVW JODQFH FRPH DW GUDPDWLF FRVWV 7KH ILUVW UHPDUN WR EH GRQH FRPHV IURP W\SRORJ\ QRW HYHU\ ODQJXDJH RI WKH ZRUOG KDYLQJ D SURSHU ZULWLQJ V\VWHP FDQ EH HDVLO\ GHVFULEHG LQ WHUPV RI ZRUGVDVVWULQJV²HJ &KLQHVH 7KH VHFRQG UHPDUN LV WKDW VSDFHV EHWZHHQ ZRUGV VHHP WR EH HTXDO RQH ZLWK HDFK RWKHU EXW WKH\ DUH QRW DW DOO IRU H[DPSOH LQ (QJOLVK WKH VSDFHV EHWZHHQ WKH IROORZLQJ SDLUV RI ZRUGV DUH GLIIHUHQW SHU VH PRUQLQJ VWDU ELUGV IO\ KRW GRJ :H FODLP WKDW PRVW RI WKH SUREOHPV RI FRPSXWDWLRQDO OLQJXLVWLFV QRZDGD\V DUH GHULYHG IURP WKH QRWLRQ RI ZRUGVDVVWULQJV LGLRPV H[SUHVVLRQV OH[LFDO LQWULFDFLHV DUH WUHDWHG DV



&KDSWHU 7KUHH

p
↔A
adpA

G AA

△

△

dep D

gov G

p
↔A
adpA

F AA

△

△

dep gov D1 > D2 G

)LJXUH  $EVWUDFW WUHHV DQG JUDPPDU FKDUDFWHUV

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²LH WKH VLQJOH PRUSKHPHV²EHORQJ WR D SDUWLFXODU FODVV  8QGHU D PDWKHPDWLFDO SHUVSHFWLYH FRQVWUXFWLRQV DUH IDPLOLHV RI DUURZV LQ D FDWHJRU\ ZKHUH WKH DGWUHHV DUH LWV REMHFWV VHH $SSHQGL[ % IRU WKH PDWKHPDWLFDO WUHDWPHQW  ,I D FODVV LV RSHQ DQG ODUJH WKH FRQVWUXFWLRQ ZLOO EH SURGXFWLYH RWKHUZLVH LI D FODVV LV FORVHG DQG VPDOO²IL[HG FDUYHG LQ WKH FRQVWUXFWLRQ DW WKH OLPLW²WKH FRQVWUXFWLRQ ZLOO EH LGLRPDWLF :LWKLQ WKH DGSRVLWLRQDO SDUDGLJP D ZRUG LV D SDUWLFXODU FRQVWUXFWLRQ²WKLQN IRU H[DPSOH WR WKH (QJOLVK FRQVWUXFWLRQ RI VWDWLYH SOXUDOV µDGG D V WR WKH VWDWLYH PRUSKHPH LI LW KDV WKH IROORZLQJ IHDWXUHV SKRQR WDFWLF PRUSKRORJLFDO HWF ¶ ,Q VXP WKHUH LV QR VSHFLDO VWDWXV RI ZRUGV SHU VH 7KH QRWLRQV RI PRUSKHPH DQG FRQVWUXFWLRQ DUH OLQJXLVWLF XQLYHUVDOV HYHU\ ODQ JXDJH LV PRUH RU OHVV JUDPPDWLFDOL]HG²RWKHUZLVH WKHUH ZLOO EH QR UHJXODULW\ LQ PRUSKHPHV LQWR WKH V\QWDJPDWLF D[LV +HQFH JUDPPDU LV PDGH E\ PRUSKHPHV WKH XQLWV DQG FRQVWUXFWLRQV WKHLU HVWDEOLVKHG SDWWHUQV RI XVDJH  ,Q WKLV FKDSWHU ZH ZLOO H[SODLQ WKH PRUSKRORJ\ RI FRQVWUXFWLRQV LQ JHQHUDO ZKLOH WKH PRUSKRO RJ\ RI ZRUGV LV GHULYHG DV D VSHFLDO FDVH LQ WKH QH[W FKDSWHUV :H VWDWH WKDW HYHU\ HOHPHQW LQ WKH WULSOH RI WKH DGWUHH²LH DGSRVLWLRQ GH SHQGHQW JRYHUQRU²KDV D GHILQLWH JUDPPDU FKDUDFWHU )LJXUH   ZKLFK FDQ EH FRQVLGHUHG E\ WKH PRPHQW DV D JHQHULF NLQG RI ODEHO VHH EHORZ IRU GHWDLOV  7KH DGSRVLWLRQ LV WKH PDUNHU RI WKH JUDPPDU FKDUDFWHU RI WKH ZKROH DGWUHH 7ZR VFHQDULRV DUH SRVVLEOH WR GHWHUPLQH WKH ILQDO JUDPPDU FKDUDFWHU RI WKH DGWUHH ,Q WKH ILUVW VFHQDULR WKH DGWUHH LQKHULWV WKH JUDPPDU FKDUDFWHU IURP WKH JRY HUQRU gov  DV LW µJRYHUQV¶ WKH DGWUHH )LJXUH  OHIW  /HW D EH WKH JHQHULF

&RQVWUXFWLRQV



JUDPPDU FKDUDFWHU RI WKH GHSHQGHQW DQG G EH WKH JHQHULF JUDPPDU FKDUDFWHU RI WKH JRYHUQRU ,I WKH JRYHUQRU JLYHV LWV JUDPPDU FKDUDFWHU WR WKH ZKROH DGWUHH ZH ZLOO VD\ WKDW WKH JUDPPDU FKDUDFWHU UDLVHV RU WKDW WKHUH ZDV D FKDUDFWHU UDLVLQJ ,Q WKH VHFRQG VFHQDULR WKH JRYHUQRU GRHV QRW FRQFXU WR GHWHUPLQH WKH IL QDO JUDPPDU FKDUDFWHU ,QVWHDG WKH ILQDO JUDPPDU FKDUDFWHU LV LPSRVHG E\ WKH DGSRVLWLRQ ZKRVH PDLQ UROH LV H[DFWO\ WR FKDQJH WKH JUDPPDU FKDUDFWHU RI WKH JRYHUQRU DQG VRPHWLPHV HJ F HYHQ WKH DGSRVLWLRQ RI WKH GHSHQGHQW )LJ XUH  ULJKW  ,I WKH JUDPPDU FKDUDFWHU RI WKH ZKROH DGWUHH LV LPSRVHG E\ WKH DGSRVLWLRQ ZH ZLOO VD\ WKDW WKHUH ZDV D FKDUDFWHU LPSRVLWLRQ ,W LV ZRUWK QRWLF LQJ WKDW WKH DGSRVLWLRQ LPSRVHV WKH WUDMHFWRU\ RI LQIRUPDWLRQ SURPLQHQFH DV ZHOO ,Q D IRUPDO ZD\ HYHU\ DGWUHH KDV D JUDPPDU FKDUDFWHU RU HTXLYDOHQWO\ HYHU\ DGWUHH EHORQJV WR D FODVV GHQRWHG E\ WKH JUDPPDU FKDUDFWHU $Q\ FRQVWUXFWLRQ WDNHV VRPH DGWUHHV²WKH SDUDPHWHUV²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µJHQHULF¶ LH LW GHFRUDWHV WKH JRYHUQRU ZLWK WKH GHSHQ GHQWV WKDW LV WKHUH LV DQ DUURZ IURP WKH JRYHUQRU WR WKH FRQVWUXFWHG DGWUHH ZKRVH LQGH[HV DUH WKH GHSHQGHQWV DQG LW KDV WKH LQGLFDWRU DV LWV ODEHO RQ WKH FRQWUDU\ D FKDUDFWHU LPSRVLWLRQ GHQRWHV D FRQVWUXFWLRQ ZKLFK LV GHYRWHG WR FRRUGLQDWH WKH JRYHUQRU ZLWK WKH GHSHQGHQWV WR EXLOG D QHZ DGWUHH SRVVLEO\ RI D GLIIHUHQW FODVV $V D PDWWHU RI IDFW DV ZH ZLOO VKRZ LQ WKH IROORZLQJ WKH JUDPPDU FKDUDFWHU RI DQ DGWUHH REWDLQHG E\ FKDUDFWHU LPSRVLWLRQ LV IL[HG LH LW GHSHQGV H[FOXVLYHO\ IURP WKH DGSRVLWLRQ DQG QRW IURP WKH JRYHUQRU RU WKH GHSHQGHQWV ,Q SDUWLFXODU LW QHYHU KDSSHQV WKDW WKH GHSHQGHQW DV LWV QDPH VXJJHVWV JLYHV LWV JUDPPDU FKDUDFWHU WR WKH DGWUHH

 *UDPPDU FKDUDFWHUV 7KHUH LV D JHQHUDO DJUHHPHQW DPRQJ OLQJXLVWV WKDW WKH SUHVHQFH RI H[SUHVVLRQV RI UHIHUHQFH LH WKLQJV DQG WKH SUHVHQFH RI SUHGLFDWLRQ LH HYHQWV DUH µFRQ



&KDSWHU 7KUHH

FHSWXDO DUFKHW\SHV¶ /DQJDFNHU  LH WKH\ DUH DOZD\VYDOLG XQLYHUVDOV RI ODQ JXDJH ,Q RWKHU ZRUGV WKH\ SHUWDLQ WR FRJQLWLRQ DQG FRPPXQLFDWLRQ DV SXW E\ 7RPDVHOOR LH QRW WR VRPH ODQJXDJHV LQ SDUWLFXODU /DQJDFNHU  7RPDVHOOR  IRU H[DPSOH  2I FRXUVH WKLQJV DQG HYHQWV DUH VKDSHG E\ ODQJXDJHV LQ YHU\ GLIIHUHQW ZD\V DQG WKH WUDGLWLRQDO JUDPPDU FDWHJRULHV RI µQRXQ¶ DQG µYHUE¶²UHS UHVHQWLQJ WKLQJV DQG HYHQWV UHVSHFWLYHO\²DUH ERXQG WRR FORVHO\ WR WKH 6WDQGDUG $YHUDJH (XURSHDQ 6SUDFKEXQG +DVSHOPDWK   +HQFH ZH GHFLGHG QRW WR XVH WKHP LQ D JHQHUDO DEVWUDFW ZD\ LQ RUGHU WR DYRLG FRQIXVLRQ  ,Q DQ DOPRVW QHJOHFWHG DUWLFOH E\ :KRUI   SXEOLVKHG SRVWKXPRXVO\ KH DGGUHVVHV H[DFWO\ WKLV SUREOHP FRPSDULQJ :HVWHUQ ODQJXDJHV VXFK DV (QJOLVK ZLWK 1RQ:HVWHUQ RQHV VXFK DV +RSL RU
&RQVWUXFWLRQV



7DEOH  7KH PRUSKRORJLF JUDPPDU FKDUDFWHUV

QDPH VWDWLYH YHUEDQW DGMXQFWLYH FLUFXPVWDQWLDO DGSRVLWLRQ

SURFHVV VWDWLYDWLRQ YHUELILFDWLRQ DGMXQFWLYDWLRQ FLUFXPVWDQWLDWLRQ DGSRVLWLRQDO

UROH IXQGDPHQWDO FKDUDFWHU IXQGDPHQWDO FKDUDFWHU PRGLILHU RI O PRGLILHU RI I VWUXFWXUDO FKDUDFWHU

V\PERO O I A E U

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µGLIIHUHQW¶ DV LWV UROH LV WR JHQHUDWH WKH VWUXFWXUH RI WKH ODQJXDJH UDWKHU WKDQ WR FRQYH\ PHDQLQJ²WKH UHDGHU FDQ WKLQN RI µ8¶ DV VWDQGLQJ IRU µXQLRQ¶

p
↔A
adpA

Iv AA

△

dep Ox

x

p
↔A
adpA

I AA

△

△

△

gov Ivx−1

dep E

gov G

)LJXUH  $EVWUDFW YHUEDQW UHODWLRQV

p
↔A
adpA

O AA

p
↔A
adpA

A AA

△

△

△

△

dep A

gov G

dep E

gov G

)LJXUH  $EVWUDFW DGMXQFWLYH UHODWLRQV



&KDSWHU 7KUHH

)LJXUHV  DQG  VKRZ WKH DGPLVVLEOH DGWUHHV LQ WHUPV RI UHODWLRQV EHWZHHQ GLIIHUHQW JUDPPDU FKDUDFWHUV $SDUW RI WKH VWDWLYHYHUEDQW UHODWLRQV )LJXUH  OHIW ²ZKLFK DUH VSHFLDO EHFDXVH RI YDOHQF\²LQ DOO WKH RWKHU UHODWLRQV WKH JUDP PDU FKDUDFWHU RI WKH JRYHUQRU LV JHQHULF G  LH HLWKHU WKH JUDPPDU FKDUDFWHU ZLOO EH UDLVHG IURP WKH JRYHUQRU RU LW ZLOO EH LPSRVHG E\ WKH DGSRVLWLRQ  ,W LV ZRUWK QRWLFLQJ WKDW WKH JHQHULF LQGLFDWRU GHQRWHG E\ ↔ FDQ EH VSHFL ILHG ERWK DV D JRYHUQPHQW ← DQG DV D GHSHQGHQF\ →  6R DV WKUHH LQVWDQFHV IRU HDFK DGWUHH DUH SRVVLEOH WKH DEVWUDFW DGWUHHV DUH H[DFWO\ WZHOYH 7KH\ DUH WKH IROORZLQJ LQ OLQHDU IRUPDW   UHODWLRQ VWDWLYHYHUEDQW adp↔ (dep)O  (gov)I I  JRYHUQPHQW VWDWLYHYHUEDQW adp← (dep)O  (gov)I I  GHSHQGHQF\ VWDWLYHYHUEDQW adp→ (dep)O  (gov)I I  UHODWLRQ DGMXQFWLYHVWDWLYH adp↔ (dep)A  (gov)G O (dep)A  (gov)G  JRYHUQPHQW DGMXQFWLYHVWDWLYH adp← O  GHSHQGHQF\ DGMXQFWLYHVWDWLYH adp→ (dep)E  (gov)G O (dep)E  (gov)G  UHODWLRQ FLUFXPVWDQWLDOYHUEDQW adp↔ I (dep)E  (gov)G  JRYHUQPHQW FLUFXPVWDQWLDOYHUEDQW adp← I  GHSHQGHQF\ FLUFXPVWDQWLDOYHUEDQW adp→ (dep)E  (gov)G I (dep)E  (gov)G  UHODWLRQ FLUFXPVWDQWLDODGMXQFWLYH adp↔ A (dep)E  (gov)G  JRYHUQPHQW FLUFXPVWDQWLDODGMXQFWLYH adp← A (dep)E  (gov)G  GHSHQGHQF\ FLUFXPVWDQWLDODGMXQFWLYH adp→ A 7KLV OLVW ZRXOG EH QRW FRPSOHWH ZLWKRXW PHQWLRQLQJ WKH LGHQWLW\ UHODWLRQV LH ZKHQ WKH JRYHUQRU DQG WKH GHSHQGHQW KDYH WKH VDPH JUDPPDU FKDUDFWHU DQG WKXV WKH UHVXOWLQJ ILQDO JUDPPDU FKDUDFWHU RI WKH DGWUHH ZLOO EH DJDLQ LGHQWLFDO )LJXUH  VKRZV WKH TXLWH REYLRXV DGWUHH RI LGHQWLW\ UHODWLRQV WKH PRVW SURPLQHQW HOHPHQW LV WKH JRYHUQRU E\ GHILQLWLRQ EHFDXVH LW FDQ µVWDQG DORQH¶ VHH DJDLQ &KDSWHU  LI QHHGHG  $V ZH ZLOO VHH GHDOLQJ ZLWK WUDQVIHUHQFH QH[W FKDSWHUV  LGHQWLW\ UHODWLRQV DUH WKH VWUXFWXUDO GHVFULSWLRQ RI D YHU\ LPSRUWDQW XQL YHUVDO SURSHUW\ RI ODQJXDJHV UHGXQGDQF\ &KLDUL  

&RQVWUXFWLRQV

p
A ← A
adp A

O A



p
A ← A
adp A

I A

△

△

△

△

dep O

gov O

dep I

gov I

p
A ←
adp A
A
A A

p
A ←
adp A
A
E A

△

△

△

△

dep A

gov A

dep E

gov E

)LJXUH  $EVWUDFW LGHQWLW\ UHODWLRQV UHGXQGDQF\

 7KH VWDWLYHYHUEDQW UHODWLRQV 7KH VWDWLYHYHUEDQW UHODWLRQV DUH WKH VNHOHWRQ RI PRVW FRQVWUXFWLRQV :LWKLQ D VLQJOH ODQJXDJH FRQVWUXFWLRQV DUH RIWHQ EXLOW DURXQG D YHUEDQW JURXS HYHQWXDOO\ WUDQVIRUPHG E\ JUDPPDWLFDOL]DWLRQ LQ VRPHWKLQJ HOVH HJ D VWDWLYH JURXS ± D SKHQRPHQRQ FDOOHG QRUPDOLVDWLRQ VHH EHORZ  7KLV NLQG RI UHODWLRQV LV UXOHG E\ YDOHQF\ DV H[SODLQHG LQ WKH SUHYLRXV FKDSWHU 6HFWLRQ   1RWH WKDW YDOHQF\ UXOHV ERWK YHUEDO DQG LQWHUMHFWLRQDO JURXSV )RU LQVWDQFH FRQVLGHU WKH IROORZLQJ LQWHUMHFWLRQDO JURXSV  $K  'HDU PH

$K

I )LJXUH  7KH FROODSVHG WUHH RI $K )LJXUH  VKRZV WKDW  KDV D YDOHQF\ YDOXH RI ]HUR VR WKH DGWUHH FROODSVHV LQ D VLPSOH OHDI



&KDSWHU 7KUHH

p
←A
A p

I22 AA A
→A A
ǫA AAp

O2 AA
←A
PH
ǫA
O2

I2 AA

1 (  ((( \RX FRQVLGHU     ZKR DP GHDU  O1 I2 A

△

{

p
←A
A

I22 AA GHDU

PH

A

O2

)LJXUH  7KH H[SOLFLW DQG UHGXFHG WUHH RI 'HDU PH

%\ FRQWUDVW )LJXUH  VKRZV D ELYDOHQW LQWHUMHFWLRQ   ,Q IDFW WKH FRQ VWUXFWLRQ GHDU < FDQ EH LQVWDQFHG E\ REOLTXH SURQRXQV VXFK DV PH KLP KHU 7KLV PHDQV WKDW D ELYDOHQW YHUE ZDV FDQFHOOHG E\ JUDPPDWLFDOL]DWLRQ EXW D WUDFH VWLOO UHPDLQV EHFDXVH RI WKH IRVVLO REOLTXH FDVH 7KLV NLQG RI FRQVWUXFWLRQ XVX DOO\ UHIHUUHG WR DV µH[KRUWDWLYHV¶ DQG µYRFDWLYHV¶ DUH EXLOW XSRQ LPSHUDWLYH IRUPV VXFK DV \RX FRQVLGHU ZKLOH WKH DGMHFWLYH LV WKH UHVXOW RI D SUHGLFDWLRQ VHH EH ORZ IRU GHWDLOV  7KH LQGLFDWRU RI JRYHUQPHQW ← LQ WKH VWDWLYHYHUEDQW UHODWLRQ RI \RX FRQVLGHU LV GXH WR WKH LPSHUDWLYH IRUP LQ IDFW WKH VWDWLYH \RX LV XVXDOO\ RPLWWHG KHQFH WKH LQIRUPDWLRQ VDOLHQFH VWDQGV RQWR WKH YHUE ([DPSOHV  DQG  VKRZ WZR IDFWV ILUVW QRW DOO YHUEDQWV DUH YHUEV VHFRQG ZLWKLQ D VLQJOH SKUDVH WKH SKUDVDO JRYHUQRU ZLOO DOZD\V EH D YHUEDQW

8QHUJDWLYHV DQG XQDFFXVDWLYHV 9DOHQF\ LV D JUHDW WRRO WR DQDO\VH WKH VWDWLYHYHUEDQW UHODWLRQ EXW LW LV QRW HQRXJK ZH QHHG D ZD\ WR GHWHUPLQH WKH LQIRUPDWLRQ SURPLQHQFH²LH LI WKH UHODWLRQ LV JHQHULF ↔  D JRYHUQPHQW ← RU D GHSHQGHQF\ →  ,Q WKLV UHVSHFW ZH IRXQG WKH XQHUJDWLYH K\SRWKHVLV RULJLQDOO\ SRVHG E\ 3HUOPXWWHU   YHU\ XVHIXO ,Q IDFW WKLV K\SRWKHVLV²IXOO\ SUHVHQWHG LQ 3HUOPXWWHU DQG 3RVWDO  ²JLYHV DFFRXQW RI ERWK QRPLQDWLYHDFFXVDWLYH DQG HUJDWLYHDEVROXWLYH ODQJXDJHV 7KLV LV D FUXFLDO IDFW IRU HYHU\ IRUPDOLVP WKDW DLPV WR EH YDOLG LQ JHQHUDO LH IRU ERWK QRPLQDWLYHDFFXVDWLYH DQG HUJDWLYHDEVROXWLYH FRQVWUXFWLRQV DV LQYRNHG E\ 'L[RQ  LQ WKH DSSHQGL[ 7KH DGSRVLWLRQDO SDUDGLJP DLPV WR EH DQ DQVZHU WR WKLV QHHG ,Q FRQVWUXFWLYH WHUPV WKH XQHUJDWLYHXQDFFXVDWLYH K\SRWKHVLV VWDWHV

&RQVWUXFWLRQV



7DEOH  7KH XQHUJDWLYHXQDFFXVDWLYH K\SRWKHVLV

QDPH

UHODWLRQ

WHVW

XQHUJDWLYHQHVV

GHSHQGHQF\

; GRHV ,

XQDFFXVDWLYHQHVV

JRYHUQPHQW

, KDSSHQV WR ;

ILUVW DFWDQW → − X ← − X

PRQRYDOHQF\

→ − I ← − I

WKDW LQWUDQVLWLYHV GRHV QRW H[LVW RU PRUH SUHFLVHO\ WKH H[SUHVVLRQ µLQWUDQVLWLYH YHUE¶ LV D K\SHURQ\P IRU HLWKHU DQ µXQHUJDWLYH YHUE¶ RU DQ µXQDFFXVDWLYH YHUE¶ :KHQ D VLQJOH VWDWLYHYHUEDQW UHODWLRQ LV DQDO\VHG D VLPSOH TXHVWLRQ VKRXOG EH SRVHG FRXQWLQJ DV DQ LQIRUPDO WHVW RI HUJDWLYHQHVV GRHV WKH VWDWLYH GR WKH YHUEDQW RU GRHV WKH YHUEDQW PDNH WKH VWDWLYH KDSSHQ" ,I WKH VWDWLYH GRHV WKHQ WKH UHODWLRQ ZLOO EH RI GHSHQGHQF\ →  DV WKH LQIRU PDWLRQ SURPLQHQFH VWDQGV LQ WKH VWDWLYH LQ WKH WHUPV LQWURGXFHG E\ 3HUOPXWWHU → −   WKH DFWDQW ZLOO EH XQHUJDWLYH  X  9LFH YHUVD LI WKH VWDWLYH KDSSHQV WR WKH YHUEDQW WKH UHODWLRQ ZLOO EH RI JRY HUQPHQW ←  DV WKH LQIRUPDWLRQ SURPLQHQFH VWD\V LQ WKH YHUE DQG WKH DFWDQW ZLOO ← − EH XQDFFXVDWLYH  X  7KH FRUUHVSRQGHQW PRQRYDOHQW YHUEDQW FRQVWUXFWLRQ ZLOO → − ← − EH XQHUJDWLYH  I DQG XQDFFXVDWLYH  I  UHVSHFWLYHO\ ,W LV ZRUWK QRWLFLQJ WKDW 3HUOPXWWHU DQG 3RVWDO  UHIHUUHG H[FOXVLYHO\ WR PRQRYDOHQW YHUEDQW FRQVWUXFWLRQV ZKLOH ZH DGRSW WKH WHUPV LQ JHQHUDO EXW DOZD\V UHIHUUHG WR WKH ILUVW DFWDQW WKH ILUVW VWDWLYHYHUEDQW UHODWLRQ LQ WHUPV RI YDOHQF\ YDOXH 7DEOH  VXPPDULVHV WKH K\SRWKHVLV DQG H[SODLQV WKH V\PEROV XVHG IRU WKH ILUVWYDOHQW DFWDQW DQG WKH PRQRYDOHQW YHUE q q
A
A
←
← A WR A WR

I2 A 2 A
I2 Aq
2 Aq A

A   /L]D /L]D
→
→ ǫA ǫA Y Y
I2 A
I2 A
1 A
1 A 3DXO

X

△

DSRORJLVHV

I2

3DXO

X

△

DSRORJLVHV

I2

)LJXUH  7KH WUHHV RI 3DXO DSRORJLVHV WR /L]D



&KDSWHU 7KUHH

D 3DXO DSRORJLVHV WR /L]D E 3DXO DSRORJLVHV )LJXUH  VKRZV WKH DGWUHHV RI DE  3DXO GRHV WKH DSRORJLHV KHQFH WKH GHSHQGHQF\ →  ZKLOH WKH DSRORJLHV KDSSHQ WR /L]D ZKR VLPSO\ UHFHLYHV WKHP HYHQ LI VKH GRHV QRW ZDQW WR WKHUHIRUH KHU VWDWLYHYHUEDQW UHODWLRQ ZLOO EH RI JRYHUQPHQW ←  ,Q E  WKH YHUE DSRORJLVHV LV XVHG DV D PRQRYDOHQW RQH LI → − WKH ILUVWYDOHQW DFWDQW LV XQHUJDWLYH  X WKH FRUUHVSRQGHQW PRQRYDOHQW YHUE ZLOO → − DOVR EH XQHUJDWLYH  I  1RWH WKDW WKH\ DUH DOO FKDUDFWHU UDLVLQJV )URP WKH IRUPDO SRLQW RI YLHZ WKH UHDGHU LV LQYLWHG WR QRWLFH KRZ WKH YDOHQFH FRQVWUXFWLRQ RSHUDWHV VLQFH µDSRORJLVH¶ LV ELYDOHQW I2  WKH YDOHQFH FRQVWUXFWLRQ LV DQ DUURZ IURP WKH DGWUHH µDSRORJLVHV¶ WR WKH DGWUHH GHSLFWHG RQ WKH OHIW RI )LJ XUH  7KLV DUURZ FRPHV IURP WKH IDPLO\ RI DUURZV JLYHQ E\ WKH YDOHQFH FRQ VWUXFWLRQ WKH IDPLO\ LV LQGH[HG E\ RUGHUHG SDLUV RI DGWUHHV WKH ILUVW FRPSRQHQW EHLQJ µ3DXO¶ DQG WKH VHFRQG FRPSRQHQW EHLQJ µ/L]D¶ 7KH YDOHQFH FRQVWUXFWLRQ LQ WKLV FDVH GHQRWHV WKH ILUVW FRPSRQHQW E\ WKH HPSW\ DGSRVLWLRQ ǫ  ZKLOH LW GH QRWHV WKH VHFRQG FRPSRQHQW E\ WKH µWR¶ DGSRVLWLRQ 7KH JUDPPDU FKDUDFWHUV RI WKHVH DGSRVLWLRQV DUH I12 DQG I22  PHDQLQJ WKDW WKH ZKROH FRQVWUXFWLRQ WDNHV WZR LQGH[HV DQG LW RSHUDWHV VWDUWLQJ IURP D PRUSKHPH RI FODVV I 2 ²WKH VSHFLILF ZD\ WR GHQRWH LQGH[HV GHSHQGV RQ WKH VRXUFH RI WKH IDPLO\ RI DUURZV LH µDSRORJLVHV¶ ([DPSOH E LV WKH UHVXOW RI D WUDQVIRUPDWLRQ ZKLFK KLGHV WKH VHFRQG LQ GH[ LQ IDFW QR YDOLG DGWUHH H[LVWV ZKHQ WKH VHFRQG LQGH[ LV DEVHQW DV WKH YDOHQFH FRQVWUXFWLRQ ZRXOG EH XQGHILQHG²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

&RQVWUXFWLRQV

q
A
← ǫA
I2 A
2 Aq
A
→ WKH YDVH ǫA
I2 A Y
1 A

△

3DXO

X

△

EURNH

I2



q
A
← ǫA
I2 A
2 Aq
A
→ WKH YDVH ǫA
I2 A Y
1 A   3DXO EURNH X I2

△

△

)LJXUH  7KH WUHHV RI 3DXO EURNH WKH YDVH  7KH YDVH EURNH

WKH DFWLYH RQH E  WKHQ WKH UHODWLRQ ZLOO EH RI JRYHUQPHQW →  7KHUHIRUH ← − ← − ERWK WKH DFWDQW  X DQG WKH YHUE  I ZLOO EH XQDFFXVDWLYH $JDLQ DOO JUDPPDU FKDUDFWHUV KDYH EHHQ UDLVHG )LOOPRUH D UHPLQGV XV WKDW WUDGLWLRQDO JUDPPDULDQV RI *HUPDQ KDYH SUHFLVH WHUPV WR GLVWLQJXLVK ELYDOHQW SKUDVHV OLNH D IURP SKUDVHV OLNH F  WKH FODVVHV RI YHUED DIIHFWD OLNH D DQG YHUED HIIHFWD OLNH F  2QH H[DPSOH RI D µFRYHUW¶ JUDPPDWLFDO GLVWLQFWLRQ LV WKH RQH WR ZKLFK WUD GLWLRQDO JUDPPDULDQV KDYH DWWDFKHG WKH ODEHOV µDIIHFWXP¶ DQG µHIIHFWXP¶ LQ *HUPDQ µDIIL]LHUWHV 2EMHNW¶ DQG µHIIL]LHUWHV 2EMHNW¶ 7KH GLVWLQFWLRQ ZKLFK LV UHSRUWHGO\ PDGH RYHUW LQ VRPH ODQJXDJHV FDQ EH VHHQ LQ VHQWHQFHV  DQG   -RKQ UXLQHG WKH WDEOH  -RKQ EXLOW WKH WDEOH )LOOPRUH D 

7KH DGSRVLWLRQDO SDUDGLJP JLYHV D FOHDU DQG SUHFLVH DFFRXQW ERWK RI FRYHUW DQG RYHUW JUDPPDWLFDO GLVWLQFWLRQV DV WKH RQH UHIHUUHG E\ )LOOPRUH LQ KLV FODVVLF DUWLFOH MXVW TXRWHG :H FDQ XQGHUVWDQG WKH WHUPV µXQHUJDWLYH¶ DQG µXQDFFXVDWLYH¶ LI ZH DGRSW D W\SRORJLFDO SHUVSHFWLYH LI D ODQJXDJH QRUPDOO\ DGRSWV D QRPLQDWLYHDFFXVDWLYH VWUDWHJ\ WKH PRUSKRORJLFDOO\ PDUNHG FDVH ZLOO EH WKH DFFXVDWLYH E\ FRQWUDVW LI D ODQJXDJH DGRSWV WKH HUJDWLYHDEVROXWLYH VWUDWHJ\ WKH PRUSKRORJLFDOO\ PDUNHG FDVH ZLOO EH WKH HUJDWLYH 'L[RQ  ±  ,Q FRQVWUXFWLYH OLQJXLVWLF WHUPV LQ WKH ILUVW VWUDWHJ\ WKH PDUNHG FDVH ZLOO EH WKH VHFRQG YDOHQF\ DFFXVDWLYH  ZKLOH WKH PDUNHG FDVH ZLOO EH WKH ILUVW RQH HUJDWLYH LQ WKH VHFRQG VWUDWHJ\  D

1JDUUNXQ ZDOODURR

WX -Erg

DUL HDWV

NDQ\LUU JUDVV



E

&KDSWHU 7KUHH

1JDUUNXQ ZDOODURR

DUL HDWV

OL -ValMinus

NDQ\LUU JUDVV

NX Dat

,Q .DONDWXQJX DQ $XVWUDOLDQ ODQJXDJH WKH HUJDWLYHDEVROXWLYH VWUDWHJ\ LV TXLWH FOHDU %ODNH    ,Q D  WKH ZDOODURR D NLQG RI ODUJH NDQJDURR LV DQ DJHQW ZLOOLQJ WR HDW JUDVV DQG WKH FRUUHVSRQGHQW FRQVWUXFWLRQ PDUNV WKH ILUVW DFWDQW ZLWK DQ HUJDWLYH PRUSKHPH ,Q E  WKH ZDOODURR LV D SDWLHQW DV WKH HDWLQJ RI JUDVV KDSSHQV WR KLP WKH YHUEDQW PRUSKHPH OL LV XVHG WR GHFUHDVH WKH YDOXH RI YDOHQF\ ValMinus   p p
A →
A
NX A
→ ǫA
I2 > EA
2 A
2 Ap
I2 Ap
A NDQ\LUU
A NDQ\LUU
← → ǫA
WXA O 1 A
Y
2 A
I1 A
I1 A 1JDUUNXQ

DUL

X

I2

1JDUUNXQ

X

△

DULOL

I2−1

)LJXUH  7KH WUHHV RI 1JDUUNXQWX DULOL NDQ\LUUNX  )LJXUH  VKRZV WKH WUHHV RI DE  &RQVLGHU WKDW WKH PRUSKRORJ\ RI ZRUGV ZDV KLGGHQ △ DV LW LV QRW WKH FXUUHQW IRFXV KHUH VHH 6HFWLRQ  GHYRWHG WR WUDQVIHUHQFH  VLPLODUO\ WKH QRWDWLRQ I22 > E LV DOVR D VLJQ RI KLGGHQ LQIRUPD WLRQ VHH 6HFWLRQ  GHYRWHG WR HSVLORQWUDQVIRUPDWLRQ  ,QVWHDG WKH GLIIHUHQFH DPRQJ VWDWLYHYHUEDQW LQGLFDWRUV VKRXOG EH QRWHG KHUH EHFDXVH LW VLJQV XQHUJD WLYHQHVV D DQG XQDFFXVDWLYHQHVV E  6RPHWKLQJ VLPLODU KDSSHQV LQ -DSDQHVH²D ODQJXDJH W\SRORJLFDOO\ GLVWDQW IURP .DONDWXQJX 
,Q~ GRJ

JD Agent

KDVtWWH UXQV

LPiVX Durative

G

,Q~ GRJ

ZD Topic

KDVtWWH UXQV

LPiVX Durative

7KLV PLQLPDO SDLU VKRZV D QHXWUDO IRUP F  ZLWK WKH XVH RI SRVWSRVLWLRQ JD DQG WKH PDUNHG IRUP G  ZLWK WKH XVH RI SRVWSRVLWLRQ ZD ,Q (QJOLVK F FDQ EH WUDQVODWHG DV D GRJ LV UXQQLQJ ZKLOH G FDQ EH VRPHWKLQJ OLNH WKDW GRJ LV UXQQLQJ RU WKH GRJ WKDW ZH DOUHDG\ WDONHG DERXW LV UXQQLQJ

&RQVWUXFWLRQV

p
A
← JD A
I1 A
1 Ap
A ,Q~
→ ǫA X
I1 A
A



p
A →
ZD A
I1 A
1 Ap
A ,Q~
→ ǫA X
I1 A
A

LPiVX

KDVtWWH

LPiVX

KDVtWWH

E

I1

E

I1

)LJXUH  7KH WUHHV RI ,Q~ ^JD_ZD` KDVtWWH LPDVX

)LJXUH  VKRZV WKH FRUUHVSRQGHQW DGWUHHV ZKLFK DUH YHU\ VLPLODU WR WKH DGWUHHV RI .DONDWXQJX LQ )LJXUH  6R LQ -DSDQHVH WKHUH DUH WZR VSHFLILF SRVW SRVLWLRQV WR LQGLFDWH WKH WUDMHFWRU\ RI LQIRUPDWLRQ SURPLQHQFH ZD → DQG JD ←  7KHVH SRVWSRVLWLRQV DUH YHU\ SRZHUIXO DV WKH\ FDQ YHUELI\ GLUHFWO\ DGMHF WLYHV DV LQ WKH IROORZLQJ SDLU RI H[DPSOHV 
<XNt VQRZ

ZD Topic

I

6RQy WKDW

EjUD URVH

VLUyL ZKLWH ZD Topic

GHVX Polite DNiL UHG

GHVX Polite

7KH -DSDQHVH ZRUGV VLUyL DQG DNi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



&KDSWHU 7KUHH

p
A
← ǫA
I1 A
1 Ap
A GHVX →
ZD A E
I1 A p
1 A
A DNiL
← ǫA A
X A A


p
A ←
ǫA
I1 A
1 Ap
A GHVX →
ZD A E
I1 A
1 A <XNt

VLUyL

X

A

6RQy

EDUj

A

X

)LJXUH  7KH WUHHV RI ZDEDVHG -DSDQHVH SKUDVHV ZLWK LDGMHFWLYHV HI 

p
←A
ǫA

I11 AA 6D

ODNVKD

X

I1

p
→A
ǫA

I21 AA LR

X

△

KR VXGDWR

I2

)LJXUH  7UHHV RI 6DODNVKD DQG LR KR VXGDWR

F LR KR VXGDWR ,WDOLDQ ([DPSOHV DEF VKRZ WKDW HYHQ D VLPSOH HYHQW OLNH VZHDWLQJ FDQ EH UHS UHVHQWHG GLIIHUHQWO\ DPRQJ GLIIHUHQW ODQJXDJHV DV VKRZQ LQ )LJXUH   ,Q &KRFWDZ D 1DWLYH $PHULFDQ ODQJXDJH WKH DFWDQW EULQJV WKH REMHFWLYH PDUNHU RI ← − WKH ILUVW SHUVRQ VD ZKLFK LQGLFDWHV WKDW WKH FRQVWUXFWLRQ LV XQDFFXVDWLYH  X  ZKLOH LQ ,WDOLDQ WKH DX[LOLDU\ IRUP KR IURP DYHUH µWR KDYH¶ LQGLFDWHV WKDW WKH → − FRQVWUXFWLRQ LV ELYDOHQW ZLWK D VWDWLYHYHUEDQW GHSHQGHQF\ DW WKH ILUVW DFWDQW  X  6RPHWLPHV WKH VWDWLYHYHUEDQW UHODWLRQ LV OHIW XQGHUVSHFLILHG )RU H[DPSOH LQ ,WDOLDQ WKHUH DUH VRPH YHUEV WKDW DFFHSW ERWK DX[LOLDU\ FRQVWUXFWLRQV ZLWK WKH → − ← − YHUE DYHUH XQHUJDWLYHQHVV I RU ZLWK WKH YHUE HVVHUH XQDFFXVDWLYHQHVV I  D

3DROR 3DXO

KD FRUVR − −→ UXQ

SHU XQ¶RUD RQH KRXU ORQJ

&RQVWUXFWLRQV

E

3DROR 3DXO

q FRUVR ← −− UXQ

F

3DROR 3DXO

FRUVH ← → UXQ



D FDVD KRPH

,Q D WKH XQGHUO\LQJ VFHQH GHSLFWV 3DXO DV ZLOOLQJ WR KDYH D UXQ IRU RQH KRXU ZKLOH LQ E WKH VFHQH LV WKDW 3DXO KDV UXQ KRPH DEUXSWO\ HJ IRU VRPH HPHUJHQF\  :KDW DERXW F " $V WKHUH LV QR DX[LOLDU\ FRQVWUXFWLRQ DW ZRUN WKH LQIRUPDWLRQ SURPLQHQFH LV OHIW XQGHUVSHFLILHG :H ZLOO GHDO ZLWK WKH DX[LOLDU\ YHUEDQW FRQVWUXFWLRQV LQ GHWDLO LQ WKH QH[W FKDSWHU +RZHYHU WKH UHDGHU LV LQYLWHG WR QRWH WKDW ZLWKLQ WKH DGSRVLWLRQDO SDUDGLJP WKHUH LV QR GLVWLQFW FDWHJRU\ RI µDX[LOLDU\ YHUEV¶ UDWKHU VWDWLYHYHUEDQW FRQVWUXFWLRQV DUH XVHG WR H[SUHVV DX[LOLDULW\

*UDPPDWLFDOL]DWLRQ DQG RQWRJHQHVLV 7KH VWDWLYHYHUEDQW UHODWLRQV DUH WKH PRVW IXQGDPHQWDO RQHV LQ DOO ODQJXDJHV DQG IRU WKLV UHDVRQ WKH\ DUH WKH ILUVW WR EH OHDUQW E\ FKLOGUHQ ,Q IDFW ZH FDQ FRQVLGHU FRQVWUXFWLRQV IURP D GLDFKURQLF SRLQW RI YLHZ DV ³KLVWRULFDO UHOLFV«D VDOYDJHG SDUW RI VRPH ODUJHU FRQVWUXFWLRQ´ 7RPDVHOOR    EXW ZH FDQ DOVR FRQVLGHU FRQVWUXFWLRQV IURP DQ RQWRJHQHWLF SHUVSHFWLYH ,W LV LQWHUHVWLQJ WR VHH WKDW DV FRQVWUXFWLRQV DUH URWHOHDUQW DQG OH[LFDOO\ ERXQGHG ZKDW LV SURGXFHG LQ WKH HDUO\ VWDJH RI FKLOGUHQ¶V VSHHFK LV H[DFWO\ WKH PRVW SURPLQHQW LQIRUPDWLRQ )RU H[DPSOH WKH VRFDOOHG µZRUG FRPELQDWLRQV¶  PRQWKV DUH FRQVWUXFWLRQ ZKHUH WKH RQO\ JURXSV SURGXFHG DUH RIWHQ WKH VWDWLYH DQG WKH YHUEDQW DV VKRZQ LQ )LJXUH  D EDOO WDEOH E WKH EDOO LV RQ WKH WDEOH ,W LV ZRUWK QRWLFLQJ WKDW WKH FLUFXPVWDQWLDO FKDUDFWHU RI WDEOH LPSRVHG E\ WKH SUHSRVLWLRQ RQ LV QRW DFWXDOO\ XVHG LQ WKH FKLOGUHQ¶V FRQVWUXFWLRQ )LJXUH   )LQDOO\ WKH µZRUG FRPELQDWLRQ¶ VWUXFWXUH²KDYLQJ WZR GLVWLQFW HOHPHQWV ZLWK D UHOHYDQW FROORFDWLRQ²FDQ EH UHGXFHG WR D VLQJOH VWUXFWXUH ZKHUH WKH RQO\ PRU SKHPHV DW ZRUN DUH WKH OH[HPHV LH WKH RQHV ZLWK WKH PRVW UHOHYDQW VHPDQWLF ORDG )LJXUH   



&KDSWHU 7KUHH

p
→A
ǫA


I22 AAp

←A

ǫA

I21 AA p


→A LV   EDOO
ǫA  WKH 2
I
p
Y AA X
→A  
R A  D EDOO Q

E > AAA Y   WDEOH WKH  D O

△

△

△

)LJXUH  7KH XQGHUO\LQJ WUHH RI WKH EDOO LV RQ WKH WDEOH

p
←A
ǫA
I22 A WDEOH

EDOO

E

X

)LJXUH  7KH ILQDO WUHH RI FKLOGUHQ¶V VSHHFK EDOO WDEOH

$IWHUZDUGV VWDUWLQJ IURP  PRQWKV FKLOGUHQ VKRZ PRUH IOH[LEOH FRQVWUXF WLRQV FDOOHG ³SLYRW VFKHPDWD´ 7RPDVHOOR   VXFK DV WKH IROORZLQJ RQHV D PRUH PLON D PRUH JUDSHV D DQFRUD PHOD PRUH DSSOH  D DQFRUD SDVWD PRUH SDVWD   ,W LV TXLWH REYLRXV WKDW WKH XQGHUO\LQJ VWUXFWXUH LV VRPHWKLQJ OLNH WKLV E , ZDQW PRUH PLON E , ZDQW PRUH JUDSHV

&RQVWUXFWLRQV



E LR YRJOLR DQFRUD PHOD , ZDQW PRUH DSSOH  E LR YRJOLR DQFRUD SDVWD , ZDQW PRUH SDVWD  ,Q WKLV UHVSHFW (QJOLVK DQG ,WDOLDQ VHHP WR EH YHU\ VLPLODU )LJXUH  VKRZV WKH FRUUHVSRQGHQW DGSRVLWLRQDO WUHHV ZKHUH WKH ILQDO RQH ULJKW LV YHU\ VLPLODU ← − WR D SURWRW\SLFDO XQDFFXVDWLYH IRUP  I 

p
A
← ǫA
I2 A 2
p A
A A
← A ǫA
Y A A A
Ap
A PLON PRUH
→A Y A

ǫ A
I21 A  ZDQW  , X I2

{

p
A
← ǫA
I2 A
2 A PRUH

PLON

A

Y

)LJXUH  7KH WUHHV RI , ZDQW PRUH PLON

D MXLFH JRQH E WKH MXLFH LV JRQH ,Q D FRQVWUXFWLYH OLQJXLVWLF SHUVSHFWLYH ZH FDQ VHH KRZ PXFK D µZRUG FRP ELQDWLRQ¶ LV VLPLODU WR D VRFDOOHG ³LQWUDQVLWLYH FRQVWUXFWLRQ´ 7RPDVHOOR  VLF  VXFK DV DE  EHFDXVH RI WKH VLPLODULWLHV RI WKH UHVSHFWLYH DGWUHHV FRP SDUH )LJXUHV  DQG   ,W LV DOVR FOHDU WKDW LQIRUPDWLRQ SURPLQHQFH LV DFTXLUHG YHU\ VRRQ E\ FKLO GUHQ )RU LQVWDQFH LQ 7RIL D 6DPRDQ ODQJXDJH WKH IROORZLQJ PLQLPDO SDLU LV DWWHVWHG 7RPDVHOOR   D

R QRIR VLWV

E

R QRIR VLWV

SHSH GROO LD Emph

SHSH GROO



&KDSWHU 7KUHH

q
A
→ A ǫ
2 A
I2 A
Aq

A

←A


ǫ A

I21 A
q A

A LV   MXLFH
→A WKH  2  ZK I
 A X A > X
A
q A
A
↔A D MXLFH

ǫ A X
I11 A A
 JR LFK    I1 X

△

{

△

q
A A
→ ǫ
X A A
A
JRQH

MXLFH

A

X

>SDVW@ >SHUIHFW@

)LJXUH  7KH WUHHV RI WKH MXLFH LV JRQH

([DPSOHV DE PHDQ VRPHWKLQJ OLNH P\ GROO VLWV ,W LV LQWHUHVWLQJ WKDW 6DPRDQ FKLOGUHQ KDYH DQ DGSRVLWLRQ LD H[DFWO\ WR UHYHUVH WKH WUDMHFWRU\ RI LQ IRUPDWLRQ SURPLQHQFH IURP JRYHUQPHQW ← ZLWKRXW PRUSKRORJLFDO PDUNLQJ WR GHSHQGHQF\ → ZLWK D VSHFLDO PRUSKRORJLFDO PDUNHU  )LJXUH  VKRZV WKDW WKH FRUUHVSRQGHQW WUHHV DUH TXLWH VLPSOH LQ RXU SHUVSHFWLYH

q
A
←A
ǫ1 A
I1 A
A

q
A
→A
LD1 A
I1 A
A

SHSH

R QRIR

SHSH

R QRIR

X

1

X

I1

I

)LJXUH  7UHHV RI R QRIR LD SHSH &RPSDUHG ZLWK JUDPPDWLFDOL]DWLRQ WKH FRQVWUXFWLRQDO DUURZ LQ RQWRJHQHWLF

&RQVWUXFWLRQV



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¶V VSHHFK LQ FRQVWUXFWLYH OLQJXLVWLF WHUPV ZRXOG UHTXLUH DW OHDVW D ZKROH ERRN GHYRWHG RQO\ WR WKLV LQWHUHVWLQJ WRSLF :KDW ZH ZDQWHG WR VKRZ KHUH LV WKDW WKH DGSRVLWLRQDO SDUDGLJP FDQ FODULI\ VRPH VWUXF WXUHV RWKHUZLVH SX]]OLQJ

 7KH DGMXQFWLYHVWDWLYH UHODWLRQV $GMXQFWLYHV DUH VWDWLYH PRGLILHUV ,Q D EURDG VHQVH WKH DGMXQFWLYHVWDWLYH UHOD WLRQ LV D JUDPPDWLFDOL]DWLRQ RI WKH VWDWLYHYHUEDQW UHODWLRQ +RZHYHU EHIRUH WR GHDO ZLWK WKLV JUDPPDWLFDOL]DWLRQ RI WKH FRUUHVSRQGHQW DGSRVLWLRQDO WUHHV²PRUH ULFK DQG FRPSOH[ WKDQ ZKDW VHHPV DW D ILUVW JODQFH²LW LV EHWWHU WR LQWURGXFH WKH DGMXQFWLYHVWDWLYH UHODWLRQV WKURXJK VLPSOHU FDVHV

$WWULEXWLYH DQG SUHGLFDWLYH DGMHFWLYHV ,Q PDQ\ ODQJXDJHV RI WKH ZRUOG D GLVWLQFWLYH VXEFODVV RI DGMXQFWLYHV LV IRXQG DGMHFWLYHV 0RUHRYHU LQ VRPH ODQJXDJHV²VXFK DV *HUPDQ²GLIIHUHQW FRQVWUXF WLRQV DUH DW ZRUN LI DGMHFWLYHV DUH DWWULEXWLYH RU E\ FRQWUDVW SUHGLFDWLYH :LWKLQ WKH DGSRVLWLRQDO SDUDGLJP WKLV GLFKRWRP\ UHSUHVHQWV WKH GLIIHUHQW WUDMHFWRULHV RI WKH LQIRUPDWLRQ SURPLQHQFH LQ WKH DGMHFWLYHQRXQ UHODWLRQ LI WKH DGMHFWLYH LV DW WULEXWLYH WKH LQIRUPDWLRQ SURPLQHQFH VWDQGV LQ WKH QRXQ DQG KHQFH WKH UHODWLRQ ZLOO EH RI JRYHUQPHQW ←  YLFH YHUVD LI WKH DGMHFWLYH LV SUHGLFDWLYH WKH LQIRU PDWLRQ SURPLQHQFH VWDQGV LQ WKH DGMHFWLYH EHFDXVH WKHUH LV D SUHGLFDWLRQ LH D VWDWLYHYHUEDQW UHODWLRQ KLGGHQ XQGHU WKH DGMHFWLYH LWVHOI²ZH ZLOO GHDO ZLWK KLGGHQ SUHGLFDWLRQV LQ WKH QH[W FKDSWHUV &RQVHTXHQWO\ SUHGLFDWLYH DGMHFWLYHV ZLOO UHODWH WR QRXQV ZLWK GHSHQGHQFLHV →  6RPH 5RPDQFH ODQJXDJHV VKRZ WKLV GLVWLQFWLRQ FOHDUHU WKDQ RWKHU ODQJXDJHV )RU H[DPSOH LQ 3RUWXJXHVH



&KDSWHU 7KUHH

D IRUWHV YHQWRV VWURQJ ZLQGV E YHQWRV IRUWHV RQO\ WKH ZLQGV WKDW DUH VWURQJ ,Q 3RUWXJXHVH WKH GLIIHUHQW FROORFDWLRQ LQWR WKH V\QWDJPDWLF D[LV RI DE VKRZV SUHFLVHO\ WKH GLIIHUHQW WUDMHFWRULHV RI LQIRUPDWLRQ SURPLQHQFH LQ D WKH DGMHFWLYH VWURQJ LV DWWULEXWLYH ZKLOH LQ E WKH VDPH DGMHFWLYH LV SUHGLFD WLYH )LJXUH  VKRZV RQ WKH OHIW WKH DWWULEXWLYH DGMHFWLYH D DQG RQ WKH ULJKW WKH SUHGLFDWLYH DGMHFWLYH ZKLFK FRQFHDOV D SUHGLFDWLRQ q q
A
A
←
→ ǫA ǫA
O A
O A AA AA





△

△

△

△

IRUWHV

YHQWRV

IRUWHV

YHQWRV

A

O

A

O

)LJXUH  0LQLPDO VWUXFWXUDO SDLU IRUWHV YHQWRV DQG YHQWRV IRUWHV 7KH GLIIHUHQFH LQ WKH DGMHFWLYHQRXQ FROORFDWLRQ RI 3RUWXJXHVH GHULYHV IURP WZR GLYHUVH /DWLQ FRQVWUXFWLRQV ,Q /DWLQ WKH (QJOLVK JURXS RXU PHPRU\ FDQ EH UHQGHUHG ZLWK WKH IROORZLQJ FRQVWUXFWLRQV D QRVWUD PHPRULD VRPHERG\¶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¶V ORYH JLYHQ WR KLV FKLOGUHQ  E DPRU SDWULV FKLOGUHQ¶V ORYH IRU WKHLU IDWKHU  ,Q /DWLQ DPRU SDWULV FDQ KDYH WZR LQWHUSUHWDWLRQV WKH PHDQLQJ RI WKH SDUWV LV RQO\ RQH EXW WKHLU VHQVHV DV D ZKROH DUH DW OHDVW WZR  ,Q WKH ILUVW LQWHUSUHWDWLRQ

&RQVWUXFWLRQV



D WKH WUDMHFWRU\ VWDUWV IURP WKH IDWKHU SDWULV  ZKLFK LV WKH PRVW SURPLQHQW HOHPHQW EHFDXVH LW JLYHV ORYH WKHUHIRUH WKH JHQLWLYHQRPLQDWLYH UHODWLRQ SDWU LV EHLQJ WKH JHQLWLYH DPRU WKH QRPLQDWLYH ZLOO EH D GHSHQGHQF\ →  %\ FRQWUDVW LQ WKH VHFRQG LQWHUSUHWDWLRQ E WKH LQIRUPDWLRQ SURPLQHQFH VWDQGV RQWR WKH ORYH WKH QRPLQDWLYH DPRU  DV WKH IDWKHU UHFHLYHV ORYH E\ VRPH ERG\ HOVH²PRVW SUREDEO\ KLV FKLOGUHQ KLP EHLQJ D IDWKHU 7KH LPSRUWDQW IDFW LV WKDW WKH UHODWLRQ LV D JRYHUQPHQW ←   )LJXUH  VKRZV WKH WZR SRVVLEOH LQWHUSUHWDWLRQV RI DPRU SDWULV ,I LW LV QRW SRVVLEOH WR GHWHUPLQH WKH ULJKW LQWHUSUH WDWLRQ WKH LQIRUPDWLRQ VDOLHQFH WUDMHFWRU\ VKRXOG EH OHIW XQGHUVSHFLILHG WKURXJK WKH XVH RI WKH DSSURSULDWH LQGLFDWRU ↔  p p
→A
←A
LV A
LV A

O AA

O AA SDWU

DPRU

SDWU

DPRU

A

O

A

O

)LJXUH  7KH WZR SRVVLEOH LQWHUSUHWDWLRQV RI DPRU SDWULV 7KH GLFKRWRP\ µDWWULEXWLYH YV SUHGLFDWLYH DGMHFWLYHV¶ KDV D ORW RI LQWHUHVWLQJ FRQVHTXHQFHV LQ SDUWLFXODU LW ZLOO EH UHSULVHG ZKHQ GHDOLQJ ZLWK FRUUHODWLYH FODXVHV 6HFWLRQ  

2WKHU LPSRUWDQW DGMXQFWLYHV $GMHFWLYHV DUH QRW WKH RQO\ FODVV RI DGMXQFWLYHV XVHG E\ ODQJXDJHV ,Q IDFW D ORW RI ODQJXDJHV KDYH DGMXQFWLYH VXEFODVVHV DSDUW  +HUH ZLWK WKH ZRUG µDSDUW¶ ZH PHDQ DGMXQFWLYHV WKDW FRQFXU WR WKH IRUPDWLRQ RI FRQVWUXFWLRQ LQ VXFK D ZD\ QRW UHGXFLEOH WR DGMHFWLYHV 2I FRXUVH DGMXQFWLYH VXEFODVVHV DUH ODQJXDJHVSHFLILF IRU LQVWDQFH VRPH ODQJXDJHV KDYH DUWLFOHV VRPH RWKHUV QRW ,W LV LPSRVVLEOH WR WUHDW WKHP FRQVWUXFWLYHO\ LQWR D VLQJOH ERRN²QRW WR PHQWLRQ D VHFWLRQ²HYHQ ZLWKLQ D VLQJOH ODQJXDJH 7KH DLP RI WKLV VHFWLRQ LV WR H[SODLQ KRZ WR EXLOG DGSRVLWLRQDO WUHHV ZLWK (QJOLVK QRQDGMHFWLYH FRQVWUXFWLRQV EHORQJLQJ WR WKH DG MXQFWLYH FDWHJRU\ 7KHUHIRUH ZKDW IROORZV LV KLJKO\ SDUWLDO GHOYLQJ LQ WKLV LVVXH LV OHIW DV D IXUWKHU ZRUN ,Q (QJOLVK WKHUH DUH DW OHDVW WKH IROORZLQJ VSHFLILF DGMXQFWLYH FDWHJRULHV  GHWHUPLQHUV VXFK DV D WKH WKDW 



&KDSWHU 7KUHH

 TXDQWLILHUV VXFK DV DOO ERWK HYHU\    QXPHUDOV VXFK DV RQH KDOI D PLOOLRQ RI  ,W VKRXOG EH REYLRXV E\ QRZ WKDW DOO DGMXQFWLYHV DUH GHSHQGHQWV dep DV WKH\ PRGLI\ VWDWLYH ZKLFK DUH JRYHUQRUV gov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¶V EHOLHIV   )LJXUH  VKRZV WKH FRUUHVSRQGHQW DGWUHHV p p
←A
→A
ǫA
ǫA

O AA

O AA WKH

HOHSKDQW

A

O

WKDW HOHSKDQW

A

O

)LJXUH  7UHHV RI WKH HOHSKDQW DQG WKDW HOHSKDQW $ VWURQJHU WHVW FRPHV IURP JUDPPDWLFDOL]DWLRQ LI WKH DGMXQFWLYH FDQ EH WUDQVIRUPHG LQWR D VWDWLYH ZLWK WKH RPLVVLRQ RI WKH RULJLQDO VWDWLYH WKDW DGMXQFWLYH ZLOO EH LQ D UHODWLRQ RI GHSHQGHQF\ →  F ,¶YH VHHQ WKH RQH G ,¶YH VHHQ WKH H ,¶YH VHHQ WKDW RQH I ,¶YH VHHQ WKDW )LJXUH  VKRZV WKH DGSRVLWLRQDO WUHHV RI HI  ,W LV LQWXLWLYH WR FRQVLGHU WKH DGWUHH RI I DV D VLQJOH OHDI²WKURXJK D IRUPDO RSHUDWLRQ FDOOHG HSVLORQ WUDQVIRUPDWLRQ VHH 6HFWLRQ  LQ WKH QH[W FKDSWHU IRU GHWDLOV  ,Q FH WKH

&RQVWUXFWLRQV



QXPHUDO RQH LV DOVR XVHG DV D VWDWLYH ,W LV LPSRUWDQW WR QRWLFH WKDW WKLV NLQG RI UXOHV DUH DOZD\V ODQJXDJHGULYHQ

p
→A
ǫA

O AA WKDW

RQH

A

O

p
→A
ǫA

O AA  WKDW O A

)LJXUH  7UHHV RI WKDW RQH DQG WKDW /DVW WKHUH LV DQRWKHU NLQG RI IXQFWLRQ WKDW VSHFLILF DGMXQFWLYH FDWHJRULHV H[ SORLWV WKH GHWHUPLQDWLRQ RI JUDPPDU FKDUDFWHU LQ FROORFDWLRQDO PRUSKHPHV )RU LQVWDQFH WKH (QJOLVK PRUSKHPH ZDON LV LPPHGLDWHO\ UHFRJQLVHG DV D VWD WLYH LI D TXDQWLILHU FRPHV EHIRUH VXFK DV LQ WKH DGMXQFWLYHVWDWLYH UHODWLRQ HYHU\ ZDON +RZHYHU WKLV NLQG RI IXQFWLRQ²FDOOHG WUDQVIHUHQFH²LV VR LPSRUWDQW WKDW D VHFWLRQ DSDUW LV GHYRWHG WR LW VHH 6HFWLRQ  

 7KH FLUFXPVWDQWLDOYHUEDQW UHODWLRQV 2QFH VWDWLYHYHUEDQW UHODWLRQV DUH VDWXUDWHG LH WKHUH DUH QR PRUH YDOHQF\ WR EH ILOOHG E\ DFWDQWV LQWR D SKUDVH DQG WKH DGMXQFWLYHVWDWLYH UHODWLRQV DUH VROYHG²E\ GHILQLWLRQV WR EH VROYHG ZLWKLQ WKH DFWDQWV²WKH FLUFXPVWDQWLDOV FDQ EH DGGUHVVHG &LUFXPVWDQWLDOV DUH WKH PRGLILHUV RI YHUEDQWV WKH\ DUH DSSHQGHG WR YHUEDQW DGWUHHV RQ WKH WRS EHLQJ H[WHUQDO DUJXPHQWV 7KH ILQDO JUDPPDU FKDUDFWHU KRZ HYHU UHPDLQV YHUEDQW²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



&KDSWHU 7KUHH

q
A
←A
IRU A
E>I A A


△

△

WKH /DG\

7KH MDQLWRU«

A>O

I33

)LJXUH  7KH FLUFXPVWDQWLDO RI J LQ HYLGHQFH

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ǫ  ([DPSOHV JK VKRZ FLUFXPVWDQWLDOYHUEDQW JRYHUQPHQW ←  WKLV LV WKH GHIDXOW FDVH EXW LW LV QRW WKH RQO\ RQH )RU LQVWDQFH VRPH FLUFXPVWDQWLDOV VKRZ D FRQVLGHUDEOH GHJUHH RI IUHHGRP LQ FROORFDWLRQ LH WKH\ FDQ EH SXW LQ GLIIHUHQW SODFHV RQ WKH V\QWDJPDWLF D[LV ZLWKRXW FOHDU FRQWUDVWLYH VLJQLILFDQFH LQ WHUPV RI LQIRUPDWLRQ SURPLQHQFH 7DNH IRU H[DPSOH WKH IROORZLQJ PLQLPDO SDLU RI ,WDOLDQ QRW WRR GLVWDQW IURP (QJOLVK  D 'RPDQL YHQJR 7RPRUURZ ,¶OO FRPH  E 9HQJR GRPDQL ,¶OO FRPH WRPRUURZ  7KH WZR YDULDQWV RI DE VHHP WR EH HTXLYDOHQW LQ WHUPV RI LQIRUPDWLRQ SURPLQHQFH²DOWKRXJK VRPH LQIRUPDQWV PD\ WKLQN WKDW E LV PDUNHG WKHUH LV QR ZLGHO\ DFFHSWHG DJUHHPHQW DERXW LW ,Q GRXEWIXO FDVHV VXFK   WKHUH ZLOO EH RQO\ RQH YDOLG DGSRVLWLRQDO DGWUHH )LJXUH   $OO FLUFXPVWDQWLDOV VHHQ XQWLO QRZ DUH LQ D UHODWLRQ RI JRYHUQPHQW ←  +RZ HYHU LQ VRPH FDVHV WKH FLUFXPVWDQWLDO LV WKH PRVW SURPLQHQW LQIRUPDWLRQ LQ WKH DGWUHH KHQFHIRUWK LW LV LQ D UHODWLRQ RI GHSHQGHQF\ → 

&RQVWUXFWLRQV



r
A
←A
ZLWKRXWA
E > I1 A 1
A
A
Ar
A SUREOHP
←A O
O\ A
1 A
E > I1 A
A
Ar
A TXLFN
←A A
IRU A
E > I1 A 1
A
A
A

△

△

WKH /DG\

7KH GRRU«

A>O

I11

)LJXUH  0DQ\ FLUFXPVWDQWLDOV DW ZRUN LQ K

q
A
←A
adp A
I A

△

△

dep E

gov I

)LJXUH  $EVWUDFW WUHH RI FLUFXPVWDQWLDOYHUEDQW UHODWLRQV JK 



&KDSWHU 7KUHH

p
A
← ǫA
I A Ap

A GRPDQL
→ ǫA E
1 A
I1 A LR

YHQJR

X

I1

)LJXUH  7UHH RI 'RPDQL YHQJR DQG 9HQJR GRPDQL

p
A
→ " A
I1 A
1 Ap
A → TXDQGR
ǫ A
1 A E
I1 A

△

WX

YHUUDL

X

I1

)LJXUH  7UHH RI 4XDQGR YHUUDL"

)RU LQVWDQFH D FLUFXPVWDQWLDO FDQ EH SURPLQHQW LI SXW LQWR DQ DSSURSULDWH FRQVWUXFWLRQ VXFK DV D TXHVWLRQ F 4XDQGR YHUUDL" :KHQ ZLOO \RX FRPH"  ,W LV REYLRXV WKDW WKH PRVW SURPLQHQW LQIRUPDWLRQ LV LQ WKH FLUFXPVWDQWLDO TXDQGR ZKHQ  DV WKH FLUFXPVWDQFH RI FRPLQJ LV H[DFWO\ WKH LQIRUPDWLRQ UH TXHVWHG E\ WKH VSHDNHU TXHVWLRQV ZLOO EH WUHDWHG H[WHQVLYHO\ LQ WKH QH[W FKDSWHU  7KH WUDMHFWRU\ RI WKH FLUFXPVWDQWLDOYHUEDQW LQGLFDWRU ZLOO EH FKRVHQ DFFRUGLQJO\ →  ,W LV LQWHUHVWLQJ WR QRWLFH KRZ WKH DGWUHH LQ )LJXUH  LV YHU\ VLPLODU WR WKH RQH LQ )LJXUH  UHIHUULQJ WR SKUDVHV DE  SRVVLEOH DQVZHUV RI F  )LQDOO\ LW LV ZRUWK QRWLFLQJ WKDW PDQ\ ODQJXDJHV PDUN WKH FLUFXPVWDQFH RI WHPSRUDOLW\ FDXVDOLW\ PRGDOLW\ ORFDWLRQ WKURXJK DGKRF FLUFXPVWDQWLDOV  ,Q (QJOLVK WKH ZRUGV WRPRUURZ WRGD\ DQG WRQLJKW DUH WKH UHVXOW RI WKH JUDP PDWLFDOL]DWLRQ RI 2OG (QJOLVK WHPSRUDO FRQVWUXFWLRQ WR +O ZKHUH WKH VWDWLYH KDV FOHDUO\ D YDOXH RI Time EHLQJ PRUURZ GD\ DQG QLJKW WHPSRUDO QRXQV

&RQVWUXFWLRQV



 7KH FLUFXPVWDQWLDODGMXQFWLYH UHODWLRQV ,Q VRPH ODQJXDJHV²IRU LQVWDQFH (QJOLVK DQG )UHQFK²FLUFXPVWDQWLDO ZRUGV DUH XVHG WR PRGLI\ DGMXQFWLYHV ,W LV LPSRUWDQW WR XQGHUOLQH WKH IDFW WKDW RQO\ FLU FXPVWDQWLDO ZRUGV FDQ EH XVHG LQ VXFK FRQVWUXFWLRQV LQ WKHVH ODQJXDJHV FDOOHG µDGYHUEV¶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←  WKH PRVW SURPLQHQW HOHPHQW EHLQJ WKH VWDWLYH SD\VDJH  $V D ILQDO QRWH SOHDVH WDNH LQWR DFFRXQW WKH IDFW WKDW VSHFLDO HPSKDVLV JLYHQ E\ WKH VSHDNHU FDQ UHYHUVH WKH LQGLFDWRUV DSSURSULDWHO\

 :KDW LV ODQJXDJH VWUXFWXUH" 1RZ LW LV SRVVLEOH WR GHVFULEH D ODQJXDJH LQ FRQVWUXFWLYH OLQJXLVWLF WHUPV ,Q RUGHU WR KDYH D ODQJXDJH WKH IROORZLQJ LQJUHGLHQWV DUH QHHGHG  WKH UXOHV WR EXLOG DGWUHHV LQ SDUWLFXODU YDOHQF\ V\QWD[ H[SODLQHG LQ &KDS WHU  ²WKHVH UXOHV DUH FDOOHG FRQVWUXFWLRQV LQ RXU IRUPDO PRGHO



&KDSWHU 7KUHH

q
A
→ ǫA
O A Aq

A WKDW
← ǫA A
O A
q A
A WRSLF
→ ǫA O
A A A


VHQVLWLYH
... > A q

A A
→ O\
E A A
 KLJK D A

△

{

q
A
→ ǫA
O A Aq

A WKDW
← ǫA A
O A
q A
A WRSLF A
→ O\ O A

E>A A

△

△

KLJK

VHQVLWLYH

A

... > A

)LJXUH  7UHHV RI WKDW KLJKO\ VHQVLWLYH WRSLF H[SOLFLW DQG ǫ WUDQVIRUPHG

 LQIRUPDWLRQ SURPLQHQFH DQG WUDMHFWRU\ LQGLFDWRUV PRUSKRV\QWD[ H[DP LQHG LQ &KDSWHUV  DQG    JUDPPDU FKDUDFWHU MXVW H[SODLQHG KHUH LQ &KDSWHU    WKH UXOHV WR WUDQVIRUP DQ DGWUHH LQ DQRWKHU DGWUHH WUDQVIRUPDWLRQ LW ZDV VNHWFKHG LQ 6HFWLRQ  DQG ZLOO IXOO\ H[SODLQHG LQ &KDSWHU  7UDQVIRUPDWLRQV QHHG D WUHDWPHQW DSDUW VLQFH WKH\ FRQVWUXFWLYHO\ GHVFULEH FRPSOH[ FRQVWUXFWLRQV LH FRQVWUXFWLRQV PDGH RI PRUH SKUDVHV  ,Q RWKHU ZRUGV FRPSOH[ FRQVWUXFWLRQV DUH FRQVWUXFWLRQV WKDW SXW WRJHWKHU PRUH YHUEDQW JRYHUQPHQWV DQG WKHLU LQSKUDVDO FRQVWUXFWLRQV MXVW SUHVHQWHG LQ WKLV FKDSWHU  7KH QH[W &KDSWHU  LV GHYRWHG WR WKLV WRSLF )XUWKHUPRUH LQ WKH QH[W FKDSWHUV ZH ZLOO GHDO ZLWK WUDQVIHUHQFH D VSHFLDO FDVH RI WUDQVIRUPDWLRQ $IWHU WKDW ZH ZLOO EH UHDG\ WR FRQVWUXH WKH GLFWLRQDU\ RI D VSHFLILF ODQJXDJH LH D VWUXFWXUH ZLWK SURSHUWLHV ZKHUH WKH IRXU LQJUHGLHQWV RI WKDW SDUWLFXODU ODQ JXDJH VWUXFWXUH FDQ EH PDSSHG LQWR VHH &KDSWHU   ,Q IDFW LQ RUGHU WR KDYH D JUDPPDU ZH QHHG D ODQJXDJH VWUXFWXUH DQG D GLFWLRQDU\ WKDW WRJHWKHU JHQHUDWH

&RQVWUXFWLRQV

q
A
←A
ǫ A
O A Aq

A XQ
←A A
ǫ A
O A A q

A
←A SD\VDJH
ǫ A ... > O
A A A q

A EHDX
→A A
PHQWA
E A A
YUDL  A D

△

{



q
A
←A
ǫ A
O A
Aq
A XQ
←A A
ǫ A
O A
A q
A
←A SD\VDJH
PHQWA O
E>A A A


△

△

YUDL

A

EHDX

A

)LJXUH  7UHHV RI XQ YUDLPHQW EHDX SD\VDJH H[SOLFLW DQG ǫ UHGXFHG

WKH VSDFH ZKHUH WR LQVWDQWLDWH WKH UXOHV RI WKH ODQJXDJH LWVHOI DQG ZKHUH WR REWDLQ WKH ZKROH VHW RI SRVVLEOH FRUUHFW SURGXFWLRQV

Chapter Four Transformations :KLOH V\QWD[ ZDV SUHVHQWHG LQ &KDSWHU  LQ D YHU\ JHQHUDO DQG DEVWUDFW ZD\ LQ &KDSWHU  ZH KDYH LQVWDQWLDWHG LW ZLWKLQ OLQJXLVWLF FRQVWUXFWLRQV &RQVWUXFWLRQV DULVH LQ D JLYHQ ODQJXDJH DV SURGXFWV RI JUDPPDWLFDOL]DWLRQ ,Q WKLV FKDSWHU ZH JLYH DFFRXQW RI JUDPPDWLFDOL]DWLRQ LQ WHUPV RI DGWUHH WUDQVIRUPDWLRQV LH LQ WHUPV RI IRUPDO UXOHV ZKHUH D JLYHQ DGWUHH EHFRPHV DQRWKHU DGWUHH *HQHUDOO\ JUDPPDWLFDOL]DWLRQ LPSOLHV D UHGXFWLRQ RI WKH UHVXOWLQJ DGWUHH LQ FRPSDULVRQ ZLWK WKH VWDUWLQJ RQH²DV ZH ZLOO VHH LQ GHWDLO VRPHWLPHV WKHUH DUH PRUH WKDQ MXVW WZR DGWUHHV LQYROYHG LQ WKH SURFHVV 8QGHU D OLQJXLVWLF SRLQW RI YLHZ JUDPPDWLFDOL]DWLRQ SKHQRPHQD²DQG KHQFH WUDQVIRUPDWLRQ SDWWHUQV²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²RU VHQWHQFH OHYHO LI \RX SUHIHU²RI ODQJXDJH DQDO\VLV ,Q SULQFLSOH WKHUH LV QR GLIIHUHQFH EHWZHHQ JUDPPDWLFDOL]DWLRQ DW PRUSKR ORJLF DQG V\QWDFWLF OHYHOV WKH UXOHV RI WUDQVIRUPDWLRQV DUH WKH VDPH 1RQHWKH OHVV LW LV XVHIXO WR IRUPDOO\ VHSDUDWH WKH SXUHO\ OLQJXLVWLF OHYHO²ZKHUH WKH UXOHV WKDW GHVFULEHG FRQVWUXFWLRQV DUH WKH VDPH UHJDUGOHVV RI WKH ODQJXDJHV²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²VHH $SSHQGL[ % IRU WKH GHWDLOV ,Q SUDFWLFH ZH GLVWLQJXLVK



&KDSWHU )RXU

WKUHH W\SHV RI WUDQVIRUPDWLRQV DORQJ ZLWK WKHLU SXUSRVHV WUHH WUDQVIRUPDWLRQV UHGXQGDQF\ WUDQVIRUPDWLRQV DQG HSVLORQ WUDQVIRUPDWLRQV 7UHH WUDQVIRUPDWLRQV RU τWUDQVIRUPDWLRQV DUH WKRVH WUDQVIRUPDWLRQV WDN LQJ DQ DGWUHH LQ LQSXW DQG JLYLQJ D GLIIHUHQWO\ VKDSHG DGWUHH LQ RXWSXW WKHUHIRUH WKH\ RSHUDWH DW WKH OLQJXLVWLF OHYHO :KHQ WKH FKDLQ RI τWUDQVIRUPDWLRQV LV RYHU UHGXQGDQF\ WUDQVIRUPDWLRQV RU ρWUDQVIRUPDWLRQV DUH LQ FKDUJH $ ρWUDQVIRUPDWLRQ JHQHUDOO\ RSHUDWHV RQ WKH PRUSKHPLF OHYHO DV LW GHDOV ZLWK WKH ILQDO PRUSKHPHV ²WKDW LV SURSHU PRUSKHPHV WKDW FDQQRW EH H[SDQGHG LQ DGWUHHV DQ\ IXUWKHU ,Q RWKHU ZRUGV JHQHUDOO\ LW WDNHV WKH ILQDO τWUDQVIRUPHG DGWUHH LQ LQSXW DQG JLYHV LQ RXWSXW DQ DGWUHH ZLWK WKH VDPH VWUXFWXUH ZLWK DW OHDVW RQH GLIIHUHQW PRUSKHPH IRU UHGXQGDQF\ UHDVRQV 6R D ρWUDQVIRUPDWLRQ FDQ JLYH DFFRXQW RI DJUHHPHQW LQ QXPEHU JHQGHU FDVH RU SHUVRQ GHSHQGLQJ RQ WKH SDUWLFXODU FRQVWUXFWLRQ DW ZRUN )LQDOO\ HSVLORQ WUDQVIRUPDWLRQ RU ǫ WUDQVIRUPDWLRQV DUH D XVHIXO ZD\ WR KLGH HPSW\ DGSRVLWLRQV ǫ DQG YRLG JRYHUQRUV DQG GHSHQGHQWV   $V LW ZLOO EH FOHDU LQ WKH QH[W VHFWLRQ WKH WUHDWPHQW RI HPSW\ DGSRVLWLRQV DQG YRLG OHDYHV ERWK JRYHUQRUV DQG GHSHQGHQWV LV GLIIHUHQW VLQFH GHVSLWH WKHLU QDPH WKH\ DUH QRW WUDQVIRUPDWLRQV EXW MXVW D FRQYHQLHQW ZD\ WR ZULWH DGWUHHV

 7KH HSVLORQ WUDQVIRUPDWLRQ $Q HSVLORQ WUDQVIRUPDWLRQ LV QRW D NLQG RI OLQJXLVWLF UXOH UDWKHU LW LV D PHUHO\ QRWDWLRQDO PDQQHU WR ZULWH PRUH FRPSDFW DGWUHHV ZLWKRXW ORVLQJ UHOHYDQW LQIRU PDWLRQ 7KLV LPSOLHV WKDW ǫ WUDQVIRUPDWLRQV DUH QRW UHODWHG ZLWK WKH RWKHU NLQGV RI WUDQVIRUPDWLRQV DQG KHQFH WKHLU H[SODQDWLRQ QHHGV RQO\ ZKDW DOUHDG\ VHHQ LQ WKH SUHYLRXV FKDSWHUV )RU WKLV UHDVRQ ZH KDYH FKRVHQ WR H[SODLQ WKHP EHIRUH WKH RWKHU WZR W\SHV RI WUDQVIRUPDWLRQV $V DOUHDG\ VHHQ VRPHWLPHV JUDPPDU FKDUDFWHUV DUH VLJQHG ZLWK D PRUSKHPLF PDUNHU VRPHWLPHV QRW²LQ WKLV ODVW FDVH WKH\ DUH SXUHO\ FROORFDWLRQDO ,Q SDU WLFXODU D FROORFDWLRQDO VWUDWHJ\ ZKLFK SHUWDLQV WR V\QWD[ QRW WR PRUSKRORJ\ LV PRUH OLNHO\ WR EH IRXQG LQ DGSRVLWLRQV DQG GHSHQGHQWV UDUHO\ LQ JRYHUQRUV DIWHU DOO LW LV REYLRXV WKDW WKH JRYHUQRU RI DOO WKH PRUSKRV\QWDFWLF VWUXFWXUH QRUPDOO\ LV HOLFLWHG²KRZHYHU DQ H[FHSWLRQ ZDV RIIHUHG LQ I  $ SXUHO\ FROORFDWLRQDO DGSRVLWLRQ ZLOO EH VLJQHG E\ DQ HSVLORQ ǫ  ZKLOH DQ DGWUHH OHDI HLWKHU JRYHUQRU RU GHSHQGHQW E\ D ER[   7KH GLIIHUHQFH LV QRW RQO\ QRWDWLRQDO EXW KHQFH LW UHVSHFWV D FRQFHSWXDO GLIIHUHQFH ZKLOH DGSRVLWLRQV DUH

7UDQVIRUPDWLRQV



KRRNV LQ WKH DGWUHHV JRYHUQRUV DQG GHSHQGHQWV DUH WKHPVHOYHV DGWUHHV ZKHUH WKH DGWUHH FRLQFLGHV ZLWK D VLQJOH HOHPHQW H[DFWO\ WKH JRYHUQRU RU WKH GHSHQGHQW  $ ZD\ WR KLGH HSVLORQV DQG ER[HV ZKHQ QHHGHG UHYHDOHG WR EH YHU\ XVHIXO ZKHQ ZH IRXQG WKH PRGHO :H ZDQW WR VWUHVV WKH IDFW WKDW ǫ WUDQVIRUPDWLRQV DUH D XVHIXO QRWDWLRQDO DUWLIDFW EXW QRWKLQJ PRUH QR LQIRUPDWLRQ LV ORVW EXW RQO\ KLGGHQ HVVHQWLDOO\ IRU KXPDQ UHDGDELOLW\ +HQFH ZKHQ ZH ZLOO WDON DERXW µFXWWLQJ RII¶ RU µHOLPLQDWH¶ ZKDW ZH UHDOO\ PHDQ LV FDQFHOOLQJ IURP WKH DFWXDO DGWUHH GUDZLQJ 7KH RQO\ ZD\ WR HOLPLQDWH YRLG GHSHQGHQWV LV ZKHQ WKHLU DGSRVLWLRQ LV HPSW\ WRR )LJXUH   :H KDYH DOUHDG\ VHHQ DQ LQVWDQFH RI LW LQ WKH SUHYLRXV FKDSWHU LQ )LJXUH  UHIHUULQJ WR H[DPSOH  

p
↔A «A
gc A p

↔A «
ǫA
F A gc  D

gov G

{

p
↔A «A
gc A


△

gov F

«

gc

)LJXUH  $EVWUDFW WUHHV RI HSVLORQ WUDQVIRUPDWLRQ DW WKH ILUVW OHYHO ,Q JHQHUDO WKHUH DUH WZR SRVVLEOH FDVHV GHSHQGLQJ RQ WKH GHSWK RI WKH DGWUHH WR EH WUDQVIRUPHG /HW adp EH D PRUSKHPLF DGSRVLWLRQ LH ZLWK D FRQFUHWH OLQJXLVWLF PDUNHU RQ WKH V\QWDJPDWLF D[LV DQG ǫ EH D FROORFDWLRQDO DGSRVLWLRQ LH QR PDUNHU RQ WKH V\QWDJPDWLF D[LV  7KH HSVLORQ WUDQVIRUPDWLRQ DW WKH ILUVW OHYHO LQ EULHI ǫ1 WUDQVIRUPDWLRQ LV DSSOLHG LQ DOO FDVHV RI JUDPPDU FKDUDFWHU LPSRVLWLRQ²UHFDOO )LJXUH  DW WKH EHJLQQLQJ RI &KDSWHU  )LJXUH  VKRZV DQ ǫ1 WUDQVIRUPDWLRQ WKH QRQWUDQVIRUPHG DGWUHH LV RQ WKH OHIW ZKLOH WKH WUDQV IRUPHG WUHH LV RQ WKH ULJKW ,W LV ZRUWK QRWLFLQJ WKDW WKH WUDQVIRUPHG WUHH EHFRPHV D OHDI ZH KDYH DOUHDG\ VHHQ DQ LQVWDQWLDWLRQ RI WKLV NLQG RI WUDQVIRUPDWLRQ DERXW FKLOGUHQ¶V VSHHFK XWWHUDQFH EDOO WDEOH   6RPHWLPHV ZH KDYH SHUIRUPHG D GLIIHUHQW NLQG RI HSVLORQ WUDQVIRUPDWLRQ ZKLFK FRPSULVHV WZR OHYHOV RI WKH DGWUHH )RU WKLV UHDVRQ LW LV FDOOHG HSVLORQ WUDQVIRUPDWLRQ DW WKH VHFRQG OHYHO LQ EULHI ǫ2 WUDQVIRUPDWLRQ  )RU LQVWDQFH WKLV LV DSSOLHG WR WKH FLUFXPVWDQWLDOEDVHG UHODWLRQV LQ JHQHUDO LH WKH FLUFXPVWDQWLDO YHUEDQW UHODWLRQV HJ   DQG WKH FLUFXPVWDQWLDODGMXQFWLYH UHODWLRQV²HJ  DQG   /HW Gx EH WKH JUDPPDU FKDUDFWHU RI ERWK JRYHUQRUV LQYROYHG gov1 DQG gov2  7KH DEVWUDFW UXOH LV VKRZQ LQ )LJXUH  7KH ǫ2 WUDQVIRUPDWLRQ



&KDSWHU )RXU

p
↔A «A
gc A p

↔A
ǫA « p
Gx A gc
↔A gov1
adpA A Gx


△ {

F

 D

gov2 Gx

q
A
↔ «A
gc A A
A q

A
↔A «
adp A gc
Gx A A
gov1 { dep gov2 Gx > F Gx

△

)LJXUH  $EVWUDFW WUHHV RI HSVLORQ WUDQVIRUPDWLRQ DW WKH VHFRQG OHYHO

VKRZV ZKDW KDSSHQV LQ FDVH RI µFODVKLQJ¶ EHWZHHQ FKDUDFWHU LPSRVLWLRQ DQG FKDU DFWHU UDLVLQJ DW WKH ILUVW VWHS ǫ1 WUDQVIRUPDWLRQ LV DSSOLHG FKDUDFWHU LPSRVLWLRQ ZKLOH DW WKH VHFRQG VWHS FKDUDFWHU UDLVLQJ µZLQV¶ VR WKDW WKH DGSRVLWLRQ LV SXW XQGHU WKH XSSHU OHYHO )LJXUH   7KHUH LV QR ZD\ WR HOLPLQDWH YRLG JRYHUQRUV HYHQ LI WKHLU DGSRVLWLRQV DUH HPSW\ WKHLU LQIRUPDWLRQ LV WRR LPSRUWDQW +RZHYHU ZH KDYH IRXQG D FRPSDFW QRWDWLRQ IRU VXFK FDVHV  /HW XV VXSSRVH WR KDYH D FKDUDFWHU UDLVLQJ ZLWK DQ YRLG JRYHUQRU DQG DQ HPSW\ DGSRVLWLRQ ZKLFK LV PDQGDWRU\ EXW D QRQYRLG GHSHQGHQW )LJXUH   :H FDQ REWDLQ D UHDOZRUOG FDVH DV VXFK IURP   ZKHUH WKDW HOHSKDQW EHFRPHV WKDW RQH DQG ILQDOO\ WKDW²VHH )LJXUH  IRU D FRPSDULVRQ 7KLV LV WKH RQO\ ZD\ WR REWDLQ D QHZ JRYHUQRU IURP D GHSHQGHQW WKH UHDGHU LV LQYLWHG WR QRWH WKDW WKH ILQDO JUDPPDU FKDUDFWHU LV WKH RQH RI WKH ROG JRYHUQRU QRW WKH RQH EHORQJLQJ WR WKH WUDQVIRUPHG GHSHQGHQW p
↔A
ǫA
G A { dep { gov D>G  dep

D

G

)LJXUH  $EVWUDFW WUHHV RI KRZ WR FRPSDFW D YRLG JRYHUQRU 7KH V\PERO > LV XVHG LQ )LJXUH  DV D VKRUWFXW IRU DQ DGWUHH ZKRVH RQO\ UHOHYDQW LQIRUPDWLRQ LV WKH JUDPPDU FKDUDFWHU FKDQJH RI WKH RQO\ H[SOLFLW PRU SKHPH DW ZRUN LQ WKDW SDUWLFXODU DGWUHH ,Q RWKHU ZRUGV WKH DGSRVLWLRQ LV HPSW\ DQG HLWKHU WKH JRYHUQRU RU WKH GHSHQGHQW LV YRLG 

7UDQVIRUPDWLRQV



)LQDOO\ LW LV ZRUWK QRWLFLQJ WKDW LQ HYHU\ HSVLORQ WUDQVIRUPDWLRQ WKHUH LV QR DV VXPSWLRQ RU PRGLILFDWLRQ RQ WKH WUDMHFWRU\ RI LQIRUPDWLRQ SURPLQHQFH  ,Q FDVH RI FRPSDFWHG YRLG JRYHUQRUV WKH LQGLFDWRU FDQ EH SXW RYHU WKH ILQDO JUDPPDU ← − FKDUDFWHU H[SOLFLWO\ LI QHHGHG HJ D > G 

 7KH PHFKDQLFV RI WUHH WUDQVIRUPDWLRQV 7UHH WUDQVIRUPDWLRQV DUH E\ IDU WKH PRVW LPSRUWDQW W\SH RI WUDQVIRUPDWLRQV DV WKH\ JLYH DQ DFFRXQW RI JUDPPDWLFDOL]DWLRQ SKHQRPHQD WKDW FDQ EH GHVFULEHG DV DGWUHHV WUDQVIRUPHG LQWR DGWUHHV )RUPDOO\ ZH XVH FRQMXJDWH DGWUHHV ZKHUH SDUWV OHDYHV RU ODUJHU VXEWUHHV RI WKH LQSXW DGWUHH DUH SHUPXWHG²IRU IXUWKHU GHWDLOV VHH 6HFWLRQ % 7R H[SODLQ KRZ LW ZRUNV OHW XV UHFDOO H[DPSOH   ZH KDYH SUHYLRXVO\ VHHQ $Q REYLRXV OLQJXLVWLF H[DPSOH RI τWUDQVIRUPDWLRQ LV WKH RQH WKDW WUDQVIRUPV D SKUDVH IURP WKH DFWLYH WR WKH SDVVLYH GLDWKHVLV D 7KH MDQLWRU ZLOO RSHQ WKH GRRU ZLWK WKH NH\ I 7KH GRRU ZLOO EH RSHQHG E\ WKH MDQLWRU :KDW ZH ZDQW WR VKRZ LV KRZ τ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△  :LWKLQ WKH FODVV RI HYHU\ SKUDVDO FRQVWUXFWLRQ ZLWK WKDW SDUWLFXODU JRYHUQRU²LH PRUSKR ORJLFDOO\ ZHOO GHILQHG²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



&KDSWHU )RXU

q
A
→ A q ZLWK A

A 3 I


3 A
→A Aq

ǫ3 A
A
∗I1 A 
←A WKHNH\  Aq
ǫ
3 A Z
A  ∗I 2 A
{ { WKH MDQLWRU
←A Aq
ǫ A
3 ∗X
A
∗I2 A
→A

WKH GRRU A

ǫ3 A ∗Y ∗I 1 A


WKH GRRU ZLOO RSHQ A
∗I3 ∗Y

△

△

△

△

△

△

△

WKH MDQLWRU ZLOO RSHQ

∗I3

∗X

q
A
→A q E\ A

A I22 A

→A Aq

E\ A
A 3
∗I1 A
←A WKH MDQLWRU Aq

ǫ2 A Y
A I1 A
{ WKH MDQLWRU
←A {
A
ǫ3 A ∗X A
∗I2 A A WKH GRRU A
A X

△

△

△

△

△

WKH GRRU

ZLOO RSHQ

∗Y

∗I

A A

△

3

ZLOO RSHQ

{ ZLOO EH RSHQ ∗I3 { I2

)LJXUH  ([DPSOH RI WUHH WUDQVIRUPDWLRQ LQ DQ DFWLYHSDVVLYH FRQVWUXFWLRQ

7UDQVIRUPDWLRQV



WKH ILQDO SDVVLYH FRQVWUXFWLRQ LH E\ )LQDOO\ WKH IRXUWK WUDQVIRUPDWLRQ RSHU DWHV DW D PRUSKHPLF OHYHO LW UHGHILQHV WKH FRQVWUXFWLRQ RI WKH YHUEDQW IRUP LQ RUGHU WR VDWLVI\ WKH UHTXHVWHG IHDWXUH RI EHLQJ SDVVLYH 7KH YDOHQF\ YDOXHV DUH UHFDOFXODWHG DFFRUGLQJO\ 7KH WUDQVIRUPDWLRQ IURP WKH DFWLYH YHUEDQW ZLOO RSHQ WR WKH SDVVLYH RQH ZLOO EH RSHQHG LV H[SODLQHG ODWHU DV LW LQYROYHV WKH WUHDWPHQW RI KLGGHQ SUHGLFDWLRQV

 +RZ UHGXQGDQF\ ZRUNV :H VKRXOG VWLOO JLYH DQ DFFRXQW RI DJUHHPHQW DQG LQ JHQHUDO UHGXQGDQF\ ZLWKLQ WKH DGSRVLWLRQDO SDUDGLJP ,Q RUGHU WR GR VR ZH VKRXOG UHGHILQH WKH QRWLRQ RI µPRUSKHPH¶ ,Q IDFW D PRUSKHPH LV D GRXEOHVLGH VLJQ DQDORJRXV WR SKRQHPHV WKH ILUVW VLGH LV WKH VLJQLILHU LH WKH H[SOLFLW PDUN RQ WKH V\QWDJPDWLF D[LV ZLOO EH FDOOHG PRUSK ZKLOH WKH RWKHU VLGH LV IRUPHG E\ HYHU\ RWKHU WUDLW FDOOHG VHPHPH 6HPHPHV XVXDOO\ FRQYH\ VHPDQWLF LQIRUPDWLRQ EXW DOVR V\QWDFWLF²VXFK DV FDVH VHPDQWLF UROH QXPEHU HWF )RU H[DPSOH WKH PRUSK RI ZDON LV µZDON¶ ZKLOH movement LV RQH RI LWV VHPHPHV 7\SRJUDSKLFDOO\ WKH PRUSKHPH LV ZULWWHQ LQ LWDOLF WKH PRUSK LQ SODLQ ZKLOH VHPHPHV DUH ZULWWHQ LQ VPDOO FDSLWDOV (DFK PRU SKHPH KDV DOZD\V RQH PRUSK D ]HUR PDUNHG PRUSK DW WKH OLPLW VLJQHG WKURXJK D ER[   DQG DW OHDVW RQH VHPHPH 6HPHPHV DUH VWULFWO\ ODQJXDJHVSHFLILF DQG WKH\ VKRXOG EH PDGH H[SOLFLW ZKLOH ZULWLQJ WKH FRQVWUXFWLYH GLFWLRQDU\²VHH &KDSWHU  IRU GHWDLOV 5HGXQGDQF\ LV D OLQJXLVWLF SKHQRPHQRQ ZKHUH D IHDWXUH ZLWKLQ D FRQVWUXF WLRQ LV PDUNHG PRUH WKDQ WKH QHFHVVDU\ LH PRUH WKDQ WKH PLQLPXP LQ RUGHU WR FRQYH\ WKH IHDWXUH LWVHOI )RU µIHDWXUH¶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



&KDSWHU )RXU

WKH ILQDO V GRHV QRW FKDQJH LQ DQ\ ZD\ WKH PHDQLQJ RI WKH YHUEDQW RU LWV OLQJXLVWLF VWUXFWXUH EXW LW SUHYHQWV WR µFURVVFKHFN¶ WKH FRUUHFWQHVV RI WKH H[SUHVVLRQ 8QOLNH WKH H[DPSOH RI WKH SUHYLRXV VHFWLRQ KHUH ZH DUH RSHUDWLQJ RQO\ DW D PRUSKHPLF OHYHO IURP D SXUHO\ OLQJXLVWLF OHYHO RI DQDO\VLV DE DUH WKH VDPH ,Q JHQHUDO ZH ZLOO ZULWH RXW RQO\ WKH VHPHPHV QHHGHG IRU RXU SXUSRVH LQ WKDW PRPHQW )RU H[DPSOH ZH FDQ UHZULWH VRPH RI WKH PRUSKHPHV RI  H[SOLFLWO\ DV IROORZV F /L]D >noun: proper, singular@ ZDONV >verb: [tense: simple present: [3rd person, singular]]@

p
→A
ǫA

I11 AA p
→A
ǫA

I11 AA

/L]D

X {

/L]D

ZDON

X

I1

>noun@ >singular@

A A AAp
←A
ǫA

I1 AA

V

p
→A
ǫA

I11 AA

{

/L]D

X

△

ZDONV

I1

ZDON

I I1 >3 person@ >singular@ rd

)LJXUH  5HGXQGDQF\ RI /L]D ZDONV ([DPSOH F VKRZV TXLWH FOHDUO\ WKDW WKH H[SOLFLW ZULWLQJ RI HYHU\ VHPHPH SHUWDLQLQJ D YHU\ VLPSOH SKUDVH VXFK DV  LV QHLWKHU IHDVLEOH QRU XVHIXO LI SRVVLEOH DW DOO  ,W LV WKH IDFW WKDW ZLWKLQ WKH FRQVWUXFWLRQ RI  ZDON LV D verb WKDW FDQ DFWLYDWH LWV VXERUGLQDWH VHPHPH simple present GHVFULELQJ WHQVH DQG WKHQ DFFRUGLQJO\ WKH UXOH RI DJUHHPHQW RI WKH WKLUG SHUVRQ VLQJXODU EHWZHHQ WKH YHUE LWVHOI DQG WKH SURSHU noun /L]D   )LJXUH  VKRZV WKH FRUUHVSRQGHQW DGWUHHV D LV RQ WKH OHIW ZKLOH LQ WKH PLGGOH WKH DJUHHPHQW LV VROYHG E\ VKRZLQJ WKH PDWFKLQJ VHPHPHV EHWZHHQ WKH YHUEDQW I DQG WKH ILUVW DFWDQW X  ,Q IDFW LI WKH ILUVW DFWDQW LV D noun: singular LW GRHV QRW PDWWHU LI proper RU common DQG WKH YHUEDQW LV D verb: [tense: simple present] WKHQ D PRGLILHU ZLWK WKH VHPHPHV [3rd person, singular] VKRXOG EH DSSOLHG WR WKH verb LQ WKLV FDVH V DFFRUGLQJ WR SKRQRWDFWLF UXOHV ZULWWHQ

7UDQVIRUPDWLRQV



LQ WKH GLFWLRQDU\  LQ RUGHU WR PDWFK WKH VHPHPHV noun: singular RI WKH ILUVW DFWDQW 7KH WUDMHFWRU\ RI LQIRUPDWLRQ SURPLQHQFH LV WKDW RI JRYHUQPHQW DV WKH PRUSKHPH V GRHV QRW FKDQJH WKH JUDPPDU FKDUDFWHU RI ZDON ZKLFK UHPDLQV WKH PRVW SURPLQHQW LQIRUPDWLRQ RI WKLV PRUSKHPLF DGWUHH $Q REVHUYDWLRQ VKRXOG EH GRQH DW WKLV SRLQW ,W LV QRW E\ FKDQFH WKDW PDQ\ UHGXQGDQF\ SKHQRPHQD DUH FDUYHG LQWR HDFK ODQJXDJH PRUSKRORJ\ DIWHU DOO PRUSKRORJ\ LV D FOHDU VLJQ RI JUDPPDWLFDOL]DWLRQ 7KLV GRHV QRW LPSO\ KRZHYHU WKDW ρWUDQVIRUPDWLRQV FDQQRW DOVR RFFXU DW D V\QWDFWLF OHYHO D /L]D ZDONV DQG 3DXO ZDONV E /L]D DQG 3DXO ZDON 7KH FRQVWUXFWLRQ KHDGHG E\ DQG DV WKH PDLQ DGSRVLWLRQ WXUQV LWV HOHPHQWV LH JRYHUQRU DQG GHSHQGHQW WDNHQ DV ZKROH LQWR D VWDWLYH DV DE VKRZ²WKH TXRWDWLRQ LQ D ZDV SXW WR KHOS WKH UHDGHU LQ WKLV UHVSHFW

p
↔A
DQGA

X AAp

→A

ǫA



I11 AA
A /L]D
A X AAp
p
>noun@
→A
←A >singular@
ǫA
ǫA

I11 AA

I1 AA A 3DXO V ZDON A X I I1 AAp rd >noun@ >3 person@
←A >singular@ >singular@
ǫA

I1 AA V

ZDON

I I1 >3 person@ >singular@ rd

)LJXUH  7KH DGWUHH RI /L]D ZDONV DQG 3DXO ZDONV



&KDSWHU )RXU

)LJXUH  VKRZV WKH DGSRVLWLRQDO WUHH RI D  WKHUH LV D ORW RI UHGXQGDQW LQIRUPDWLRQ LQ LW VR LW LV IDU FRPPRQ WR XVH WKH FRQVWUXFWLRQ H[HPSOLILHG E\ E LQVWHDG ,Q WKLV FRQVWUXFWLRQ ZKHUH WKH JRYHUQRU DQG WKH GHSHQGHQW RI DQG DUH ERWK VWDWLYH DQG singular WKH UHVXOWLQJ DGWUHH ZLOO EH plural DV WKH DJUHHPHQW ZLWK WKH YHUE ZDON WHVWLILHV LQ WKLV FDVH WKURXJK WKH DEVHQFH RI WKH PRUSKHPH V²)LJXUH 

q
A
→A
ǫ A
I11 A
A A q

A ZDON
↔A I1
DQG A
X A
>plural@ A
A 3DXO

/L]D

O

O

>noun@

>noun@

>singular@

>singular@

)LJXUH  7KH DGWUHH RI /L]D DQG 3DXO ZDON

,Q WKH VHTXHO ZH ZLOO VKRZ VRPH RI WKH PRVW LPSRUWDQW DQG ZHOONQRZQ SKHQRPHQD WKDW LQYROYH VRPH W\SHV RI WUDQVIRUPDWLRQV VXFK DV SDVVLYL]DWLRQ QRUPDOLVDWLRQ DX[LOLDU\ FRQVWUXFWLRQV DQG VR RQ

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

7UDQVIRUPDWLRQV



7R EH DQ XQH[SHFWHG ELYDOHQW YHUE 7KHUH DUH D ORW RI FRQVWUXFWLRQV EDVHG RQ HVVH QRW RQO\ DX[LOLDU\ LQ QDWXUH :H FDQ OLVW WKH IROORZLQJ SURWRW\SLFDO SURSHU HVVHFRQVWUXFWLRQV LQ (QJOLVK WKDW VKRZ WKH SDWWHUQV RI XVH RI WR EH DV ³D IXOO YHUE ZKHQ LW FRPELQHV ZLWK DGMHFWLYHV DQG QRXQV´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µFRSXOD¶ LV WKDW HVVHFRQVWUXFWLRQV KDYH DOZD\V EHHQ ZURQJO\ WUHDWHG DV PRQRYDOHQW FRQVWUXFWLRQV ZKLOH WKH\ DUH ELYDOHQW 7KH DGSRVLWLRQDO WUHH RI D VKRZV ZKDW VKRXOG EH HYLGHQW WKHUH DUH WZR VWDWLYH LQYROYHG LQ HVVHFRQVWUXFWLRQV QRW MXVW RQH²)LJXUH  OHIW 7KH DQRPDO\ LV LQ WKH LQIRUPDWLRQ SURPLQHQFH ERWK WKH ILUVW DQG WKH VHFRQG DFWDQWV DUH QRW SURPLQHQW KHQFH WKH\ DUH LQ D UHODWLRQ RI JRYHUQPHQW ←  ZKLOH WKH SURPLQHQFH LV LQ WKH DGMHFWLYH TXLHW ZKLFK LV LQ D UHODWLRQ RI GHSHQGHQF\ 



&KDSWHU )RXU

p
→A
ǫA

I22 AAp

←A

ǫA

I21 AA p


←A LV /L]D
ǫA 2 I X

Y AAp
→A D
ǫA A

Y AA TXLHW

JLUO

A

Y

p
→A
ǫA

I22 AAp

←A

ǫA p



I21 AA
→A /L]D LV
ǫA 2 X I

Y AA TXLHW  A Y

)LJXUH  7KH DGWUHHV RI /L]D LV D TXLHW JLUO

7KLV LV FRQILUPHG E\ E  WKH LQIRUPDWLRQ EHORQJLQJ WR WKH VHFRQG DFWDQW DQG QRW SURPLQHQW LV FRPSOHWHO\ ORVW DQG RQO\ D WUDFH LV FRQVHUYHG²VLJQHG E\ WKH ER[   7KH UHDGHU LV LQYLWHG WR QRWLFH WKDW WKH LQIRUPDWLRQ SURPLQHQFH RI WKH DGMHFWLYH → LV UHWDLQHG 2I FRXUVH ZH FDQ REWDLQ E IURP D ZLWK D VHULHV RI WUHH WUDQVIRUPDWLRQV WKLV LPSOLHV WKDW WKH HVVHFRQVWUXFWLRQV ZLWK DGMHFWLYHV OLNH WKH RQH LQ H[DPSOH E  DUH UHGXFHG IRUPV RI WKH PDLQ HVVH FRQVWUXFWLRQV H[HPSOLILHG E\ D  7KH LPSHUDWLYH FRQVWUXFWLRQV H[HPSOLILHG E\ FG DUH WKH SURGXFW RI IXU WKHU WUDQVIRUPDWLRQV SHUIRUPHG RQ WKH ILUVW DFWDQW ZKLFK UHWDLQV RQO\ WKH VH PHPHV RI WKH second person: singular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²ZH VD\ µSDUWLDOO\¶ EHFDXVH WKH YHUEDQW PRUSK LV VWLOO H[SUHVVHG DV LQ VWXG\LQJ D RU SUHSDUHG F   )LJXUH  VKRZV WKH DGSRVLWLRQDO WUHH RI D  ZKLFK H[HPSOLILHV WKH SUHVHQW SURJUHVVLYH FRQVWUXFWLRQ LQ (QJOLVK ,Q SDUWLFXODU LV LV WKH PRUSKHPH RI WKH DX[LOLDU\ YHUE V\PERO I2aux DQG VWXG\ LV WKH PRUSKHPH RI WKH PRUSKHPH RI WKH KHOSHG YHUE V\PERO I2mean  3OHDVH QRWH WKDW WKH DGWUHH RI WKH DFWLYH DQG VDW

7UDQVIRUPDWLRQV

p
→A
A

I22 AAp

←A

ǫA

I21 AA p


←A  EH
ǫA I2

Y AAp X
→A D
ǫA A

Y AA



p
→A
A

I22 AAp

←A

ǫA p



I21 AA
→A  EH
ǫA I2

Y AA X

TXLHW

JLUO

TXLHW

A

Y

A

 Y

)LJXUH  7KH DGWUHHV RI %H D TXLHW JLUO 

q
A
→ ǫA
I2 A
2 Aq

A

← ǫA

I2 A
1 A q

A 3DXO LV →A
LQJ 2 X I aux aux
A
Yaux Aq
A 
← ǫA D
I2 A
2 Aq
A PDWKV
→ A Ymean
ǫ2 A I1
A   3DXO VWXG\ Xmean

I2

)LJXUH  7KH DGWUHH RI 3DXO LV VWXG\LQJ PDWKV



&KDSWHU )RXU

XUDWHG FRQVWUXFWLRQ 3DXO VWXGLHV PDWKV LV SUHVHUYHG²H[FHSW IRU WKH UHGXQGDQF\ YHUEDO PDUNHU V ,Q RUGHU WR IXQFWLRQ SURSHUO\ WKH (QJOLVK JUDPPDU UHTXLUHV WKDW WKH YHUEDQW VWXGLHV LV GHDFWLYDWHG E\ WKH DGSRVLWLRQ LQJ E\ LPSRVLWLRQ RI WKH JUDPPDU FKDUDFWHU 7KH VHFRQG DFWDQW RI WKH KHOSHG FRQVWUXFWLRQ V\PERO Ymean VDWXUDWHV WKH VHFRQG DQG ODVW YDOHQF\  )LQDOO\ WKH PRUSKHPH PDWKV LV WKH UHVXOW RI D FRPPRQ IRUP RI JUDPPDWLFDOL]DWLRQ FDOOHG OH[LFDOL]DWLRQV LQ IDFW HYHQ LI PRUSKRORJLFDOO\ LW LV D SOXUDO PDWKV  LW LV XVHG DV D VLQJXODU LWHP DQG KHQFH LW FDQ EH OLVWHG DV D XQDQDO\VDEOH OH[LFDO HQWU\ LQ WKH (QJOLVK FRQVWUXFWLYH GLFWLRQDU\±VHH &KDSWHU  ← − ,Q WKH FDVH RI XQDFFXVDWLYH YHUEV  I  OLNH 3DXO LV G\LQJ WKH VHFRQG PRU SKHPH EHFRPHV YRLG V\PERO   7KH UHQGHULQJ RI WKH JRLQJ WR IXWXUH FRQVWUXFWLRQ H[HPSOLILHG LQ E LV VOLJKWO\ PRUH FRPSOH[ DV WKHUH DUH WZR DX[LOLDU\ YHUEDQWV WKH ILUVW EHLQJ DQ HVVHFRQVWUXFWLRQ ZKLOH WKH VHFRQG RQH LV WKH SURSHU JRLQJ WR FRQVWUXFWLRQ I2aux+  ZKHUH WKH PHDQLQJIXO YHUE DFWV DV WKH VHFRQG DFWDQW²VHH )LJXUH  OHIW 7KLV VHFRQG DX[LOLDU\ FRQVWUXFWLRQ JRLQJ WR XSRQ IUHTXHQF\ RI XVDJH ZDV FRPSOHWHO\ JUDPPDWLFDOL]HG VR WKDW ZH FDQ WUHDW LQJ WR DV D VLQJOH DGSRVLWLRQ²VHH )LJXUH  ULJKW²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−−→ 3DXO EHLQJ WKH ILUVW DFWDQW RI WKH DFWLYH IRUP ZKLFK GRHV WKH SUHSDUDWLRQ Xact 

7UDQVIRUPDWLRQV



p
A
→ ǫA
I2 A
2 Ap q

A
A ←

ǫA
→A ǫ A

I2 A
1
A p
I22 A

A 3DXO LV → AAq


LQJ A 2 Iaux
A

Y A Xaux
aux Ap
←A

A
ǫ2 A

← A
I1 A
WR D
I2 A

AA
2 Ap

q

A
A 3DXO LV {

→
→A ǫA 2 Xaux Iaux

2 A
LQJ A p

I1 A
+ WR A
A   3DXO JR q

I > Yaux AA
← ǫA 2
A Iaux+
Y A Xaux+ JR
aux+ Ap
→A ǫ I aux+
A
2 A 
←
I2 > O A ǫA D
2 A AA


I2 Ap
A PDWKV VWXG\ PDWKV
→ ǫA Y I2 Y
2 A
I1 A   3DXO VWXG\ X I2 )LJXUH  7KH DGWUHHV RI 3DXO LV JRLQJ WR VWXG\ PDWKV



&KDSWHU )RXU

ZKLOH PDWKV EHLQJ WKH VHFRQG DFWDQW RI WKH SUHSDUHG VXEMHFW KDSSHQHG WR EH VWXG ←−− LHG Yact  7KH SDVVLYH FRQVWUXFWLRQ FDQ EH REWDLQHG E\ D FKDLQ RI WUDQVIRUPDWLRQV )URP WKHP ZH UHWDLQ WKHVH DEVWUDFW QDPHV IRU WKH WZR DFWDQWV HYHQ LQ WKH SDVVLYH IRUP LQ RUGHU WR XQGHUVWDQG EHWWHU KRZ WKH SDVVLYH FRQVWUXFWLRQ ZRUNV

q
A
→A
E\ A
E>I A Aq

A 3DXO
→A Xact
ǫ2 A
I2 A
Aq
A

←A

ǫ2 A

I1 A

A q

A LV PDWKV
→A 2 ǫ Iaux
A Yact { Xpass
A > YauxA A q

A  PDWKV 
→A Yact
2 G A
I2 > A A
Aq
A  PDWKV 
→A Yact
ǫ2 A
I2 A A
  SUHSDUH 3DXO Xact

I2

)LJXUH  7KH DGWUHH RI 0DWKV LV SUHSDUHG E\ 3DXO )LJXUH  VKRZV WKH DGSRVLWLRQDO WUHHV RI WKH SDVVLYH FRQVWUXFWLRQV LQ  FG  7KH ILUVW REYLRXV IDFW LV WKH SHUPXWDWLRQ RI WKH WZR DFWDQWV LQ WKH SDVVLYH ←−− FRQVWUXFWLRQ PDWKV SDVVHV IURP WKH UROH RI WKH VHFRQG WR WKH ILUVW DFWDQW Yact { ←−−− Xpass  SOHDVH QRWH WKDW WKH WUDMHFWRU\ RI WKH LQIRUPDWLRQ SURPLQHQFH GRHV QRW

7UDQVIRUPDWLRQV



−−→ FKDQJH →  &RQYHUVHO\ WKH ILUVW DFWDQW Xact JRHV RXW RI YDOHQF\ EHFRPLQJ D FLUFXPVWDQWLDO E  7KLV KDSSHQV EHFDXVH WKH Preparer 3DXO FDQ EH VDIHO\ RPLWWHG DV LQ G  H 3DXO LV SUHSDUHG I %H SUHSDUHG ,W LV LQWHUHVWLQJ WR VHH WKDW IRU SXUHO\ VHPDQWLF UHDVRQV WKH ILUVW DFWDQW RI −−→ WKH DGYDQFHG IRUP Xact FDQ EH DGYDQFHG LQ WKH SDVVLYH IRUP H  URXJKO\ PHDQLQJ WKDW 3DXO KDV UHDOO\ SUHSDUHG WKH H[DP RI PDWKV RU ZKDWHYHU WKH VHFRQG DFWDQW Yact FDQQRW EH UHWULHYHG DQ\PRUH  q q
A
A
→ A
→ A ǫ ǫ
2 A
2 A
I2 A
I2 A
Aq
Aq

A

A

← A

← A ǫ ǫ

2 A

2 A

I1 A

I1 A
q
A
q
A
A
A  3DXO LV \RX EH  A
→ A
→ 2 2 ǫ ǫ X I X I act act aux aux
>Y A
>Y A A A aux aux { A
A
q
A A
q
A
A  
→A
→A Yact Yact
2 G A
2 G A
I2 > A A
I2 > A A
Aq
Aq
A
A  
→ A
→ A ǫ ǫ Yact Yact
2 A
2 A
I2 A
I2 A
A
A    3DXO SUHSDUH \RX SUHSDUH 

Xact

I2

Xact

I2

)LJXUH  7KH DGWUHHV RI ^3DXO LV  %H` SUHSDUHG^  ` )LQDOO\ ZLWK WKH LPSHUDWLYH FRQVWUXFWLRQ I DOVR WKH ILUVW DFWDQW EHFRPH XQGHILQHG LQ VHPDQWLF WHUPV LQ IDFW WKH LPSHUDWLYH FRQVWUXFWLRQ RI WKH 2nd person VLPSO\ RPLWV WKH UHIHUUHG SHUVRQ SUHIHUULQJ WR IROORZ D SUDJPDWLF VROXWLRQ



&KDSWHU )RXU

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²VHH DJDLQ 6HFWLRQ  DERXW WKH GLFKRWRP\ HUJDWLYHQHVV YV DFFXVDWLYHQHVV LI QHHGHG /HW XV WDNH WKH IROORZLQJ H[DPSOHV LQ (QJOLVK %ODNH  ZLWK PRGLILFDWLRQV  D 7KH VKDK VOHSW LQ WKH EHGV D $ FDPHO VWHSSHG RQ WKH SDFNDJH 7KH FRQVWUXFWLRQV ; VOHSW LQ < DQG ; VWHSSHG RQ < DOORZ SDVVLYL]DWLRQ DV WKHLU ILUVW DFWDQW LV LQ D UHODWLRQ RI GHSHQGHQF\ →  7KHVH DUH WKH FRUUHVSRQGHQW FRPSOH[ SKUDVHV WKH DGWUHHV DUH LQ )LJXUHV  DQG   E

Yact 7KH EHGV

ToBe ZHUH

E

7KH SDFNDJH

ZDV

→ − ( I > A) + adp VOHSW LQ VWHSSHG RQ

E\ E\ E\

−−→ Xact WKH VKDK D FDPHO

7KHUH LV DQRWKHU FODVV RI ELYDOHQW YHUEV ZKHUH WKLV WUDQVIRUPDWLRQ LV QRW DO ORZHG WKLV LV YDOLG LQ (QJOLVK EXW QRW RQO\  VLQFH WKH WUDMHFWRU\ RI LQIRUPDWLRQ SURPLQHQFH RI WKH ILUVW DFWDQW LV UHYHUVHG +HUH DUH WKH H[DPSOHV %ODNH   D 7KH LFH FXEH PHOWHG LQ WKH RYHQ D 7KH WRRWKSDVWH RR]HG LQWR WKH VLQN D /LWWOH 5HG 5LGLQJ +RRG YDQLVKHG LQ WKH ZRRGV ,I WKH WUDQVIRUPDWLRQ FKDLQ VKRZQ E\ )LJXUH  LV DSSOLHG WKH UHVXOW LV XQ JUDPPDWLFDO²VLJQHG E\ WKH DVWHULVN  

7UDQVIRUPDWLRQV



q
A
→A
E\ A
E>I A A
AAq


A
→A WKH VKDK
ǫ A Xact
I22 A
A AAq



A

←A

ǫ A

I21 A A

AA
q



A ZHUH
→A WKH EHGV I2aux
ǫ A Yact
A > YauxA
A AA
q

A 
→A Yaux
W LQ A
I22 > A A A
AAq


A ((
→A ( WKH(EHGV
ǫ A Yact
I21 A A
AA

  VOHHS  (( ( WKH(VKDK 2 Imean Xact

△

△

△

△

)LJXUH  7KH DGWUHH RI ZHUH VOHSW



&KDSWHU )RXU

q
A
→A
E\ A
E>I A A
AAq


A
→A D FDPHO
ǫ A Xact
I22 A
A AAq



A

←A

ǫ A

I21 A A

AA q




A ZDV
→A WKH SDFNDJH I2aux
ǫ A Yact
A > YauxA
A AA q


A 
→A Yaux
SHG RQA
I2 > A A A
2 AAq


A
→A ((( WKH(SDFNDJH (
ǫ A Yact
I21 A A
AA



△

△

△

△

(( WKH(FDPHO ( Xact

VWHS

I2mean

)LJXUH  7KH DGWUHH RI ZDV VWHSSHG

7UDQVIRUPDWLRQV

E

∗(Y

7KH RYHQ

ToBe ZDV

E

7KH VLQN

ZDV

E

7KH ZRRGV



← − ( I > A) + adp PHOWHG LQ RR]HG LQWR

ZHUH

E\

YDQLVKHG LQ

E\ E\

← − X) WKH LFH FXEH

WKH WRRWKSDVWH E\

/LWWOH 5HG 5LGLQJ +RRG

7KH DFWLYHSDVVLYH WUDQVIRUPDWLRQ LV D JRRG WHVW RI WKH LQIRUPDWLRQ SURPL QHQFH FRQILJXUDWLRQ RI WKH FRQVWUXFWLRQ LQ DQDO\VLV LI LW LV SRVVLEOH WKH VWDWLYH → − YHUEDQW UHODWLRQ RI WKH ILUVW DFWDQW ZLOO EH D GHSHQGHQF\  X  RWKHUZLVH LW ZLOO ← − EH D JRYHUQPHQW  X  7KH WUDMHFWRULHV RI WKH RWKHU DFWDQWV LI DQ\ FDQ EH IRXQG WKURXJKRXW WKH H[SOLFLW DSSOLFDWLRQ RI WKH DFWLYHSDVVLYH WUDQVIRUPDWLRQ DV ZHOO

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← − ← − → − ELYDOHQW YHUEV I2 ZLWK X XQDFFXVDWLYH  I XQHUJDWLYH  X UHSDLQW UHDSSHDU

UHVQHH]H UHZDVK XQIROG

VQHH]DEOH ZDVKDEOH SHULVKDEOH

XQVZLP GUDIWHH DEVHQWHH

GDQFHH 8VXDOO\ WKH WUDQVIRUPDWLRQV²HLWKHU IURP YHUEDQWV DGMXQFWV RU FLUFXPVWDQ WLDOV²LQWR VWDWLYHV DUH UHIHUUHG LQ WKH OLWHUDWXUH DV QRUPDOLVDWLRQV DQRWKHU FRP PRQ FDVH RI JUDPPDWLFDOL]DWLRQ &RQVWUXFWLYH DGSRVLWLRQDO JUDPPDUV VKRZ WKDW VRPH LQIRUPDWLRQ RI WKH SUHGLFDWLRQ WKDW LV EHKLQG QRUPDOLVDWLRQ LV QRW ORVW EXW RQO\ KLGGHQ WKH DGPLVVLEOH QRUPDOLVDWLRQV GHULYHG IURP FHUWDLQ DIIL[HV UHTXLUH XQDFFXVDWLYH KLGGHQ SUHGLFDWLRQV RWKHUZLVH WKH\ GR QRW ZRUN DW DOO 7KH SRZHU RI JUDPPDWLFDOL]DWLRQ FDQQRW EH XQGHUHVWLPDWHG SDUDSKUDVLQJ D FODVVLF VWDWH PHQW E\ *LYyQ JUDPPDWLFDOL]DWLRQ LV WKH GULYLQJ IRUFH WKDW WUDQVIRUPV \HVWHU GD\¶V SKUDVHRORJ\ LQ WRGD\¶V PRUSKRORJ\ DQG ILQDOO\ LQWR WRPRUURZ¶V V\QWD[ $QRWKHU FXH IRU HUJDWLYHQHVV RU DFFXVDWLYHQHVV LQ (QJOLVK LV JLYHQ E\ WKH GRXEOH QRUPDOLVDWLRQ LH REWDLQHG LQ WZR VWHSV ,Q WKH ILUVW VWHS WKH YHUE LV



&KDSWHU )RXU

QRPLQDOLVHG E\ WKH VXIIL[ LQJ ZKLFK DFW DV DQ DGSRVLWLRQ LPSRVLQJ LWV JUDPPDU FKDUDFWHU ,Q WKH VHFRQG VWHS WKH UHVXOW LV FRQVWUXHG LQWR D VWDWLYH JURXS E\ WKH JHQLWLYH GHWHUPLQHU LI WKH YHUE ZDV XQDFFXVDWLYH RU E\ RI FRQVWUXFWLRQV LI LW ZDV XQHUJDWLYH :H FDQ H[SDQG WKH SUHYLRXV H[DPSOHV LQ WKH IROORZLQJ ZD\ F 6KDK¶V VOHHSLQJ F 7KH FDPHO¶V VWHSSLQJ F 7KH PHOWLQJ RI WKH LFH FXEH F 7KH RR]H RI WKH WRRWKSDVWH F 7KH YDQLVKLQJ RI /LWWOH 5HG 5LGLQJ +RRG

p
→A
·V A

A > OAAp
→A 6KDK
LQJA O

O AA  VOHHS D I

p
←A
RI A p

O AA
→A A
ǫA A AA

O AAp
A A WKH →
ǫA A A

A > OAA AAp
←A LFH FXEH
ǫA O O

O AAp
→A WKH
LQJA A

O AA PHOW  I D

)LJXUH  7UHHV RI 6KDK¶V VOHHSLQJ DQG 7KH PHOWLQJ RI WKH LFH FXEH ,W LV ZRUWK QRWLFLQJ WKDW WKLV GLFKRWRP\ µJHQLWLYH GHWHUPLQHU FRQVWUXFWLRQ¶ YV µRI FRQVWUXFWLRQ¶ LV RQO\ D WHQGHQF\ QRW D JHQHUDO UXOH RI (QJOLVK²LW VWDQGV RQ D VWDWLVWLFDO QRQGHWHUPLQLVWLF EDVLV :KDW ZH ZDQWHG WR VKRZ KHUH ZDV WKH IDFW WKDW D VWURQJ FRUUHODWLRQ H[LVWV EHWZHHQ WKH LQIRUPDWLRQ SURPLQHQFH VWDQGLQJ LQ WKH VWDWLYHYHUEDQW UHODWLRQ DQG WKH DGPLWWHG WUDQVIRUPDWLRQV LQWR VWDWLYHV 9HU\ RIWHQ DGMXQFWLYHEDVHG UHODWLRQV FDQ EH QHVWHG RQH LQWR WKH RWKHU UH FXUVLYHO\ WKH WUHHV GHVFULELQJ WKH VWUXFWXUH RI F DUH JRRG H[DPSOHV RI

7UDQVIRUPDWLRQV



LW )LJXUH  VKRZV WKH WUHHV RI F OHIW DQG F ULJKW  ZKLOH WKH RWKHU RQHV TXLWH VLPLODU DUH OHIW WR WKH UHDGHU ,Q F  WKH 6D[RQ JHQLWLYH 6KDK¶V LV D FRQVWUXFWLRQ WKDW WDNHV WKH VWDWLYH JUDPPDU FKDUDFWHU RI 6KDK DQG WUHDWV LW DV LI LW ZHUH DGMXQFWLYH 0RUHRYHU LW UHTXHVW DQRWKHU VWDWLYH DV WKH JRYHUQRU LQ WKLV FDVH VOHHSLQJ²D VWDWLYH UHVXOWHG IURP JUDPPDU FKDUDFWHU LPSRVLWLRQ %\ FRQWUDVW LQ F DQ H[DPSOH RI WKH VRFDOOHG µQRXQSOXVQRXQ¶ (QJOLVK FRQVWUXFWLRQ ZLWK LFH FXEH ZKLFK LV YHU\ VLPLODU WR 6D[RQ JHQLWLYH²WKH RQO\ GLIIHUHQFH LV EHLQJ WKH DEVHQFH RI WKH DGSRVLWLRQ PDUNHU FRPSDUH ZLWK 6KDK¶V VOHHSLQJ  2Q WKH ULJKW PHOWLQJ LV VLPLODU WR VOHHSLQJ ZKLOH WKH DUWLFOHVWDWLYH UHODWLRQ WKH PHOWLQJ LV VLPLODU WR WKH H[DPSOH WKH HOHSKDQW D )LJXUH   7KH LQGLFDWRUV LQ WKH ILQDO DGWUHHV DUH GXH WR WKH RULJLQDO VWDWLYHYHUEDQW FRQVWUXF WLRQV WKDW JLYHV UDLVH WR QRUPDOLVDWLRQ DV ZH KDYH SUHYLRXVO\ H[SODLQHG

3UHVHQWDWLYHV 2QH RI WKH PRVW LPSRUWDQW IXQFWLRQ RI QDWXUDO ODQJXDJH LV GHL[LV LH WKH IXQFWLRQ RI UHIHUULQJ H[WUDOLQJXLVWLF HQWLWLHV RU HQWLWLHV RXW RI WKH MRLQW DWWHQWLRQDO IUDPH ,Q RUGHU WR DFFRPSOLVK WKLV YHU\ VSHFLDO IXQFWLRQ DOO ODQJXDJHV KDYH GHYHORSHG D VHW RI KLJKO\ JUDPPDWLFDOL]HG FRQVWUXFWLRQV GHYRWHG WR GHL[LV ,Q (QJOLVK²DV ZHOO DV LQ PDQ\ ODQJXDJHV EHORQJLQJ WR WKH 6WDQGDUG $YHUDJH (XURSHDQ 6SUDFKEXQG²WKHUH DUH D ORW RI GHLFWLF FRQVWUXFWLRQV ZKHUH WKH YHUE WR EH LV LQYROYHG ,W LV ZRUWK QRWLFLQJ WKDW VXFK FRQVWUXFWLRQV DULVH YHU\ HDUO\ GXULQJ ILUVW ODQJXDJH OHDUQLQJ 7RPDVHOOR   )RU LQVWDQFH D VWDQGDUG FRQVWUXFWLRQ FDQ EH XVHG IRU LGHQWLILFDWLRQ SXUSRVHV DE  D ,W¶V D FDU QRW D EDQDQD  E 7KDW¶V WKH HOHSKDQW QRW WKH RWKHU RQH WKHUH LQ WKH ]RR  $QRWKHU FRPPRQ SXUSRVH RI WKH VWDQGDUG HVVHFRQVWUXFWLRQ LQ FKLOGUHQ¶V VSHHFK LV SRVVHVVLRQ DE  D 7KDW¶V P\ PXP QRW \RXUV  E ,W¶V 3DXO¶V EURWKHU QRW &KDUOHV¶  ,W LV ZRUWK QRWLFLQJ WKDW WKH PRVW SURPLQHQW LQIRUPDWLRQ LV RQ WKH VHFRQG DF WDQW DV ZH DOUHDG\ KDYH VKRZQ LQ   +RZHYHU WKHUH DUH VSHFLDO FRQVWUXFWLRQV WKDW FDQ FRQILJXUH WKHVH WUDMHFWRULHV GLIIHUHQWO\ ,Q SDUWLFXODU WKHUHFRQVWUXFWLRQV DUH IUHTXHQW LQ HDUO\ FKLOG ODQJXDJH /DNRII   



&KDSWHU )RXU

F 7KHUH DUH P\ VKRHV QRW P\ VRFNV  G 7KHUH LV /L]D QRW 3DXO  D 0\ VKRHV DUH WKHUH QRW LQ WKH JDUGHQ  E /L]D LV WKHUH QRW DW KRPH  $QDORJRXV FRQVWUXFWLRQV FDQ EH SXW DW ZRUN WKURXJK WKH XVH RI KHUH H +HUH¶V D JLIW QRW D FDNH  F 3DXO LV KHUH QRW LQ KLV RIILFH  /HW WKH FRQVWUXFWLRQV H[HPSOLILHG LQ  EH H[WHUQDO HUHFRQVWUXFWLRQV ZKLOH WKH FRQVWUXFWLRQV LQ  ZLOO EH LQWHUQDO HUHFRQVWUXFWLRQV E\ FRQWUDVW 7KH WHUPV µH[WHUQDO¶ DQG µLQWHUQDO¶ UHIHU WR WKH SUR[LPLW\ RI WKH FLUFXPVWDQWLDO JURXS HQGLQJ LQ HUH WR WKH YHUEDQW p p
→A
→A
ǫA
K A

I22 AAp

E > I22AAp
←A
→A HUH
ǫA P\ VKRHV
ǫ A E

I2 AAp 2 Y

I1 AAp 2 A

←A   ←
WKA
ǫA X

Y

I2 AA E > I2AA 1

△

HUH

DUH

3DXO

LV

E

I

X

I2

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

7UDQVIRUPDWLRQV



&RQVWUXFWLRQV EDVHG RQ KDEHUH 7KH YHUE KDEHUH LV D OX[XU\ WKDW QRW PDQ\ ODQJXDJHV RI WKH ZRUOG LQKHULWHG IURP /DWLQ (YHQ ZLWKLQ 6WDQGDUG $YHUDJH (XURSHDQ PRVW 6ODYLF ODQJXDJHV GR QRW VKRZ DX[LOLDU\ KDEHUHFRQVWUXFWLRQV 7KLV LV HYHQ PRUH WUXH RXW RI WKDW 6SUDFK EXQG IRU LQVWDQFH 7XUNLVK XVH YDUFRQVWUXFWLRQV DQG \RN FRQVWUXFWLRQV WR H[ SUHVV UHVSHFWLYHO\ RZQHUVKLS DQG ODFN RI RZQHUVKLS 

NHGL FDW

P P\

YDU EHWKHUH

)LJXUH  VKRZV WKH DGSRVLWLRQDO WUHH RI WKH 7XUNLVK SKUDVH NHGLP YDU XVXDOO\ DQG ULJKWO\ WUDQVODWHG LQ (QJOLVK DV µ, KDYH JRW D FDW¶ %XW WKHUH LV QR KDEHUHFRQVWUXFWLRQ KHUH UDWKHU D µEHWKHUH¶ YDU ZLWK D PRUSKHPH PDUNLQJ possession DQG person: 1st , singular P 

p
→A
ǫA

I22 AAp
←A P
ǫA Y

I2 AA 1 NHGL

YDU

X

I2

)LJXUH  $GWUHH RI 7XUNLVK NHGLP YDU ,Q (QJOLVK JUDPPDUV WKH SURSHU XVH RI WR KDYH PHDQLQJ possess LV GLVWLQ JXLVKHG E\ WKH DX[LOLDU\ FRQVWUXFWLRQV G  VHH $OH[DQGHU  ±  D 3DXO KDV D %HQWOH\ E 3DXO KDV JRW D %HQWOH\ F 3DXO KDV JRW D )RUG G 3DXO KDV ZDVKHG KLV FDU ,Q RXU SHUVSHFWLYH WKH XVDJH RI WR KDYH HLWKHU SURSHUO\ RU DX[LOLDU\ UDLVHV YHU\ VLPLODU FRQVWUXFWLRQV LQGHHG ,W LV LQWHUHVWLQJ WR QRWH WKDW LQ %ULWLVK (QJOLVK WKH FRQVWUXFWLRQ LQYROYLQJ WKH SHUIHFW IRUP RI WR JHW E LV HTXLYDOHQW WR WKH



&KDSWHU )RXU

SODLQ IRUP D  ZKLOH LQ $PHULFDQ (QJOLVK E LV D PDUNHG IRUP ZKHUH WKH SRVVHVVLRQ E\ WKH $PHULFDQ 3DXO RI KLV )RUG LV perfect LH SHUKDSV 3DXO QRZ GRHV QRW SRVVHVV D )RUG DQ\PRUH 7KH UHDGHU LV LQYLWHG WR QRWLFH WKDW WKH DGSRVLWLRQDO WUHHV RI WKH KDYHJRW FRQVWUXFWLRQ E DQG WKH VWDQGDUG DX[LOLDU\ KDEHUHFRQVWUXFWLRQ G DUH SUHWW\ WKH VDPH²VHH )LJXUH  OHIW ,W LV ZRUWK QRWLFLQJ WKDW WKH DGMHFWLYDWLRQ SHUIRUPHG E\ WKH Participle FRQVWUXFWLRQ DFWLYDWHG E\ HG WKH DVSHFW Perfect LH FRPSOHWHG DFWLRQ DQG WKHUHIRUH LW LV D SUHGLFDWLYH DGMHFWLYH →  1RQHWKH OHVV DV WKH DX[LOLDU\ VHFRQG DFWDQW Yaux LV RPLWWHG WKLV IDFW LV QRW SHUFHLYHG E\ WKH VSHDNHU²WKH RSSRVLWH ZRXOG EH WUXH LI WKH VHQWHQFH ZHUH 3DXO KDV KLV FDU ZDVKHG  WKLV ODVW FDVH ZH ZLOO VHH LQ 6HFWLRQ  GHYRWHG WR FRUUHODWLYHV

q q
A
A
← A
← A ǫ ǫ
2 A
2 A I2 I2
A
A
Aq
Aq
A

A
→A
→


A ǫ ǫ
2 A

2 A
I1 I1



A A q



q A A
A A
3DXO 3DXO KDV KDV A
→ A
→ 2 2 ǫ ǫ X X I I aux aux aux
aux
Y A Yaux A aux A
A
A
q A
q
A
A   →A
→ A
ǫ HG Y Y aux aux
2 A A
2
I2 > A A
I2 > A A
Aq Aq

A
A A
→ A
→ D %HQWOH\ KLV FDU ǫ ǫ A

2 2 A Ymean Y mean
I1 A
I1 A A
A
    3DXO JRW ZDVK 3DXO

△

△

Xmean

I2mean

Xmean

I2mean

)LJXUH  7KH DGWUHHV RI 3DXO KDV JRW D %HQWOH\ DQG 3DXO KDV ZDVKHG KLV FDU $V ZH KDYH DOUHDG\ VHHQ DERXW DX[LOLDU\ HVVHFRQVWUXFWLRQV DOVR DX[LOLDU\ KDEHUHFRQVWUXFWLRQV DUH FRPSOH[ DV WKH\ LQYROYH SKUDVHV WXUQHG LQWR VWDWLYHV LH KLGGHQ SUHGLFDWLRQV²VHH JRW F DQG ZDVKHG G  7KH VHFRQG DF

7UDQVIRUPDWLRQV



WDQW EHORQJLQJ WR WKH DX[LOLDU\ FRQVWUXFWLRQ Yaux LV RPLWWHG EXW WKH IDFW WKDW DQ DGMXQFWLYH SUHGLFDWLRQ LV DW ZRUN LV QRW WKDW LV ZK\ WKH DGWUHH VLJQV LW H[SOLFLWO\ 7KHVH KLGGHQ SUHGLFDWLRQV KDYH JRW H[SOLFLW LQ HI  H

−−→ Xact 3DXO

I2mean JRW

I

−−→ Xact 3DXO

I2mean ZDVKHG

←−− Yact D )RUG ←−− Yact KLV FDU

7KH UHDGHU LV LQYLWHG WR QRWH WKDW WKH VWUXFWXUH RI WKH SUHGLFDWLRQV EHLQJ KLGGHQ LV VWLOO UHFRJQLVDEOH ,Q IDFW WKH KDEHUHFRQVWUXFWLRQV LQ (QJOLVK UHWDLQ WKH VHFRQG DFWDQW RI WKH DFWLYH FRQVWUXFWLRQ RI WKH PHDQLQJIXO YHUE Yact  ZKLOH LWV ILUVW DFWDQW LV RPLWWHG EHLQJ WKH VDPH RI WKH KDEHUHFRQVWUXFWLRQ ,Q 5RPDQFH ODQJXDJHV²VXFK DV ,WDOLDQ²WKH FKRLFH EHWZHHQ HVVH DQG KD EHUHFRQVWUXFWLRQV ZLWKLQ WKH VDPH PHDQLQJIXO YHUE KDV VRPH LQWHUHVWLQJ DQG QRQ LPPHGLDWHO\ HYLGHQW FRQVHTXHQFHV D 3DROD KD FRUVR OD PDUDWRQD HQWUR TXDWWUR RUH E 3DROD q FRUVD D FDVD F 3DROD q FRUVD OD PDUDWRQD HQWUR TXDWWUR RUH G ""3DROD KD FRUVD OD PDUDWRQD HQWUR TXDWWUR RUH ,Q DE D FRQVWUXFWLYH SDLU RI H[DPSOHV LV VKRZQ WKH PHDQLQJIXO YHU EDQW LV D SDVW SDUWLFLSOH RI WKH YHUE µWR UXQ¶ FRUUHUH  7KH VHFRQG DFWDQW RI WKH PHDQLQJIXO YHUE FDQ EH H[SUHVVHG RQO\ LI WKH SURSHU KDEHUHFRQVWUXFWLRQ LV DW ZRUN RWKHUZLVH WKH UHVXOW LV VWULFWO\ XQJUDPPDWLFDO F  0RUHRYHU ZLWKLQ WKH KDEHUHFRQVWUXFWLRQ QRUPDOO\ WKH SDVW SDUWLFLSOH FRUVR GRHV QRW DJUHH ZLWK WKH JHQGHU RI WKH ILUVW DFWDQW²WKDW LV ZK\ G LV QRW DFFHSWDEOH H[FHSW SHU KDSV LQ FDVH RI UHDOO\ VXEVWDQGDUG PDUNHG UHJLVWHUV RI WKH ,WDOLDQ ODQJXDJH 7KH DGWUHHV RI DE DUH TXLWH GLIIHUHQW²FRPSDUH )LJXUH  DQG  6RPH REVHUYDWLRQV FDQ EH GRQH (YHQ LI 3DROD LV D SURSHU QDPH femminile µIHP LQLQH¶  LW GRHV QRW DJUHH ZLWK WKH participio µSDUWLFLSOH¶ LQ WKH KDEHUHFRQVWUXF WLRQ D  ZKLOH DJUHHPHQW LV UHTXLUHG LQ WKH HVVHFRQVWUXFWLRQ E  )XU WKHUPRUH WKH VWUXFWXUH RI WKH KLGGHQ SUHGLFDWLRQ KDV D UHOHYDQW HOHPHQW RI GLIIHU HQFH LQ IDFW WKH VHFRQG DFWDQW RI WKH PHDQLQJIXO YHUE Ymean FDQ EH H[SUHVVHG OD PDUDWRQD RU RPLWWHG  LQ D 



&KDSWHU )RXU

q
A
←A
HQWUR2A
E > I2 A
q A
A A
← A A ǫ
O A A
A A
Aq A
A A TXDWWUR A
← A H A A
A
O A A
>plurale@ A Aq
A  RU
← A ǫ O O
2 A
I2 A
A
A
A
A
A
Aq q
A
A →A
→ A
ǫ ǫ
Y A
2 A I1 aux
A
A q
A
q A
A
A  KD
←
→ A A D V Yaux I2

A A X A

A A
>femminile@A
>participio@Aq
A  R 3DRO A
← ǫ X A X
2 A I2 >maschile@
A Aq

A A OD PDUDWRQD
→ ǫ
2 A Y I1 A
A


△

△

   3DROD X

△

 FRU UH I2mean

)LJXUH  7KH DGWUHH RI 3DROD KD FRUVR OD PDUDWRQD HQWUR TXDWWUR RUH

7UDQVIRUPDWLRQV

q
A
←A
D 2A
E > I2 A
A q A
A A
←A A
D A O A
A Aq A

A  FDV
→A O O
ǫ2 A
I2 A A

A
A
A
A Aq
q
A
A
←A
→A
ǫ2 A
ǫ A
I1 A
Yaux A A A q
q

A
A q 
←A
→A I2 Yaux
D A
V A X A
A
A
>femminile@A
>participio@ A q
A 3DRO  D
→A X X A
ǫ2 A >femminile@
I2 A
Aq
A 
←A Ymean
ǫ2 A
I1 A
A  FRU UH    3DROD 2 Imean X

△

)LJXUH  7KH DGWUHH RI 3DROD q FRUVD D FDVD





&KDSWHU )RXU

$V D VLGH QRWH D UHYHDOV KRZ WKH QXPHUDO TXDWWUR µIRXU¶ UHTXLUHV WKH DFWLYDWLRQ RI WKH PRUSKHPH H ZKLFK SOXUDOLVHV WKH IHPLQLQH PRUSKHPH RU µKRXU¶  ,Q RUGHU WR KHOS WKH UHDGHU ZH KDYH UHZULWWHQ DE ZLWK D VSHFLDO HPSKDVLV RQ WKH PDLQ GLIIHUHQFHV

D

→ − X 3DROD 3DXOLQH

KD FRUVR UXQ

E

← − X 3DROD 3DXOLQH

q FRUVD UXQ

← − Y OD PDUDWRQD ZLWKLQ IRXU KRXUV

HQWUR TXDWWUR RUH

D FDVD KRPH

7KH GLFKRWRP\ µDWWULEXWLYH YV SUHGLFDWLYH¶ DGMHFWLYHV VWLOO UXOHV ZLWKLQ ,WDOLDQ KDEHUHFRQVWUXFWLRQV D 0DULR KD ODYDWR OD FDPLFLD 0 KDV ZDVKHG KLV VKLUW E 0DULR KD OD FDPLFLD ODYDWD 0 KDV KLV VKLUW JRW ZDVKHG )LJXUH  VKRZV WKH UHOHYDQW GLIIHUHQFHV EHWZHHQ D  WKH VWDQGDUG XQPDUNHG KDEHUHFRQVWUXFWLRQ DQG WKH PDUNHG FRQVWUXFWLRQ LH ZLWK WKH KLG GHQ SUHGLFDWLRQ SXW LQ HPSKDVLV ZLWK D GLIIHUHQW FROORFDWLRQ WKH GHSHQGHQF\ → EHWZHHQ WKH VWDWLYH OD FDPLFLD DQG WKH SDUWLFLSOH ODYDW^RD` WRJHWKHU ZLWK DJUHHPHQW DUH FOHDU VLJQV RI WKH SUHVHQFH RI GLIIHUHQW FRQVWUXFWLRQV DW ZRUN ,Q SDUWLFXODU E KLGHV D FRUUHODWLYH SUHGLFDWLRQ²VHH 6HFWLRQ  EHORZ

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

7UDQVIRUPDWLRQV



q
A
←A
ǫ2 A q
I2 A
A AAq
←A


ǫ2 A

A
I2 A

→A
AAq ǫ

2 A


I1 A

A AA

→A

q



ǫ2 A
A KD I1 A


←A 3DROR 2

AA I
ǫ A
q
X Y aux A

A KD AA
→A 3DROR

ǫ I2 A
X 
Yaux A ODYDWR OD FDPLFLD AA
Y aux
I2 > A >masch.@

△

△

△

△

△

ODYDWD

OD FDPLFLD

I2 > A >femm.@

>femm.@

Yaux

)LJXUH  7KH DGWUHHV RI 3DROR KD ^ODYDWR OD FDPLFLD  OD FDPLFLD ODYDWD`

LQJFRQVWUXFWLRQV DQG RWKHU JHUXQGV 7KH (QJOLVK LQJFRQVWUXFWLRQV DUH ³KDOIYHUE DQG KDOIQRXQ ZKLFK PDNHV WKHP D VHULRXV FKDOOHQJH IRU DQ\ WKHRU\ RI JUDPPDWLFDO VWUXFWXUH´ +XGVRQ    7KH FKDOOHQJH LV KRZ WR WUHDW WKLV VRUW RI µGRXEOH QDWXUH¶ +XGVRQ  XVHV H[DPSOHV IURP FRQWHPSRUDU\ DQG 2OG (QJOLVK LQ RUGHU WR GHDO ZLWK LQJ FRQVWUXFWLRQV DQG KH VWDWHV ,I ZH WKLQN RI D JHUXQG LQ WHUPV RI WKH SKUDVH WKDW LW KHDGV WKH IROORZLQJ JHQHUDOLVDWLRQ LV DOPRVW WUXH  $ SKUDVH KHDGHG E\ D JHUXQG LV D DQ RUGLQDU\ FODXVH DV IDU DV LWV LQWHUQDO VWUXFWXUH LV FRQFHUQHG EXW E DQ RUGLQDU\ QRXQ SKUDVH RU '3 LQ WHUPV RI LWV H[WHUQDO GLVWULEXWLRQ +XGVRQ   HPSKDVLV LQ WKH RULJLQDO 

,Q WKH WHUPV RI FRQVWUXFWLYH DGSRVLWLRQDO JUDPPDUV JHUXQGV LQ JHQHUDO DQG (QJOLVK LQJFRQVWUXFWLRQV LQ SDUWLFXODU DUH KLGGHQ SUHGLFDWLRQ 7KLV LPSOLHV WKDW



&KDSWHU )RXU

IURP WKH SRLQW RI YLHZ RI WKH JRYHUQLQJ SKUDVH WKH JHUXQG SOD\V WKH UROH RI VRPHWKLQJ GLIIHUHQW IURP D SUHGLFDWLRQ I  LQ SUDFWLFH WKH JURXS RI PRUSKHPHV SHUWDLQLQJ WR WKH JHUXQG WDNHQ DV D ZKROH SOD\V WKH UROH RI D VWDWLYH O  DQ DGMXQFWLYH A RU D FLUFXPVWDQWLDO E  ,Q WKH FDVH RI (QJOLVK LQJFRQVWUXFWLRQV WKH UROH SOD\HG LV PDLQO\ VWDWLYH O  DV QRWHG E\ +XGVRQ    0HHWLQJ SHRSOH LV HDV\

q
A
→A
ǫ2 A
I2 A A
q A
A A
→A A
ǫ A A
Yaux A Aq A
( ( A
( ( VRPHWKLQJ HDV\ (
←A Ybe A
ǫ2 A
I1 A A
q
A LV
→A I2be
LQJ A X be A
Aq

A 
←A D
ǫ2 A
I2 A
Aq A
SHRSOH
→A Ymeet
ǫ2 A
I1 A A
PHHW  I2meet Xmeet )LJXUH  7KH DGWUHH RI 0HHWLQJ SHRSOH LV HDV\

7UDQVIRUPDWLRQV



7KH JURXS RI PRUSKHPHV PHHWLQJ SHRSOH WDNHQ DV D ZKROH SOD\V WKH UROH RI WKH ILUVW DFWDQW RI WKH YHUEDQW LV ZKLOH ZLWKLQ LWV LQQHU VWUXFWXUH SHRSOH LV WKH VHFRQG DFWDQW LH ZKR LV PHW  ZKLOH WKH ILUVW DFWDQW ZKR PHHWV LV KLGGHQ E\ WKH LQJFRQVWUXFWLRQ LWVHOI²VHH )LJXUH  ,Q RUGHU WR KHOS WKH UHDGHU ZH KDYH XVHG VXEVFULSWV WR GLVWLQJXLVK WKH DFWDQWV EHORQJLQJ WR WKH LQJFRQVWUXFWLRQV OLNH Xmeet IURP WKH RQHV EHORQJLQJ WR WKH PDLQ H[SOLFLW FRQVWUXFWLRQ HJ Ybe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fix LV ZHOO KLGGHQ LQ WKH DGWUHH $OVR WKHUH LV D QHHG WR DYRLG WKH UHSHWLWLRQ RI WKH PDFKLQH DV D VHFRQG DFWDQW IRU IL[ :H ZLOO GHDO ZLWK JRDOV VXFK WKHVH LQ &KDSWHU  GHYRWHG WR FRQVWUXFWLYH SUDJPDWLFV 7KH VLJQ I22 > Yneed LV D FRPSDFW IRUP WR LQGLFDWH WKDW WKH SUHGLFDWLRQ RI IL[ LV KLGGHQ DV D VWDWLYH WKDQNV WR WKH XVH RI WKH DGSRVLWLRQ LQJ (QJOLVK LQJFRQVWUXFWLRQV FDQ DOVR SOD\ WKH UROH RI DGMXQFWLYHV EXW RQO\ DV WKH UHVXOW RI D IXUWKHU JUDPPDU FKDUDFWHU FKDQJH IURP VWDWLYH WR DGMXQFWLYH GHQRWHG E\ I > A  3DXO LV D ZRUNLQJ FODVV KHUR )LJXUH  VKRZV WKH DGSRVLWLRQDO WUHH RI WKH VHFRQG DFWDQW RI WKH HVVH FRQVWUXFWLRQ DV WKH UHVW GRHV QRW VKRZ DQ\WKLQJ QHZ²WKH FRPSOHWH DGWUHH EHLQJ OHIW WR WKH UHDGHU 7KH JHUXQG ZRUNLQJ LV D PRGLILHU RI FODVV DQG WKHQ ZRUNLQJ FODVV PRGLILHV WKH JRYHUQRU KHUR 3DUDSKUDVLQJ ZKDW VDLG E\ +XGVRQ   WKH (QJOLVK LQJFRQVWUXFWLRQ LV D KLGGHQ SUHGLFDWLRQ SOD\LQJ WKH UROH RI D VWDWLYH EXW KHUH WKLV UHVXOWLQJ VWDWLYH LV DJDLQ FKDQJHG LQ LWV JUDPPDU FKDUDFWHU E\ D IXUWKHU FRQVWUXFWLRQ ,Q IDFW WKLV RQH LV DQRWKHU H[DPSOH RI WKH VRFDOOHG µQRXQSOXVQRXQ¶ FRQVWUXFWLRQ D VRUW RI FROORFDWLRQDO 6D[RQ JHQLWLYH ZKHUH WKH PDUNHU ¶V JRW ORVW ZH KDYH DOUHDG\ VHHQ VXFK FRQVWUXFWLRQ²VHH DJDLQ )LJXUH  LI QHHGHG



&KDSWHU )RXU

q
A
←A
ǫ A
I22 A
A A q
A
A A
→A A
LQJ A A
I2 > YneedA 2 A A
A Aq
A
A ((( A
→A WKH(PDFKLQH ( ǫ A A
Yfix A
I21 A A A
Aq A

A IL[ (
→A ((( VRPHERG\ ( 2 Ifix
ǫ A Xfix
I21 A A
A


△

△

△

△

WKH PDFKLQH

QHHGV

Xneed >3 person@ >singular@

I2need >3 person@ >singular@

rd

rd

)LJXUH  7KH DGWUHH RI 7KH PDFKLQH QHHGV IL[LQJ

(QJOLVK LQJFRQVWUXFWLRQV FDQ SOD\ WKH UROH RI DWWULEXWLYH DGMXQFWLYHV DV MXVW VHHQ RU HYHQ SUHGLFDWLYH D 3DXO LV D GHDG PDQ ZDONLQJ E ""3DXO LV D ZDONLQJ GHDG PDQ ,Q D ZH VHH DQRWKHU SDUWLFXODU LQJFRQVWUXFWLRQ ,Q IDFW WKH JHUXQG ZDONLQJ LV SXW DIWHU WKH JRYHUQRU PDQ 7KLV FROORFDWLRQ LV D VLJQ RI DGMXQFWLYH SUHGLFDWLRQ²UHFDOO WKH GLVFXVVLRQ RI WKH UHOLFV RI /DWLQ ZLWKLQ ODQJXDJHV EHLQJ LQ FRQWDFW RU GLUHFWO\ GHVFHQGDQWV OLNH 3RUWXJXHVH LQ SDUWLFXODU VHH DJDLQ  DE LQ 6HFWLRQ  LI QHHGHG 7KLV IDFW LV WHVWHG WKURXJK E  ZKLFK LV

7UDQVIRUPDWLRQV



q
A
←A
ǫ A
Ybe A AAq


A D
←A A
ǫ A
A > Ybe A AA
q

A KHUR
←A Ybe
ǫ A
O A AA
q

A FODVV
→A O
LQJ A
I22 > O A AAq


A 
→A D ZRUN 
ǫ2 A Ywork
I1 A AA



△

△

 ZRUNHU  Xwork

ZRUN

I2work

)LJXUH  7KH DGWUHH RI D ZRUNLQJ FODVV KHUR

KDUGO\ DFFHSWDEOH ZLWKLQ WKH VDPH VFHQH ZKHUH WKH VDPH VWUXFWXUH²DQG KHQFH DGWUHH²RI  ZDV SXW DW ZRUN 7KH JURXS GHDG PDQ ZDONLQJ LV DQ LGLRPDWLF H[SUHVVLRQ DQG FRXOG EH FRQ VLGHUHG DV FRPSOHWHO\ XQSURGXFWLYH IUR]HQ LH ZKLFK FDQQRW EH IXUWKHU JUDP PDWLFDOL]HG ,Q WKLV FDVH WKH DGWUHH ZLOO EH UHGXFHG WR D VLQJOH OHDI %XW LI ZH VWLSXODWH WKDW WKH SOXUDO GHDG PHQ ZDONLQJ LV DFFHSWDEOH HYHQ LI QRW ZLGHO\ XVHG ZH FDQ FRQVLGHU WKLV FRQVWUXFWLRQ VWLOO DQDO\VDEOH LQ SDUWV )LJXUH  VKRZV H[DFWO\ WKLV LQWHUSUHWDWLRQ ZDONLQJ LV DQ DGMXQFWLYH ZKLFK PRGLILHV WKH JURXS GHDG PDQ WDNHQ DV D ZKROH²LQ IDFW LW KDV QR VHQVH WKDW ZDONLQJ PRGLILHV PDQ DORQH LI ZH FRQVLGHU WKH PHDQLQJ RI WKH ZKROH H[SUHVVLRQ 7KH FROORFDWLRQ RI



&KDSWHU )RXU

q
A
← A ǫ
Y A be
A
Aq
A D
→A A ZK A

A A
Aq
A

→ A
ǫ
Y A
be
A

A
q
A GHDG PDQ
→A I>A Ybe
LQJ A
O A
A R ZDON  Xwalk I1walk )LJXUH  7KH DGWUHH RI D GHDG PDQ ZDONLQJ

ZDONLQJ LQGLFDWHV WKDW WKH JHUXQG SOD\LQJ WKH UROH RI D VWDWLYH LQ LWVHOI EHFRPHV → −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ÎWDQ LH µLQ WKH RXW VLGH RI¶ 1RW DOO JHUXQGV LQ DOO ODQJXDJHV VKDUH WKH IHDWXUHV VHHQ IRU (QJOLVK )RU LQVWDQFH LQ ,WDOLDQ JHUXQGV SOD\ WKH UROH RI FLUFXPVWDQWLDOV GLUHFWO\ QRW RI VWD

7UDQVIRUPDWLRQV



r
A
←A
ZLWKRXWA
E>I A A
AA r


A
→A «
LQJ A I
I3 > O A 3
A AAr


A KLP
←A Z
ǫ A
I32 A A
AAr

(
A ((( VRPHWKLQJ (
←A Y
ǫ A
I31 A A
AA

  WHOO /L]D I33 X

△

)LJXUH  7KH DGWUHH RI ZLWKRXW WHOOLQJ KLP

WLYHV²IRU WKLV ODVW UROH ,WDOLDQ XVH LQILQLWLYH IRUPV )XUWKHUPRUH WKH WUDMHFWRU\ RI LQIRUPDWLRQ SURPLQHQFH RI WKH KLGGHQ YHUEDQW OHDGV WKH ODQJXDJH WR FKRRVH EHWZHHQ DQ HVVH RU KDEHUHFRQVWUXFWLRQ FKRLFH WKDW KDV D ORW RI FRQVHTXHQFHV D

$YHQGR WHOHIRQDWR /LVD 3DROR SLDQVH $IWHU WKH SKRQH FDOO E\ /L]D 3DXO FULHG

E WHOHIRQDWR /LVD 3DROR SLDQVH F

(VVHQGR SDUWLWD /LVD 3DROR SLDQVH $IWHU WKH OHDYLQJ E\ /L]D 3DXO FULHG

G

3DUWLWD /LVD 3DROR SLDQVH $IWHU WKH OHDYLQJ E\ /L]D 3DXO FULHG



&KDSWHU )RXU

r
A
→A
QGR A
I2 > E > IA A
2 A
A r

A
←A 3DROR SLDQVH
H A I
I2 A 2
>2a coniug.@A
A
Ar
A

→A

ǫ A

I2 A
1
A

A

A
r
A   K D { DY /LVD  
→A 2 Iaux Xaux
ǫ A
Yaux A
A
A r
A
A 
→A Yaux
A D { DWR

2 A
I2 > A A
>participio@ A
Ar 
A   3DROR
→A Y
ǫ A
I2 A 1 A
A
A


△

/LVD

WHOHIRQ

Xmean

I2mean

)LJXUH  7KH DGWUHH RI $YHQGR WHOHIRQDWR

7UDQVIRUPDWLRQV



r
A
→A
QGR A
I2 > E > IA A
2 AA

r
A
→A 3DROR SLDQVH
H A I
I22 A
>2a coniug.@A AAr


A

←A

ǫ A

I21 A
A

AA


r

A   HVV /LVD
→A I2aux Xaux
ǫ A
Yaux A A
AA
r

A 
→A Yaux
LW A
I1 > A A 1
>participio A @ AAr


A D
→A A
ǫ A >femminile@
I11 A
A AA



△

/LVD

SDUW

Xmean

I1mean

)LJXUH  7KH DGWUHH RI (VVHQGR SDUWLWD



&KDSWHU )RXU

,QILQLWLYH D OX[XU\ 7KH LQILQLWLYH FRQVWUXFWLRQ LV D OX[XU\ IHZ ODQJXDJHV LQ WKH ZRUOG SHUPLW WKHP VHOYHV IRU LQVWDQFH ZLWKLQ WKH %DONDQ 6SUDFKEXQG URXJKO\ IURP $OEDQLDQ WR 5RPDQLDQ  LW LV ORVW HYHQ LI WKHVH ODQJXDJHV EHORQJV WR WKH 6WDQGDUG $YHUDJH (XURSHDQ &RPULH    ,Q 5RPDQFH ODQJXDJHV WKH LQILQLWLYH RI /DWLQ VXUYLYHV LQ GLIIHUHQW IRUPV ,Q PRVW FDVHV WKH UROH SOD\HG E\ WKH LQILQLWLYH LV WR XVH WKH YHUE DV D VWDWLYH ZKLOH VRPH RU DOO DFWDQWV DUH KLGGHQ²WKH VDPH UROH RI (QJOLVK LQJFRQVWUXFWLRQ MXVW VHHQ DV JHUXQGV SOD\ WKH UROH RI FLUFXPVWDQWLDOV D

$ /LVD WR/L]D

E

$ /LVD WR/L]D

SLDFFLRQR OLNH3rd pers: plur

EDOODUH GDQFHInf

F

$ /LVD WR/L]D

SLDFL OLNH2nd pers: sing

EDOODUH GDQFHInf



3DROR 3DXO

SLDFH OLNH3rd pers: plur

YXROH ZDQWV

SURYDUH WU\Inf

EDOODUH GDQFHInf

DG DQGDUH JRInf

D IDUH GRInf

XQD YDFDQ]D D KROLGD\

,Q ,WDOLDQ SLDFH  DFWLYDWHV D FRQVWUXFWLRQ UHYHUVHG FRPSDUHG WR WKH (QJOLVK OLNH WKH ILUVW DFWDQW LV WKH LQILQLWLYH EDOODUH  ZKLOH ZKDW LV D VXEMHFW LQ (QJOLVK LV DQ REOLTXH²D VRUW RI GDWLYH²LQ ,WDOLDQ EHFDXVH RI WKH SUHVHQFH RI WKH SUHSRVLWLRQ D 7KLV H[DPSOH VKRZV WKDW WKH LQILQLWLYH FDQ SOD\ WKH UROH RI ZKDWHYHU DFWDQW HYHQ WKH ILUVW RQH )LJXUH   EF VKRZV WKDW WKH ,WDOLDQ LQILQLWLYH LV 3a persona: singolare µrd SHUVRQ VLQJXODU¶  $V ZH ZLOO VHH EHORZ RWKHU 5RPDQFH ODQJXDJHV PDUN WKH SHUVRQ RI WKH LQILQLWLYH H[SOLFLWO\ ,Q ,WDOLDQ LW LV SRVVLEOH WR QHVW DQ LQILQLWLYH LQWR DQRWKHU LQILQLWLYH UHFXUVLYHO\  VKRZV D UDWKHU H[WUHPH H[DPSOH EXW IRXQG LQ FROORTXLDO FRQWHPSRUDU\ ,WDOLDQ )LJXUH   ,W LV ZRUWK QRWLFLQJ WKDW WKH QHVWHG LQILQLWLYH VKRXOG EH KHDG E\ WKH SUHSRVLWLRQ D RU DG IRU SKRQRWDFWLF UHDVRQV  

/DPHQWR , UHJUHW

HOHV WKH\

WHU KDYH

HP Inf: 3rd -Pers: Pl

SHUGLGR ORVW

R FRPERLR WKH WUDLQ

6RPHWLPHV LQIRUPDWLRQ KLGLQJ LV RQO\ SDUWLDO ,Q WKH VR FDOOHG µLQIOHFWHG LQ ILQLWLYH¶ WKH person RI WKH ILUVW DFWDQW LV UHWDLQHG ZLWKLQ WKH LQILQLWLYH LWVHOI WKLV RFFXUV LQ 5RPDQFH ODQJXDJHV VXFK DV 3RUWXJXHVH *DOLFLDQ DQG 6DUGLQLDQ ZKLFK DUH FRQVHUYDWLYH LQ WKLV UHVSHFW 6FLGD    VKRZV DQ H[DPSOH LQ 3RU WXJXHVH IURP 0DGHLUD  ²VHH )LJXUH 

7UDQVIRUPDWLRQV



q
A
→A
D2 A
I2 A Aq

A /LVD
←A Y
ǫ2 A
I1 A A q

A SLDFH
→A I2
DUH A X piace
A >3 Pers: Sing@
Aq
A 
→A Y
ǫ2 A
I1 A A
  EDOO /LVD I2 X )LJXUH  7KH DGWUHH RI $ /LVD SLDFH EDOODUH

:KDW FDQ EH GRQH DEOHFRQVWUXFWLRQV 7KH DEOHFRQVWUXFWLRQ LQ (QJOLVK IRU H[DPSOH NQRZOHGJHDEOH²DORQJ ZLWK LWV DOORPRUSK LEOH HJ LQ FRUUXSWLEOH IRU SKRQRWDFWLF UHDVRQV²ZDV WDNHQ IURP /DWLQ EHFDXVH RI WKH ORQJ FRQWDFW ZLWK WKLV ODQJXDJH DQG )UHQFK 6WHLQ    ,W LV D JRRG H[DPSOH RI KLGGHQ SUHGLFDWLRQ DV DQ DGMHFWLYH RI FRXUVH RI WKH → − SUHGLFDWLYH W\SH I > A  ,WV IXQFWLRQ LV WR LQGLFDWH WKDW WKH VHFRQG DFWDQW LQ WKH DFWLYH FRUUHVSRQGHQW FRQVWUXFWLRQ Yact FDQ EH GRQH D

0DULR 0DULR

KD KDV

XQD FDPLFLD D VKLUW

ODYDELOH ZDVKDEOH

D VHFFR WR GU\

E 0DULR KD ODYDELOH XQD FDPLFLD D VHFFR F 0DULR KD XQD ODYDELOH FDPLFLD D VHFFR 7KH ,WDOLDQ VHQWHQFH D PHDQV µ0DULR KDV JRW D VKLUW ZKLFK FDQ EH GU\ FOHDQHG¶ ODYDUH D VHFFR EHLQJ D LGLRPDWLF FRQVWUXFWLRQ ZKHUH WKH IOH[LEOH SDUW LV



&KDSWHU )RXU

q
A
←A
ǫ2 A
I2 A
AAq


A

→A

ǫ2 A

I1 A AA

q


A 3DROR YXROH
→A DUH X I2
2 A I > Y
2 A AAq


A

→A

ǫ2 A

I1 A
AA


q

A   3DROR SURY
→A X I2
DG DUHA 2
I2 > Y A AAq



A

→A

ǫ2 A

I1 A AA q




A   3DROR DQG
→A D DUH X I2
2 A
I2 > Y A AAq


A
→A XQD YDFDQ]D
ǫ2 A Y
I1 A AA



△

3DROR

I

X

I2

)LJXUH  7KH DGWUHH RI 3 YXROH SURYDUH DG DQGDUH D IDUH XQD YDFDQ]D

7UDQVIRUPDWLRQV



q
A
→A
ǫ A
I22 A
A AA q


A
→A ODPHQWR
HP A I21
I2 > Ylam.A
A AAq



A

→A

ǫ A

I21 A

A AA
q



A HOHV WHU
→A Xter I2ter
ǫ A
Yter A A
AA

q
A 
→A Y ter
LGR A
I22 > A A A
AAq


A
→A R FRPERLR
ǫ A Yperd
I21 A
A AA

 HOHV SHUG  Xperd I2perd

△

△

)LJXUH  7KH DGWUHH RI /DPHQWR HOHV WHUHP SHUGLGR R FRPERLR



&KDSWHU )RXU

q
A
←A
ǫ2 A
I2 A Aq

A

→A

ǫ2 A

I1 A

A q

A 0DULR KD
→A ǫ X I2
Y A A
A q

A
→ A XQD FDPLFLD D
A A Y
A
Aq
A
→A VHFFR
ELO A I>A
A A Aq

A H
→A A
ǫ2 A >sing@
I2 A
Aq
A D
→A I
ǫ2 A >1a coniug@
I2 A
Aq
A (((
→ A (FDPLFLD XQD (
ǫ2 A Y
I1 A
A

△

△

△

0DULR

ODY

X

I2

)LJXUH  7KH DGWUHH RI 0DULR KD XQD FDPLFLD ODYDELOH D VHFFR

7UDQVIRUPDWLRQV



WKH YHUEDQW ODYDUH µWR ZDVK¶  ZKLOH D VHFFR LV IL[HG²VHFFR EHLQJ LWVHOI GHULYHG IURP WKH YHUE VHFFDUH DQG WKHUHIRUH LQ WKH DGWUHH LWV JUDPPDU FKDUDFWHU LV VLJQHG DSSURSULDWHO\ WKURXJK I > A EF VKRZ WKDW WKH FROORFDWLRQ RI WKH ,WDOLDQ FRQVWUXFWLRQ KHDG E\ DELOH LV IL[HG WKH DGMHFWLYH FRPHV PDQGDWRULO\ DIWHU WKH QRXQ RQ ZKLFK WKH KLGGHQ SUHGLFDWLRQ LV SHUIRUPHG 7KH FRUUHVSRQGHQW DGWUHH )LJXUH  KLGHV D FRUUHODWLYH FRQVWUXFWLRQ²VHH 6HFWLRQ  EHORZ 7KH DGSRVLWLRQ DELOH LV IXUWKHU DQDO\VDEOH LQ ,WDOLDQ EHFDXVH WKDW ODQJXDJH PDUNV WKH ILUVW FRQMXJDWLRQ DQG WKH RWKHU RQHV GLIIHUHQWO\²ZLWK D DQG L UHVSHF WLYHO\ ZKLOH LQ (QJOLVK WKH\ DUH UHOLFV FRPSOHWHO\ IL[HG LQ WKH PRUSKHPHV DEOH DQG LEOH  )XUWKHUPRUH WKH ILQDO VXIIL[ H LV D PDUNHU RI WKH VLQJXODU Sing 

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dep LV DOZD\V VWDWLYH ZKLOH WKH JRYHUQRU gov FDQ EH VWDWLYH RU YHUEDQW 

/H OLYUH WKH ERRN

GH RI

3LHUUH 3HWHU



8QH WDVVH D FXS

GH RI

WKp WHD



8QH VDOOH D URRP

GH RI

FODVVH FODVV

7KH H[DPSOHV DERYH VKRZ WKDW WKH JRYHUQRU RI WKH JURXS KHDG E\ GH LV DO ZD\V D VWDWLYH OH OLYUH µWKH ERRN¶   ZKLFK LQ (QJOLVK FRUUHVSRQGV WR WKH 6D[RQ JHQLWLYH 3HWHU¶V ERRN  XQH WDVVH µD FXS¶   VDPH FRQVWUXFWLRQ DV LQ (QJOLVK  XQH VDOOH µD URRP¶   ZKLFK LQ (QJOLVK FRUUHVSRQGV WR WKH FROOR FDWLRQDO 6D[RQ JHQLWLYH µQRXQSOXVQRXQ¶ FODVVURRP  7KH FRUUHVSRQGHQW DGWUHH LQ )LJXUH  DUH TXLWH REYLRXV QRZ WKH XVXDO FRPSDFW QRWDWLRQ IRU DWWULEXWLYH DGMHFWLYDWLRQ A > O ZDV VXEVWLWXWHG ZLWK WKH H[SOLFLW QRWDWLRQ DV WKH DWWHQWLRQ KHUH LV H[DFWO\ SXW RQ WKLV UHODWLRQ DQG DOVR DV WKHVH DGWUHHV DUH VPDOO HQRXJK



&KDSWHU )RXU

q
A
→ ǫA
O A AA
q

A
→A OH OLYUH A
GH O A AA

 3LHUUH D O

△

q
A
→ ǫA
O A AA
q

A
→ A XQH WDVVH A
GH O A AA

 WKp D O

△

q
A
→ ǫA
O A AA q


A
→A XQH VDOOH A
GH O A AA

 FODVVH D O

△

)LJXUH  $GWUHHV RI )UHQFK GH JRYHUQHG E\ VWDWLYHV

7KH VLWXDWLRQ LV GLIIHUHQW LI WKH JRYHUQRU LV D YHUEDQW LQ WKLV FDVH WKH SUHSR VLWLRQ GH LQWURGXFHV FLUFXPVWDQWLDOV EHORQJLQJ WR YDULRXV VHPDQWLF UROHV HJ instrument   manner   place   

-H pFULUH , ZULWH

GH ZLWK

OD PDLQ JDXFKH WKHOHIWKDQG



-H UpSqWH , UHFLWH

GH IURP

PpPRLUH PHPRU\



/H WUDLQ WKH WUDLQ

SDUWL GH FRPH IURP

3DULV« 3DULV«

3OHDVH QRWH WKDW WKH (QJOLVK WUDQVODWLRQV RI WKH SUHSRVLWLRQ GH LQ WKH H[DPSOHV DERYH DUH LQGLFDWLYH LW LV QRW SRVVLEOH WR WUDQVODWH WKH SUHSRVLWLRQ ZLWKRXW WKH FRQFHUQHG VWDWLYH EHFDXVH RI JUDPPDWLFDOL]DWLRQ )RU LQVWDQFH WKH )UHQFK GH PpPRLUH LQ  LV DQ LGLRP OLNH WKH (QJOLVK FRQVWUXFWLRQV IURP PHPRU\ RU E\ KHDUW²SOHDVH QRWH WKH GLIIHUHQW SUHSRVLWLRQV +RZHYHU WKH (QJOLVKVSHDNLQJ VWXGHQW RI )UHQFK FDQ EH KHOSHG KHUH DV KH EHFRPHV DZDUH WKDW WKLV FODVV RI GH FRQVWUXFWLRQV LV FLUFXPVWDQWLDO LQVWHDG RI VWDWLYH DQG KH NQRZV WKLV IDFW VLPSO\ ORRNLQJ DW WKH JRYHUQRU )LJXUH  OHIW DQG PLGGOH  $ GLVFRXUVH DSDUW VKRXOG EH GRQH IRU   GHSLFWHG LQ )LJXUH  ULJKW KHUH D GHFRQVWUXFWLRQ LV QHVWHG LQWR D SUHGLFDWLYH DGMHFWLYDWLRQ JRYHUQHG E\ D Participe: Pass´e µSDUWLFLSOH SDVW¶  D W\SH RI FRQVWUXFWLRQ DOUHDG\ VHHQ EHIRUH (YHQ LI WKLV SDVW SDUWLFLSOH LV QRW H[SUHVVHG   WKH FRQVWUXFWLRQ FRQVHUYHV LWV WUDFH LQGHHG

7UDQVIRUPDWLRQV





q
A
←A
GH A
E A

△

AA

△

OD PDLQ JDXFKH MH pFULUH

O



q
A
→ ǫA
O A A
q
A
←A OH WUDLQ
GH O E A
A

q
A
←A A
GH E AA



△

△

PpPRLUH

MH UpSqWH

O

I

I

△

3DULV

O

△

 SDUWL  I>A pass´e@

>participe:

)LJXUH  $GWUHHV RI )UHQFK GH JRYHUQHG E\ YHUEDQWV

5HVXOWDWLYHV 5HVXOWDWLYH DUH FRQVWUXFWLRQV ZKHUH WKHUH LV D PDLQ SKUDVH UHVSRQVLEOH RI WKH DFWXDO DFWLRQ DQG D KLGGHQ SUHGLFDWLRQ ZKHUH WKH YHUEDQW LQGLFDWHV WKH UHVXOW RI WKH DFWXDO DFWLRQ :H ZLOO VLJQ WKURXJK DSSURSULDWH VXEVFULSWV ERWK WKH PDLQ SKUDVH HJ Imain DQG LWV UHVXOW HJ Iresult   /L]D ZLSHG WKH WDEOH FOHDQ ,Q  ZH KDYH DQ H[DPSOH LQ (QJOLVK 7KH PDLQ SKUDVH LV H[SOLFLW /L]D ZLSHG WKH WDEOH ZKLOH WKH UHVXOW FOHDQ LV WKH UHVLGXDO PRUSKHPH WKDW LQGLFDWHV WKH UHVXOW RI WKH KLGGHQ SKUDVH /L]D FOHDQ WKH WDEOH 7KH DGSRVLWLRQDO WUHH RI  LV LQ )LJXUH  7KH VXUYLYLQJ YHUEDQW PRU SKHPH FOHDQ LQGLFDWLQJ WKH UHVXOW EHFRPHV D SUHGLFDWLYH DGMHFWLYH RI WKH VHFRQG DFWDQW RI WKH PDLQ SKUDVH WKH WDEOH 7KH DGWUHH VKRZV²XQGHU WKH FDQFHOOHG PRU SKHPHV²WKH VWUXFWXUH RI WKH FRUUHVSRQGHQW FRUUHODWLYH SKUDVH ZKLFK LV ZULWWHQ H[SOLFLWO\ LQ FRUU  FRUU /L]D ZLSHG WKH WDEOH ZKLFK VKH FOHDQHG  5HVXOWDWLYHV DUH YHU\ SRZHUIXO FRQVWUXFWLRQV HYHU\WKLQJ LQVLGH WKHP JHWV KLGGHQ VDYH ZKDW LV UHDOO\ QHHGHG LH WKH YHUEDQW PRUSKHPH WXUQHG LQWR D SUHG LFDWLYH DGMHFWLYH D

X 3DXO

Imain KDV JRW

Y KLV FDU

→ − Iresult > A ZDVKHG



&KDSWHU )RXU

q
A
←A
ǫ A
I22 A A
Aq


A

→A

ǫ A

I21 A
A

q A

A /L]D
→A ZLSHG X A
 ZK I2
Y A A
A
q
A
→A WKH WDEOH A
 HG Y
A A A
Aq
A

→A D
ǫ A
I22 A A
Aq
A
 LFK 
→A Y
ǫ A
I21 A A
A
 FOHDQ VKH  I2 X

△

△

)LJXUH  7KH DGWUHH RI /L]D ZLSHG WKH WDEOH FOHDQ

7UDQVIRUPDWLRQV

E

X +H

Imain GURYH

Y KHU



→ − Iresult > A PDG

,W LV ZRUWK QRWLFLQJ WKDW HYHQ WKH VRFDOOHG µSVHXGRUHIOH[LYH¶ FRQVWUXFWLRQV LQ UHDOLW\ DUH RQO\ D VSHFLDO FDVH RI UHVXOWDWLYHV ZKHUH WKH KLGGHQ SUHGLFDWLRQ LV JRYHUQHG E\ DQ HVVHFRQVWUXFWLRQ ZKLFK JRW ORVW VHH H[DPSOHV E  

 7KH ZKLFK KXQW &RUUHODWLYHV DUH DOO WKRVH ZRUGV WKDW WUDQVIRUP D VHFRQGDU\ SKUDVH²RU HYHQ D VHQWHQFH LH D JURXS RI SKUDVHV²LQWR D VWDWLYH DQ DGMXQFWLYH RU D FLUFXPVWDQWLDO RI WKH PDLQ SKUDVH ,Q (QJOLVK VRPH RI WKHVH ZRUGV DUH ZKR LQWR VWDWLYH  ZKLFK LQWR DGMXQFWLYH  ZKHQ LQWR FLUFXPVWDQWLDO  %\ H[WHQVLRQ ZH ZLOO UHIHU WR WKH WUDQVIRUPHG VHFRQGDU\ SKUDVHV DV µFRU UHODWLYHV¶ WRR 7KH WHUP µUHODWLYH¶²XVHG LQ PDQ\ JUDPPDU WUDGLWLRQV²LQ RXU FRQWH[W LQGLFDWHV D VSHFLDO W\SH RI FRUUHODWLYHV :K\ ODQJXDJHV KDYH GHYHORSHG FRUUHODWLYHV" ,Q HYHU\ ODQJXDJH WKHUH DUH FODVVHV RI PRUSKHPHV GHYRWHG WR SXW LQWR UHODWLRQ WZR SKUDVHV WDNHQ DV VLQJOH OHDYHV /HW WKH PDLQ SKUDVH EH WKH JRYHUQRU Igov  ZKLOH WKH VHFRQGDU\ SKUDVH ZLOO EH WKH GHSHQGHQW Idep  7KH\ FDQ EH FODVVLILHG DORQJ WKHLU WUDMHFWRU\ RI LQIRUPDWLRQ SURPLQHQFH VRPH OHDYH WKH SURPLQHQFH XQGHUVSHFLILHG ↔  VRPH RWKHUV JLYH PRUH SURPLQHQFH WR WKH GHSHQGHQW SKUDVH →  ZKLOH RQ WKH FRQWUDU\ WKH DUH VRPH FRQMXQFWLRQV WKDW JLYH PRUH SURPLQHQFH WR WKH JRYHUQRU ←  6RPH H[DPSOHV RI (QJOLVK FRQMXQFWLRQV SHU W\SH DUH VKRZQ LQ 7DEOH 

D

Igov $OIUHG FDQ SD\ $OIUHG SHXW SD\HU $OIUHG SXz SDJDUH

← − I EHFDXVH SDUFH TXH SHUFKp

E

Igov $OIUHG FDQ SD\ $OIUHG SHXW SD\HU $OIUHG SXz SDJDUH

→ − I KHQFH GRQF GXQTXH

Idep KH LV ULFK LO HVW ULFKH q ULFFR Idep KH LV ULFK LO HVW ULFKH q ULFFR

,Q DE ZH KDYH SURYLGHG D PLQLPDO SDLU VKRZLQJ WKH GLIIHUHQW LQIRUPD WLRQ SURPLQHQFH KHDG E\ D VLQJOH FRQMXQFWLRQ RU LQ FDVH RI )UHQFK SDUFH TXH



&KDSWHU )RXU

7DEOH  6RPH (QJOLVK FRQMXQFWLRQV DQG WKHLU WUDMHFWRU\ → − ← → ← − WUDMHFWRU\ I I I H[DPSOHV EXW ERWK DQG ZKLOH LI HLWKHU RU KRZHYHU VR « « « SURPLQHQFH Idep I? Igov D JUDPPDWLFDOL]HG H[SUHVVLRQ  ,W LV ZRUWK QRWLFLQJ WKDW WKH VWUXFWXUH LV WKH VDPH LQ (QJOLVK )UHQFK DQG ,WDOLDQ²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

$ W\SRORJLFDO FRPSDULVRQ RI FRUUHODWLYHV ,I ZH ORRN DW FRUUHODWLYH DGSRVLWLRQ IURP D EURDG W\SRORJLFDO SHUVSHFWLYH ZH ZLOO QRWH WKDW WKHVH ZRUGV DUH IRUPHG E\ WZR SDUWV DQ DGSRVLWLRQ²XVXDOO\ WKH SUHIL[²ZKLFK LV DSSHQGHG WR WKH PDLQ SKUDVH Igov  DQG GRHV QRW FKDQJH DQG D IOH[LEOH SDUW²XVXDOO\ WKH ILQDO²ZKLFK DFWV DV D SURQRXQ LQ WKH FRUUHODWLYH SKUDVH Idep  )ROORZLQJ &LFHUR¶V WD[RQRP\ SURSRVHG LQ 'H LQYHQWLRQH D FODV VLF ZRUN DERXW UKHWRULFV ZKLFK KLJKO\ LQIOXHQFHG :HVWHUQ FXOWXUH 3HUHOPDQ DQG 2OEUHFKWV7\WHFD   ZH FDQ VKRZ D W\SRORJLFDO FRPSDULVRQ RI WKH PDLQ FRU UHODWLYHV 7DEOH  IL[HG SDUWV LQ EROG   1HYHUWKHOHVV WKLV GRXEOH QDWXUH RI WKH FRUUHODWLYH DGSRVLWLRQV DOVR VWDQGV RXW RI WKH :HVWHUQ FXOWXUH ,Q IDFW LQ 7DEOH  ZH KDYH LQWURGXFHG ERWK ODQJXDJHV

7UDQVIRUPDWLRQV



r
A
A ← A
EHFDXVH
I A
A
A Ar

A

A

←
ǫ A
I2 A
2

A

A Ar

r
A
A SD\
A
A → I>O
ǫ A
→ ǫ A
I2 A
I2 A 2 1
A
A
A
A A A r


A A $OIUHG FDQ
A A X I2gov
→ A ǫ A
Y A A
A A
A A
Ar A
A ULFK 
A A Y
→ ǫ A
I2 A 1
A
A A
KH

LV

X

I2dep

)LJXUH  7KH DGWUHH RI $OIUHG FDQ SD\ EHFDXVH



&KDSWHU )RXU

q
A
→A KHQFH
I A AAq


A

←
ǫA
I2 A
2 AAq


q

A
A SD\ →A
→ A
ǫ ǫ I>O
I2 A
I2 A 2 1 AA AA

q

A
A $OIUHG FDQ A
→ 2 ǫA X I gov A
Y A AAq AA


A ULFK 
→ ǫA A Y
I2 A 1 AA

KH

LV

X

I2dep

)LJXUH  7KH DGWUHH RI $OIUHG FDQ SD\ KHQFH

EHORQJLQJ WR WKH 6WDQGDUG $YHUDJH (XURSHDQ 6SUDFKEXQG DQG ODQJXDJHV EHORQJ LQJ WR RWKHU 6SUDFKEXQG HJ .LVZDKLOL EHORQJLQJ WR WKH %DQWX DQG 7XUNLVK EHORQJLQJ WR WKH 7XUNLVK ,W LV FOHDU WKDW UHJDUGOHVV RI WKH 6SUDFKEXQG ZH FDQ DOZD\V ILQG D IOH[LEOH DQG D IL[HG SDUW LQ DOPRVW HYHU\ FRUUHODWLYH :H VD\ µDOPRVW¶ EHFDXVH VRPHWLPHV JUDPPDWLFDOL]DWLRQ²LQIOXHQFHG E\ ODQJXDJH SROLF\ DQG SODQQLQJ LVVXHV LQ SDU WLFXODU WKH FKRLFH RI WKH ZULWLQJ V\VWHP²FDQ KDYH DV D VLGH UHVXOW WR PDNH WKLV VWUXFWXUDO GLIIHUHQFH RSDTXH ,Q WKRVH FDVHV ZH ZLOO SXW DQ HSVLORQ DFFRUGLQJO\ $ IXUWKHU FODULILFDWLRQ LV QHHGHG IRU WKH WD[RQRPLF HOHPHQW SHUVRQD ,Q VRPH ODQJXDJHV WKHUH LV D VHPHPH Animate LQ DFWLRQ HJ LQ (QJOLVK ZKR IRU DQLPDWH DQG ZKLFK IRU LQDQLPDWH  7KLV LV WKH FDVH RI (QJOLVK ,WDOLDQ &DWDODQ )UHQFK ,QGRQHVLDQ 7XUNLVK ,Q RWKHU FDVHV WKLV GLVWLQFWLRQ VLPSO\ GRHV QRW KROG DV LQ *HUPDQ 'XWFK /DWLQ 3ROLVK /LWKXDQLDQ DQG -DSDQHVH )LQDOO\ LQ .LVZDKLOL WKHUH LV D VXEWOH GLVWLQFWLRQ LQ WKLV VHQVH DV WKH IOH[

7UDQVIRUPDWLRQV



7DEOH  $ W\SRORJLFDO FRPSDULVRQ RI WKH PDLQ FRUUHODWLYHV /DQJXDJH

SHUVRQD

IDFWXP

FDXVD

ORFXV

WHPSXV

PRGXV

(QJOLVK

ZK^LFK|R`

ZKDW

ZK\

ZKHUH

ZKHQ

KRZ

*HUPDQ

ZHU

ZDV

ZDUXP

ZR

ZDQQ

ZLH

'XWFK

ZLH

ZDW

ZDDURP

ZDDU

ZDQQHHU

KRH

/DWLQ

TXLV

TXLG

^TXDUH

XEL

TXDQGR

TXR

|FXU`

PRGR

,WDOLDQ

^TXDOH|FKL`

FRVD

SHUFKp

GRYH

TXDQGR

FRPH

&DWDODQ

^TXDO|TXL`

TXq

SHU TXq

RQ

TXDQ

FRP

)UHQFK

^TXHO|TXL`

TXRL

SRXU

R

TXDQG

FRP

TXRL

PHQW

3ROLVK

NXULV

NDV

NR˙ GHO

NXU

NDGD

NDLS

/LWKXDQLDQ

NWR

FR

GODF]HJR

JG]LH

NLHG\

MDN

,QGRQHVLDQ

^\DQJ PDQD

DSD

PHQJ

GL

NDSDQ

EHW

DSD

PDQD

^QL\H

^QHUH

QH

|QHGHQ

|KDQL`

]DPDQ

GRNR

LWVX

|VLDSD` 7XUNLVK

^KDQJL|NLP`

QH

DSD QDVÕO

|QLoLQ` -DSDQHVH

GRQR

GRUH

GR

VKLWH

.LVZDKLOL

DPED

^\H|\R

QLQL

GR

FKLUD

NZD

DPED

QLQL

^SR

|R|OR|FKR

|NR

|Y\R|]R`

|PR`

ZDNDWL

MLQVL JDQL



&KDSWHU )RXU

LEOH SDUW DSSHQGHG WR WKH IL[HG DPED LQYROYHV QRW RQO\ DQLPDWHQHVV EXW DOVR DJUHHPHQW ZLWK JHQGHU DQG QXPEHU DQG IXUWKHUPRUH LW LQWURGXFHV WKH ORFDWLYH 7RVFDQR DQG 6HZDQJL   ,Q WKH QH[W VHFWLRQV ZH ZLOO GHDO ZLWK FRUUHODWLYHV LQ GHWDLOV $V DOUHDG\ VDLG WKH IXQFWLRQ RI D FRUUHODWLYH DGSRVLWLRQ LV WR WUDQVIRUP D GHSHQGHQW SKUDVH Idep LQWR DQ DGMXQFWLYH A  FLUFXPVWDQWLDO E RU VWDWLYH O HOHPHQW ,W LV ZRUWK QRWLFLQJ WKDW FRUUHODWLYH DGSRVLWLRQV DUH SUHGLFDWLYH DQG WKHUHIRUH WKH\ UHWDLQ WKH LQIRUPDWLRQ SURPLQHQFH LH WKHLU WUDMHFWRU\ LV RI GHSHQGHQF\

$GMXQFWLYH FRUUHODWLYHV ,Q &RPULH¶V DQDO\VLV RI UHODWLYH FODXVH IRUPDWLRQ D FODVVLF LQ WKH OLWHUDWXUH ZH ILQG D VHW RI H[DPSOHV WKDW KHOS XV WR VHH KRZ WKH DGSRVLWLRQDO WUHHV RI DGMXQFWLYH FRUUHODWLYHV DUH VWUXFWXUHG 7KHVH H[DPSOHV DUH LQ (QJOLVK DV ³(QJOLVK SUHVHQWV HVVHQWLDOO\ QR HYLGHQFH RI DQ\ NLQG RI UHVWULFWLRQ VLQFH LW LV SRVVLEOH WR UHODWLYL]H RQ IRU LQVWDQFH VXEMHFW GLUHFW REMHFW QRQGLUHFW REMHFW DQG SRVVHVVRU LQ WKH SRVVHVVLYH FRQVWUXFWLRQ´ &RPULH    D WKH PDQ >ZKR ERXJKW WKH ERRN IRU WKH JLUO@ E WKH ERRN >ZKLFK WKH PDQ ERXJKW IRU WKH JLUO@ F WKH JLUO >IRU ZKRP WKH PDQ ERXJKW WKH ERRN@ G WKH ER\ >ZKRVH ERRN WKH PDQ ERXJKW IRU WKH JLUO@ 7KH YHUE WR EX\ LV TXDGULYDOHQW LQ WKH GHIDXOW DFWLYH VDWXUDWHG FRQVWUXFWLRQ WKH ILUVW DFWDQW LV WKH Buyer D  )LJXUH   WKH VHFRQG RQH WKH Object to Be Bought E  )LJXUH   WKH WKLUG RQH WKH Seller WKH IRXUWK DF WDQW EHLQJ WKH Price :LWK D GLIIHUHQW DUUDQJHPHQW WKH VDPH DFWDQWV DUH YDOLG LQ YHUEV OLNH WR VHOO  ,Q F WKH WKLUG DQG IRXUWK DFWDQWV DUH RPLWWHG ZKLOH DQ H[WHUQDO FLUFXPVWDQWLDO LV LQVHUWHG LH WKH JLUO ZKLFK H[SUHVV WKH Benefactive VHPHPH²KHUH WKHUH LV D GRQDWHOLNH SUHGLFDWLRQ FRPSOHWHO\ KLGGHQ ,W LV LQWHU HVWLQJ WKDW LQ (QJOLVK WKH Benefactive FDQ EH UHIHUUHG E\ WKH IOH[LEOH SDUW RI WKH FRUUHODWLYH DGSRVLWLRQ F  )LJXUH   ZKLOH WKH Price FDQQRW H WKH ERRN >IRU  SRXQGV WKH PDQ ERXJKW IRU WKH JLUO@ )XUWKHUPRUH LQ G WKH VHPHPH UHIHUUHG E\ WKH FRUUHODWLYH LV WKH Possessor ZKLFK LV RQH RI WKH PRVW LPSRUWDQW VHPHPHV LQ DOO ODQJXDJHV RI WKH

7UDQVIRUPDWLRQV



ZRUOG²VHH )LJXUH  DEFG VKRZ WKDW WKH JUDPPDU FKDUDFWHU RI ZK EHORQJV WR WKH FODVV RI SUHGLFDWLYH DGMHFWLYHV

r
A
→A
ZK A
I > A > OA
A
A
r A
A
→A WKH PDQ
IRU A O
E>I A A
A
Ar

A
←A WKH JLUO
ǫ A O
I42 A
A
A
Ar
A
→A WKH ERRN
ǫ A Y
I41 A
A
A
A

△

△

△

△

R

X

ERXJKW

I4dep

)LJXUH  7KH DGWUHH RI WKH PDQ ZKR ERXJKW WKH ERRN IRU WKH JLUO

&LUFXPVWDQWLDO FRUUHODWLYHV &RUUHODWLYHV H[SUHVVLQJ Time DUH PRUH OLNHO\ WR EH DSSHQGHG WR WKH PDLQ SKUDVH Igov DV FLUFXPVWDQWLDOV EHFDXVH QRUPDOO\ VHPHPHV H[SUHVVLQJ Time DUH QRW SDUW RI WKH LQYDOHQW DUJXPHQWV D >:KHQ 3DXO ZLOO FRPH EDFN@ /L]D ZLOO VPLOH



&KDSWHU )RXU

q
A →A
ZK
A > OA A q

A →A
IRU WKH ERRN
E > IA O
Aq
A
← WKH JLUO ǫA
I42 A O
Aq
A
→ LFK ǫA
I41 A Y A


△

△

△

△

△

WKH PDQ

ERXJKW

X

I4dep

)LJXUH  7KH DGWUHH RI WKH ERRN ZKLFK WKH PDQ ERXJKW IRU WKH JLUO

q
A →A
ZK
A > OA A q

A →A
IRU WKH JLUO
E > IA O
Aq
A
← RP ǫA
I4 A O
2 Aq
A → WKH ERRN
ǫ A
I4 A Y
1 A

△

△

△

WKH PDQ

X

△

ERXJKW

I4dep

)LJXUH  7KH DGWUHH RI WKH JLUO IRU ZKRP WKH PDQ ERXJKW WKH ERRN

7UDQVIRUPDWLRQV



q
A
→A
ZK A
A>O A A
q
A
→A WKH ER\
IRU A O
E>I A Aq

A
←A WKH JLUO
ǫ4 A O
I2 A
Aq

A

→A

ǫ4 A

I1 A A
q

A
→A ERXJKW WKH PDQ
ǫ A I4dep X Y
A
A

△

△

△

RVH

ERRN

A

Y

△

)LJXUH  7KH DGWUHH RI WKH ER\ ZKRVH ERRN WKH PDQ ERXJKW IRU WKH JLUO

E >7RPRUURZ@ /L]D ZLOO VPLOH )LJXUH  VKRZV WKH DGSRVLWLRQDO WUHH RI D  )URP WKH SRLQW RI YLHZ RI WKH PDLQ SKUDVH WKH ZKROH FRUUHODWLYH :KHQ 3DXO ZLOO FRPH EDFN LV D FLUFXP VWDQWLDO HTXLYDOHQW WR WRPRUURZ RI E  VDYH IRU VHPDQWLFV

6WDWLYH FRUUHODWLYHV 6RPHWLPHV D FRUUHODWLYH SKUDVH GLUHFWO\ SOD\V WKH UROH RI DQ DFWDQW ,Q WKRVH FDVHV WKH H[WHUQDO JUDPPDU FKDUDFWHU RI WKH FRUUHODWLYH ZLOO EH VWDWLYH ZKLOH WKH LQWHUQDO JUDPPDU FKDUDFWHU FDQ EH VWDWLYH DGMXQFWLYH RU FLUFXPVWDQWLDO DOLNH D , ZRQGHU >KRZ PDQ\ HUURUV , GLG@



&KDSWHU )RXU

q
A
→A
ZK A
E > I11 A A
Aq

A

→A

ǫ A

I11 A
A

A

q
A /L]D
←A ZLOO VPLOH X
ǫ A I1
I11 A A
Aq

A HQ
→A E
ǫ A
I11 A
A
Aq
A 3DXO
→A X
ǫ A
I1 A
A
A

△

EDFN

E

△

ZLOO FRPH

I1

)LJXUH  7KH DGWUHH RI :KHQ 3DXO ZLOO FRPH EDFN /L]D ZLOO VPLOH

7UDQVIRUPDWLRQV



E >:KDW WLPH@ LV LW" )RU LQVWDQFH LQ D WKH LQWHUQDO FRUUHODWLYH LV D FLUFXPVWDQWLDODGMXQFWLYH UHODWLRQ²VHH )LJXUH  DQG 6HFWLRQ  DJDLQ LI QHHGHG 7KH WUDMHFWRULHV DUH DGMXVWHG DFFRUGLQJO\ DV WKH PRVW SURPLQHQW LQIRUPDWLRQ LV SXW LQ KRZ PDQ\ ,Q E WKH PRVW SURPLQHQW DFWDQW²WKH VHFRQG RQH LQ DQ HVVHFRQVWUXF WLRQ²LV WDNHQ E\ WKH FRUUHODWLYH ZKLOH WKH LQWHUURJDWLYH FRQVWUXFWLRQ UHYHUVH WKH FROORFDWLRQ RI WKH DFWDQWV WKHPVHOYHV )LJXUH  

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µGHPRQVWUDWLYHV¶ $OH[DQGHU  IRU (QJOLVK  :KDW LV LQWHUHVWLQJ IRU XV LV WKHLU PRUSKRORJ\ WKH IOH[LEOH SDUW FRUUHVSRQGV WR WKH W\SHV XVHG EHIRUH LH SHUVRQD IDFWXP HWF ZKLOH WKHUH LV D IL[HG SDUW ZKRVH IXQFWLRQ LV H[DFWO\ WR EH D FRUUHODWLYH DQVZHU )RU WKLV UHDVRQ LQ )LJXUH  OHIW  ZKLFK LOOXVWUDWHV WKH DGSRVLWLRQDO WUHH RI F  WKH ZRUG WKHUH ZDV DQDO\VHG DV WKHUH WK EHLQJ WKH IL[HG FRUUHODWLYH DQVZHU ZKLOH HUH H[SUHVVHV WKH Locative 7KLV NLQG RI DQVZHU LV GHLFWLF LH WKH VHPHPH²HJ H[SUHVVLQJ ORFDWLRQ SHUVRQ IDFW DQG VR RQ²FDQ EH LQGLYLGXDWHG ZLWK SUHFLVLRQ ,Q WKLV VHQVH ZH VD\ WKDW WK LV D FRQVWUXFWLYH H[LVWHQWLDO FRUUHO DWLYH DQVZHU ∃  %\ FRQWUDVW WKHUH DUH QRQFRQVWUXFWLYH H[LVWHQWLDO DQVZHUV ∃ LQ (QJOLVK OLNH VRPH RU PDQ\ ,Q (QJOLVK XQFRXQWDEOH QRXQV UHIHU WR D FODVV RI HOHPHQWV ZKRVH H[LVWHQFH LV QRQFRQVWUXFWLYH IRU LQVWDQFH WKH ZRUG SHRSOH UHIHUV WR D FODVV RI SHUVRQV EXW WKH LQGLYLGXDOV WKDW IRUP SHRSOH FDQQRW EH IRXQG ZLWK SUHFLVLRQ LH LW LV LPSRVVLEOH WR QDPH DQ LQGLYLGXDO RI WKH FODVV



&KDSWHU )RXU

q
A
→A
K A
I22 A AAq


A

→A

ǫ2 A

I1 A
AA q




A , ZRQGHU
→A ǫ X I2gov
2 A
I2 > O A
AAq


A

←A

ǫ2 A

I1 A AA

q


A , GLG
→A 2 ǫ X I
A dep Y
A AA
q

A
→A HUURUV
ǫ A Y
A A AA



△

RZ

PDQ\

E

A

)LJXUH  7KH DGWUHH RI , ZRQGHU KRZ PDQ\ HUURUV , GLG

7UDQVIRUPDWLRQV



p
A → A
ZK
I2 A
2 Ap

A

← ǫA

I2 A

1 A p
A LW LV
← ǫA X I2
Y A A
DW

WLPH

A

Y

)LJXUH  7KH DGWUHH RI :KDW WLPH LV LW"

7DEOH  &RQVWUXFWLYH H[LVWHQWLDO FRUUHODWLYH DQVZHUV LQ YDULRXV ODQJXDJHV /DQJXDJH

SHUVRQD

IDFWXP

FDXVD

ORFXV

WHPSXV

PRGXV

(QJOLVK

WKDW

WKDW

EHFDXVH

WKHUH

WKHQ

VR

*HUPDQ

GHU

GDV

GDUXP

GD

GDQQ

VR

&DWDODQ

WDO

DL[z

SHU DL[z

DOOj

OODYRUV

DL[t

3ROLVK

WDPWHQ

WDPWR

GODWHJR

WDP

ZWHG\

ZWHQ VSRVyE

-DSDQHVH

NRQR

NRUH

PRWWH

D NRVR

VDWH

NR

FKLUD



&KDSWHU )RXU

 &DXVDWLYHV DQG IDFWLWLYHV 8QWLO QRZ ZH KDYH SXW WRJHWKHU WZR RU PRUH SKUDVHV ZKHUH SDUW RI WKH SUHGLFD WLRQ JRW KLGGHQ E\ FRQVWUXFWLRQ EXW ZH QHYHU GHDOW ZLWK H[SOLFLW YDOHQF\ YDOXH DXJPHQWDWLRQ ,Q WKLV VHFWLRQ ZH GHDO ZLWK VRPH FRPPRQ FRQVWUXFWLRQV WKDW LQ FUHDVH WKH YDOHQF\ YDOXH RI WKH YHUEDQW ZLWK D VSHFLDO DWWHQWLRQ WR ZKDW KDSSHQV WR WKH LQYROYHG DFWDQWV $ VWDQGDUG FRQVWUXFWLRQ WKDW LQFUHDVH WKH YDOHQF\ YDOXH LV WKH FDXVDWLYH XVHG WR LQWURGXFH DQ H[WUD LQYDOHQW DFWDQW WKH Cause DQLPDWH RU QRW  ZKR FDXVH WKH VWDQGDUG DFWLRQ WR EH GRQH 6RPHWLPHV FDXVDWLYH DUH FRPSOHWHO\ JUDPPDWLFDO L]HG WKDW LV WKH YHUE LWVHOI FRQWDLQV WKH VHPHPH Cause )RU H[DPSOH WKH (QJOLVK YHUE WR NLOO LV WKH FDXVDWLYH RI WKH YHUE WR GLH ,Q RWKHU FDVHV WKHUH DUH OHVV JUDP PDWLFDOL]HG FRQVWUXFWLRQV ZKHUH WKH VWDQGDUG DFWLRQ LV VWLOO UHFRJQLVDEOH ZLWKLQ WKH FDXVDWLYH FRQVWUXFWLRQ LWVHOI /HW Q EH WKH H[WUD YDOHQW ZKLFK EULQJV WKH VHPHPH Cause :H ZLOO VKRZ KRZ WKH FDXVDWLYH FRQVWUXFWLRQ LQFUHDVHV WKH QXPEHU RI WKH ZKROH VHW RI LQYDOHQW DFWDQWV E\ RQH

D

→ − X .DUO &KDUOHV

E

← − Q ,FK ,

F

← − Q ,FK ,

← − Y GLH %OXPHQ WKH IORZHUV

JLHVW ZDWHU3rd Pers

ODVVH PDNH

→ − X .DUO &KDUOHV

← − Y GLH %OXPHQ WKH IORZHUV

ODVVH PDNH

← − Y GLH %OXPHQ WKH IORZHUV

JLH‰HQ ZDWHUInf

JLH‰HQ ZDWHUInf

→ − X YRQ .DUO  E\ &KDUOHV

([DPSOH D VKRZV WKH VWDQGDUG DFWLRQ² QRWH WKDW %OXPHQ JLH‰HQ LV DQ LGLRPDWLF H[SUHVVLRQ LQ *HUPDQ 7KH FDXVDWLYH FRQVWUXFWLRQ E LV VKRZQ LQ )LJXUH  ZKHUH WKH LQILQL WLYH EHFDPH H[FHSWLRQDOO\ DQ DGSRVLWLRQ ZKLOH WKH H[WUD DFWDQW Q OHW WKH VWDQGDUG DFWLRQ KDSSHQ WKHUHIRUH LWV WUDMHFWRU\ LV RI JRYHUQPHQW ←  ,Q F WKHUH LV WKH VRFDOOHG µFDXVDWLYH SDVVLYH¶ ZKHUH WKH RULJLQDO GRHU LV RPLWWHG DV LQ WKH SDVVLYH EXW LW FDQ EH UHFRYHUHG DV DQ H[WHUQDO DUJXPHQW X  

7UDQVIRUPDWLRQV



q
A
→A
JLH‰HQA
I2+1 A 3
A
Aq
A
→A GLH %OXPHQ
ǫ A Y
I2+1 A 2 >Acc@
A
Aq
A .DUO
←A X
ǫ A
I2+1 A 1
A
A

△

△

,FK

ODVVH

Q

I2+1 cause

)LJXUH  7KH DGWUHH RI ,FK ODVVH .DUO GLH %OXPHQ JLH‰HQ

7KH PRVW H[WUHPH YDOHQF\ DXJPHQWDWLRQ KDSSHQV ZLWK TXDGULYDOHQW YHUEV 4+1  DV LQ WKH IROORZLQJ H[DPSOH )LJXUH   Icause

→ −  Q 3DXO

PDNHV

→ − X /L]D

EX\

← − Y D FDU

→ − Z E\ 5RQ¶V

← − W IRU  SRXQGV

,QFUHGXOLW\ FRQVWUXFWLRQV DV KLGGHQ FDXVDWLYHV 7KHUH LV D SDUWLFXODU FDVH RI YDOHQF\ DXJPHQWDWLRQ LQ FKLOGUHQ VSHHFK FDOOHG µLQFUHGXOLW\ FRQVWUXFWLRQ¶ E\ 7RPDVHOOR   D KLP EH D GRFWRU E P\ PRWKHU ULGH D WUDLQ F KHU ZDVK WKH GLVKHV 2XU DQDO\VLV VKRZV WKDW DQ DFWDQW OLNH KLP LQ D FDQ EH FRQVLGHUHG D ³VXEMHFW LQ WKH DFFXVDWLYH FDVH´ 7RPDVHOOR  VLF ±  EXW SHUKDSV



&KDSWHU )RXU

r
A
←A
IRU A
I4+1 A

A AAr
A
→A  SRXQGV
E\ A W
I4+1 A 4 A
AAr


A
←A 5RQ·V
EX\ A Z
I4+1 A 3 A
AAr


A
→A D FDU
ǫ A Y
I4+1 A 2
A AAr


A /L]D
→A X
ǫ A
I4+1 A 1
A AA






5

△

△

△

△

△

3DXO

PDNHV

Q

I4+1 cause

)LJXUH  7KH DGWUHH RI 3DXO PDNHV /L]D EX\ D FDU E\ 5RQ¶V IRU  SRXQGV

7UDQVIRUPDWLRQV



LW LV EHWWHU WR VHH LQFUHGXOLW\ FRQVWUXFWLRQV DV UHOLFV RI FDXVDWLYH FRQVWUXFWLRQV JRYHUQHG E\ D FRPSOHWHO\ KLGGHQ PDNHOHWKHOS DV LQ   VHH )LJXUH  D OHW KHU GR LW E KHOS KLP SXW KLV VKRHV F PDNH WKLV VWD\ RSHQ

q
A
←A A
GR 2+1 A
I3 Aq

A LW
→A ǫ Y
2+1 A
I2 A
Aq
A KHU
←A ǫ X
2+1 A I
1 A
A  \RX O HW   2 Q Icause )LJXUH  7KH DGWUHH RI OHW KHU GR LW

Chapter Five Constructive dictionaries /LQJXLVWLF NQRZOHGJH LV D ZKROH ZKLOH D VWULFW VHSDUDWLRQ RI DXWRQRPRXV OHYHOV VKRXOG QRW EH FRQVLGHUHG²D WHQHW IROORZHG E\ FRJQLWLYH OLQJXLVWV HJ /DQ JDFNHU  ²QRQHWKHOHVV LW LV XVHIXO WR DQDO\VH ODQJXDJHV RQ GLIIHUHQW OHYHOV IURP VRXQG WR WKRXJKW SKRQRORJ\ PRUSKRV\QWD[ VHPDQWLFV DQG SUDJPDWLFV ,Q WKH SUHYLRXV FKDSWHUV ZH KDYH WUHDWHG PRUSKRV\QWD[ LQ GHWDLOV ZKLOH VHPDQ WLFV SOD\HG D PLQRU UROH  :H GLVWLQJXLVK HQF\FORS GLF YV GLFWLRQDU\ NQRZOHGJH ZLWKLQ D ODQJXDJH PHDQLQJ FDQQRW EH UHGXFHG FRPSOHWHO\ WR XVH²XQOLNH ZKDW DUJXH WKH IROORZHUV RI WKH VRFDOOHG µSDQHQF\FORS GLF¶ DSSURDFK WR ODQJXDJH²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²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



&KDSWHU )LYH

IL[HV XVHG WR GHQRWH WKH WLPH RI EHLQJ RI ZKDW GHQRWHG E\ WKH VXIIL[HG QRXQ DV LQ WKH IROORZLQJ SDLUV ER\ { ER\KRRG  GLFWDWRU { GLFWDWRUVKLS H[DPSOHV IURP 6WHLQ  ±  9LFH YHUVD WZR PRUSKHPHV ZKLFK KDYH WKH VDPH PRUSK EXW GLIIHUHQW VH PHPHV DUH FDOOHG KRPRQ\PV WKH (QJOLVK PRUSK µEDFKHORU¶ FDQ EH UHIHUUHG WR DW OHDVW IRXU GLIIHUHQW PRUSKHPHV EDFKHORU1  µDQ XQPDUULHG DGXOW PDQ¶ EDFKHORU2  µD PDOH ELUG RU PDPPDO ZLWKRXW D PDWH¶ EDFKHORU3  µD SHUVRQ ZKR KDV WDNHQ D ILUVW XQLYHUVLW\ GHJUHH¶ EDFKHORU4  µD NQLJKW VHUYLQJ XQGHU WKH EDQQHU RI DQRWKHU NQLJKW¶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verb >tense >person >3rd, singular@@@@ &RQYHUVHO\ HDFK VHPHPH KDV DW PRVW RQH SDUHQW )RU LQVWDQFH WKH VHPHPH tense LV K\SRQ\P\ RI verb ZKLOH 3rd DQG singular DUH FKLOGUHQ RI person 7KH ZKROH IDPLO\ EHORQJLQJ WR person LV K\SRQ\P\ RI tense ,W LV REYLRXV WKDW VHPHPHV DQG WKHLU FRQILJXUDWLRQV DUH VWULFWO\ ODQJXDJH ERXQG LQ /LKLU DQ $XVWURQHVLDQ ODQJXDJH VSRNHQ LQ WKH 1HZ ,UHODQG 3URYLQFH RI 3DSXD 1HZ *XLQHD WKHUH LV D ULFK GLVWLQFWLRQ LQ WKH K\SRQ\PLHV RI WKH VHPHPH number EH\RQG singular DQG plural LW KDV WKH IROORZLQJ K\SRQ\PV dual trial paucal IRU WZR WKUHH IHZ UHIHUHQWV RWKHUZLVH WKH JHQHULF plural LV XVHG &RUEHWW    ,W VLPSO\ KDV QR VHQVH WR XVH WKH VHPHPH paucal LQ WKH (QJOLVK FRQVWUXFWLYH GLFWLRQDU\ EHFDXVH LQ (QJOLVK WKLV VHPHPH GRHV QRW H[LVW²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

&RQVWUXFWLYH GLFWLRQDULHV



 7UDQVIHUHQFH (YHU\ ODQJXDJH UHJDUGOHVV RI WKH 6SUDFKEXQG LW EHORQJV WR KDV D FODVV DSDUW ZLWKLQ LWV PRUSKHPHV GHYRWHG WR FRQYH\ WKH PRVW SDUW RI VHPDQWLFV ,Q RXU SHU VSHFWLYH VHPDQWLFV LV UHSUHVHQWHG WKURXJK WKH UHODWLRQV EHWZHHQ VHPHPHV DQG DOVR WKURXJK WKH UHODWLRQV IURP VHPHPHV WR WKH QRQOLQJXLVWLF ZRUOG WKDW LV WKH UHIHUHQFH 0RUSKHPHV EHORQJLQJ WR WKH FODVV UHIHUULQJ WKH ZRUOG DUH FDOOHG OH[ HPHV 7KH FODVV FRQWDLQLQJ DOO WKH OH[HPHV RI ODQJXDJH LV FDOOHG WKH OH[LFRQ :KLOH WKH FRQFHSW RI µZRUG¶ LV FHQWUDO RQO\ LQ WKH JUDPPDU WUDGLWLRQV RI WKH 6WDQGDUG $YHUDJH (XURSHDQ WKH GLVWLQFWLRQ RI OH[HPHV ZLWKLQ D ODQJXDJH¶V PRU SKHPH VHW LV JHQHUDO )RU H[DPSOH LQ -DSDQHVH QRQOH[HPHV DUH ZULWWHQ LQ NDQD V\OODELF VFULSW  ZKLOH OH[HPHV DUH ZULWWHQ LQ NDQML &KLQHVH ORJRJUDSKLF FKDU DFWHUV 


&KDSWHU )LYH

WUXH F  7KHUHIRUH OH[HPHV FRQYH\ WKH PRVW SDUW RI PHDQLQJ LH WKH\ KDYH PRUH VHPHPHV WKDQ QRQOH[LFDO PRUSKHPHV %XW WKH GLFKRWRP\ µIL[HG YV RSHQ VHWV RI ZRUG FODVVHV¶ LV XQVDWLVI\LQJ ZLWKLQ D FRQVWUXFWLYH SHUVSHFWLYH   WKHUH DUH VRPH FRQVWUXFWLRQV SDUWLDOO\ JUDPPDWLFDO L]HG WKDW FDQ EH SXW DW ZRUN RQO\ E\ D IL[HG VHW RI PRUSKHPHV DQG WKHUHIRUH WKLV VHW IRUPV D IL[HG ZRUG FODVV 7KHUHIRUH ZH QHHG PRUH VROLG FULWHULD WR GLVWLQJXLVK WKH RSHQ VHW RI OH[HPHV IURP WKH JHQHULF VHW RI PRUSKHPHV 7KH FULWHULD ZH QHHG DUH WKH JUDPPDU FKDUDFWHUV ,W ZDV 7HVQLqUH WKH ILUVW WR XVH JUDPPDU FKDUDFWHUV WR ILQG WKH LQQHU VWUXFWXUH RI V\QWD[ LQ WKH V ,Q SDUWLFXODU KH IRXQG WKDW WKHUH DUH VRPH PRUSKRORJLFDO DQG V\QWDFWLF VWUDWHJLHV ZKRVH PDLQ SXUSRVH LV WR µWXUQ¶ WKH SKUDVDO RU VXESKUDVDO JURXS RI PRUSKHPHV 7KLV SKHQRPHQRQ ZDV FDOOHG LQ )UHQFK WUDQVODWLRQ ZKLOH LQ (QJOLVK ³DQ HTXLY DOHQW PD\ EH WUDQVIHUHQFH DV WKH ZRUG WUDQVODWLRQ KDV DOUHDG\ WKH PHDQLQJ RI WKH )UHQFK µWUDGXFWLRQ¶´ 7HVQLqUH   RXU WUDQVODWLRQ   )URP D IRUPDO SRLQW RI YLHZ D WUDQVIHU D VLQJOH DFW RI WUDQVIHUHQFH LV RQO\ DQ DGWUHH WUDQVIRUPDWLRQ +RZHYHU LW KDV D UHOHYDQW OLQJXLVWLF PHDQLQJ PRVW WUDQVIHUV DUH VR DFFOLPDWHG WR VSHDNHUV E\ JUDPPDWLFDOL]DWLRQ WKDW WKH\ DUH QR ORQJHU DZDUH RI WKHLU H[LVWHQFH 7UDQVIHUHQFH FDQ EH VWDWLYH DGMXQFWLYH YHUEDQW RU FLUFXPVWDQWLDO IROORZLQJ WKH JUDPPDU FKDUDFWHU RI WKH 7HVQHULDQ WUDQVIpUHQGH OLWHUDOO\ µWUDQVIHUZRUWK¶  LH WKH PRUSKHPH ZKHUH WR VWDUW WKH WUDQVIHU FKDLQ ZKLFK SRVVHVVHV D SURSHU JUDPPDU FKDUDFWHU :KDW 7HVQLqUH FDOOHG D WUDQVIpUHQGH IRU XV LV VLPSO\ D OH[ HPH ,Q RWKHU ZRUGV D OH[HPH LV D PRUSKHPH ZKLFK FDUULHV D JUDPPDU FKDUDFWHU RI LWV RZQ DQG VR LW FDQ VWDQG DV WKH JRYHUQRU LQ DQ DGSRVLWLRQDO WUHH )LJXUH   &RQYHUVHO\ QRQOH[LFDO PRUSKHPHV DOZD\V SHUIRUPV WUDQVIHUHQFH VWDUWLQJ IURP D OH[HPH $W WKH OLPLW WKH WUDQVIHU FDQ EH UHGXQGDQW HJ O > O 

q
A
↔A
adp A
G A A


q
A
↔A
adp A
F A A


△

△

△

△

dep D

lexeme G

dep D1 > D2

lexeme G

)LJXUH  7KH SODFH RI OH[HPHV LQ WKH DEVWUDFW DGSRVLWLRQDO WUHH VWUXFWXUH

&RQVWUXFWLYH GLFWLRQDULHV



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²KLVWRULFDO DQG KLVWRULF ZKLFK DUH QRW WKH VDPH²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definite, collective, plural@ E ULFK > WKH ULFK A > O + >-definite, collective, plural@ 6RPHWLPHV D WUDQVIHU LV PDUNHG LH WKH JUDPPDU FKDUDFWHU RI WKH WUDQVIHUUHG ZRUG LH WKH UHVXOW DW WKH HQG RI D WUDQVIHU WKH 7HVQHULDQ WUDQVIpUp  KDV RQH RU PRUH VHPHPHV WKDW PDUN WKH WUDQVIHU LWVHOI DV LQ DE  6XFK PDUNHG WUDQVIHUV DUH DGWUHH WUDQVIRUPDWLRQV ZKHUH WKH OH[HPH FDQ EHORQJ RQO\ WR D OLPLWHG OLVW ZLWK SUHFLVH IHDWXUHV WKDW ERXQG WKH DSSOLFDWLRQ RI WKH WUDQVIRUPDWLRQ )LJXUH  VKRZV WKH DEVWUDFW FRQVWUXFWLRQV EHKLQG D  7KH FRQVWUXF WLYH GLFWLRQDU\ RI WKH ,WDOLDQ JUDPPDU ZLOO KDYH D VHFWLRQ GHYRWHG WR DGMXQF WLYH OH[HPHV VXFK DV WKH JRYHUQRU RI D  DQG D VHFWLRQ GHYRWHG WR DEVWUDFW



&KDSWHU )LYH

lexeme A >anim: hum@ >qual@

{

r
A
←A
ǫ A
A>O A
+[-def] A
A
+[coll] Ar +[pl]
A L
→A A
ǫ A >m: pl@
O A A
A
A
L lexeme O A >m: pl@ >anim: hum@ >qual@

)LJXUH  7KH FRQVWUXFWLRQ RI WKH DGMHFWLYHWRVWDWLYH WUDQVIHU L ULFFKL

DGWUHHV²LH FRQVWUXFWLRQV   ,I WKH DGMXQFWLYH OH[HPH KDV WKH SURSHU VHPHPHV LQ WKH SUHVHQW FDVH animate: human DQG quality WKHQ WKLV FRQVWUXFWLRQ LV DGPLV VLEOH 7KH FRQVWUXFWLRQ LWVHOI LPSRVHV VRPH VHPHPHV WKH PDVFXOLQH JHQGHU m DQG WKH SOXUDO pl LQ WKH OHDYHV 7KH SOXUDO DOVR ODEHOV WKH ZKROH JURXS DORQJ ZLWK WKH VHPHPH collective DQG WKH PDUNHG ODFN RI definition LH WKH IDFW WKDW WKH PHPEHUV RI WKH JURXS WKH ULFK WKH SRRU DQG VR RQ FDQQRW EH LQGLYLGXDWHG RU LI \RX SUHIHU LQ PDWKHPDWLFDO WHUPV WKH VHW GHQRWHG E\ WKH DGWUHH LV QRQ FRQVWUXFWLYH WKDW LV LW LV QRW SRVVLEOH D IRUWLRUL WR LQGLFDWH DQ HOHPHQW LQ WKH VHW LQ D FDQRQLFDO ZD\ ,Q JHQHUDO JUDPPDU FKDUDFWHUV DQG WKH VHPDQWLF FRQILJXUDWLRQ RI D OH[HPH LH WKH UHTXLUHG VHPHPHV GHWHUPLQH WKH FRQGLWLRQV HQDEOLQJ WKH DSSOLFDWLRQ RI D FRQVWUXFWLRQ RQ KDYLQJ WKDW OH[HPH DV D JRYHUQRU

 6WUDWHJLHV RI JUDPPDU FKDUDFWHU FKDQJH :KRUI  GLVWLQJXLVKHG OH[HPHV LQ WZR FDWHJRULHV OH[HPHV E\ VHOHFWLRQ DQG OH[HPHV E\ FROORFDWLRQV /H[HPHV E\ VHOHFWLRQV DUH DOO WKRVH OH[HPHV ZKRVH JUDPPDU FKDUDFWHU LV NQRZQ DW D ILUVW JODQFH DPRQJ KLV H[DPSOHV LQ (QJOLVK KH JDYH SROLFH O  HOHSKDQW O  KRQHVW A 

&RQVWUXFWLYH GLFWLRQDULHV



%\ FRQWUDVW OH[HPHV E\ FROORFDWLRQ DUH GHILQHG RQO\ LI SXW LQWR WKH V\QWDJ PDWLF D[LV ZH FDQ KDYH FXHV DERXW WKHLU PRVW SUREDEOH JUDPPDU FKDUDFWHU EXW ZH FDQQRW EH FHUWDLQ )RU LQVWDQFH WKH (QJOLVK OH[HPH ZDON LV SUREDEO\ D YHUEDQW I  EXW LW FDQ DOVR EH D VWDWLYH O RU HYHQ D DGMXQFWLYH A  D , ZDON LQ WKH SDUN YHUEDQW FROORFDWLRQ  E /HW¶V KDYH D ZDON VWDWLYH FROORFDWLRQ  F :DONLQJ GLVWDQFH DGMXQFWLYH FROORFDWLRQ  ,Q   WKH SURSHU JUDPPDU FKDUDFWHU RI ZDON LV GHILQHG E\ WKH FRQVWUXFWLRQV ZKHUH LW LV FROORFDWHG PRUH VSHFLILFDOO\ D O + ZDON E A + determiner + ZDON F ZDONLQJ + O :KLOH VHOHFWLRQ LV D SURSHUW\ RI FHUWDLQ OH[HPHV FROORFDWLRQ LV D VWUDWHJ\ XVHG WR FKDQJH WKH JUDPPDU FKDUDFWHU RI OH[HPHV²D VWUDWHJ\ EDVHG RQ V\QWD[ 2I FRXUVH VHOHFWLYH OH[HPHV FDQ FKDQJH WKHLU JUDPPDU FKDUDFWHU E\ FROORFDWLRQ )RU LQVWDQFH LQ HOHSKDQW LYRU\ WKH VWDWLYH OH[HPH HOHSKDQW ZDV WXUQHG LQWR DQ DGMXQFWLYH O > A E\ FROORFDWLRQ $SDUW IURP FROORFDWLRQ WKHUH DUH RQO\ RWKHU WKUHH SRVVLEOH VWUDWHJLHV WR PRG LI\ WKH JUDPPDU FKDUDFWHU RI OH[HPHV ZLWKLQ ZRUG PRUSKRORJ\ XVHG DORQH RU WRJHWKHU GHULYDWLRQ DEODXW DQG VXSSOHWLRQ

'HULYDWLRQ ,Q RUGHU WR FKDQJH WKH JUDPPDU FKDUDFWHU RI OH[HPHV PRVW ODQJXDJHV KDYH PRU SKHPHV GHYRWHG WR WKLV WDVN WKDW DUH PRUSKRORJLFDOO\ DSSOLHG WR OH[HPHV 7KLV NLQG RI WUDQVIHUHQFH LV XVXDOO\ FDOOHG GHULYDWLRQ ZH UHWDLQ WKH FRPPRQ XVH EH FDXVH WKHUH LV QR DPELJXLW\ ,Q IDFW WKH UHVXOW RI D GHULYDWLRQ LV DOZD\V D ZRUG 6RPHWLPHV GHULYDWLRQ LV SHUIRUPHG QRW WR OH[HPHV EXW WR VSHFLDO FODVVHV RI ZRUGV WUHDWHG OH[LFDOO\ )RU H[DPSOH WKH (QJOLVK PRUSKHPH IROG LV D QXPEHU DGMHFWLYHV WUDQVIHUUHU LW LV DSSOLHG WR ZRUGV GHQRWLQJ FDUGLQDO QXPEHUV WUHDWHG DV OH[HPHV   LQ RUGHU WR IRUP DGMHFWLYHV WKDW VKRZ WKH DPRXQW RI WKH QXPEHU



&KDSWHU )LYH

VSHFLILHG KDYLQJ DV PDQ\ SDUWV DV VWDWHG LQ WKH FDUGLQDO QXPEHU WKUHHIROG WZR KXQGUHGIROG 6WHLQ    ,I D PRUSK FDQ SHUIRUP GLIIHUHQW GHULYDWLRQV LH LQYROYLQJ GLIIHUHQW JUDP PDU FKDUDFWHU FKDQJHV RU PDUNLQJ WKH WUDQVIHU ZLWK GLIIHUHQW VHPHPHV LW ZLOO EH WUHDWHG DV EHORQJLQJ WR GLIIHUHQW KRPRQ\PLF PRUSKHPHV )RU H[DPSOH WKHUH DUH PDQ\ (QJOLVK PRUSKHPHV V ZLWK YHU\ GLIIHUHQW YDOXHV 6WHLQ     WKH HOHSKDQWV O > (O + plural   KHVKH EHJV I > (I + UG person: singular   WKH JDSHV I + human: state > (O + plural, human: state: quality   RQ 0RQGD\V O + time > (E + time: durative  7KH H[DPSOH VKRZV WKH PRVW FRPPRQ XVDJH RI WKH PRUSK µV¶ LQ WKH (QJOLVK ODQJXDJH WR SOXUDOLVH QRXQV ,QVWHDG  VKRZV DQRWKHU FRPPRQ FRQVWUXFWLRQ LQ (QJOLVK WR PDUN WKH WKLUG SHUVRQ VLQJXODU RI YHUEV 7KH H[DPSOH  VKRZV D PRUH OLPLWHG FRQVWUXFWLRQ DV WKH YHUE VKRXOG GHVFULEH D VWDWH FRQGLWLRQ RU GLVHDVH PDGH VWDWLYH E\ WKH FRQVWUXFWLRQ HJ WKH MLWWHUV WKH VWUDQJOHV ,Q RWKHU ZRUGV WKH OH[HPH VKRXOG EH D verb ZLWK DW OHDVW WKH IROORZLQJ VHPHPHV human: state 7KH FRQVWUXFWLRQ LWVHOI OHDGV DV D UHVXOW D VWDWLYH JURXS RI PRUSKHPHV KDYLQJ WKH FRQILJXUDWLRQ VKRZQ LQ   )LQDOO\ WKH GHULYDWLRQ VKRZQ LQ  VKRZV D GXUDWLYH FRQVWUXFWLRQ ZKLFK FDQ EH DSSOLHG RQO\ WR VWDWLYH OH[HPHV KDYLQJ time DV WKH FRUH VHPHPH

$EODXW 6RPH ODQJXDJHV²WKH *HUPDQ RQHV LQ SDUWLFXODU EXW QRW RQO\²FDQ µURWDWH YRZ HOV¶ LQ RUGHU WR FKDQJH JUDPPDU FKDUDFWHU RU WR DGG RU FKDQJH SDUWLFXODU VHPHPHV )RU H[DPSOH LQ (QJOLVK WKHUH LV D *HUPDQLF YHUEDO SDUDGLJP LH D SDUWLFX ODU YHUEDQW FRQVWUXFWLRQ WKDW FKDQJHV WKH SUHVHQW WHQVH LQ WKH SDVW WHQVH DQG LQ WKH SDVW SHUIHFW DV VKRZQ LQ 7DEOH  7KH WUDQVIHU KHUH LV YHUEDQWWRYHUEDQW I > I  WKH UHOHYDQW LQIRUPDWLRQ LV WKH FKDQJH RI WKH K\SRQ\P RI tense ,Q +HEUHZ GHULYDWLRQ LV SHUIRUPHG WKURXJK JLYHQ YRZHO SDWWHUQV ZKLOH OH[ HPHV DUH SUHFLVH VHTXHQFHV RI FRQVRQDQWV 7KH SULQFLSOH LV WKH VDPH DV EHIRUH LH DEODXW 7DEOH  

&RQVWUXFWLYH GLFWLRQDULHV



7DEOH  *HUPDQLF YHUEDQW FRQVWUXFWLRQ LQ (QJOLVK SHUIRUPHG E\ DEODXW

LDX LDX LDX

SUHVHQW VLQJ GULQN EHJLQ

SDVW VDQJ GUDQN EHJDQ

SHUIHFW VXQJ GUXQN EHJXQ

7DEOH  6WDWLYH HH DQG YHUEDQW —D WUDQVIHUV LQ +HEUHZ H[DPSOH

E¶U¶N G¶U¶N J¶E¶U

HH EHUHN GHUHN JHEHU

µNQHH¶ µURDG¶ µVWURQJ PDQ¶

—D E—UDN G—UDN J—EDU

µKH NQHHOHG¶ µKH PDUFKHG¶ µKH ZDV VWURQJ¶

,Q VXFK FDVHV LW FRXOG EH GLIILFXOW WR GHILQH ZKLFK LV WKH GHIDXOW JUDPPDU FKDUDFWHU DQ LQGLFDWLRQ LV WR WDNH WKH JUDPPDU FKDUDFWHU RI WKH FLWDWLRQ IRUP )RU H[DPSOH IRU E¶U¶N WKH FLWDWLRQ IRUP LV XVXDOO\ EDUDN ZKLFK LV D YHUEDQW PHDQLQJ µWR NQHHO WR EOHVV¶

6XSSOHWLRQ 7KH JUDPPDU RI ODQJXDJHV LV WKH UHVXOW RI JUDPPDWLFDOL]DWLRQ 7KLV PHDQV WKDW WKH PRVW IUHTXHQW SDWWHUQV RI XVDJH JLYHV UDLVH WR SURGXFWLYH FRQVWUXFWLRQV DQG WKH\ IRUP ZKDW VSHDNHUV FDOO µUXOHV¶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²TXLWH RIWHQ OH[LFDOO\ ERXQG²XVHG WR SHUIRUP D VLQJOH WUDQVIHUHQFH DUH QRW UDUH LQ QDWXUDO ODQJXDJHV   PRXVH > PLFH O > (O + plural   WRRWK > GHQWLVW O + object: topic > (O + topic: human: profession 



&KDSWHU )LYH

 JR > ZHQW > JRQH )RU LQVWDQFH WKH (QJOLVK SOXUDO RI PRXVH LV QRW PRXVHV²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—Q ³UHODWHG WR 'XWFK JDDQ DQG *HUPDQ JHKHQ´ 2[IRUG 'LFWLRQDU\  ZKLOH WKH SDVW IRUP GHULYHV IURP WKH SDVW IRUP RI DQRWKHU *HUPDQLF YHUE ZHQG ZKLFK VXSSOLHG WKH ODFN RI SDVW IRUP LQ JR (YHU\ WLPH D ODQJXDJH LV IRUFHG WR XVH XQUHODWHG OH[LFDO PDWHULDO LQ RUGHU WR SHUIRUP WUDQVIHUHQFH LW ZRUNV E\ VXSSOHWLRQ DQG WKH XQUHODWHG PDWHULDO LV FDOOHG µVXSSOHWLYH¶ EHFDXVH LW VXSSOLHV D IDLOXUH RI JUDPPDWLFDOL]DWLRQ /XFNLO\ WKHUH LV QR QDWXUDO ODQJXDJH FRPSOHWHO\ VXSSOHWLYH DV JUDPPDWLFDOL]DWLRQ GRHV ZRUN ZHOO PRVW RI WKH WLPHV 

 7RZDUG FRQVWUXFWLYH GLFWLRQDULHV $ UHDVRQDEOH FRQVWUXFWLYH GLFWLRQDU\ RI D ODQJXDJH ZRXOG UHTXLUH DQ HQWLUH YRO XPH QRW MXVW D VLQJOH VHFWLRQ )XUWKHUPRUH LW LV VLPSO\ LPSRVVLEOH WR ZULWH GRZQ D FRPSOHWH GLFWLRQDU\ RI D OLYLQJ ODQJXDJH²FRQVWUXFWLYH RU QRW²EHFDXVH DQ\ FRUSXV LV RQO\ D VQDSVKRW RI D SDUWLDO ODQJXDJHLQXVH DQG LQ D JLYHQ PRPHQW WKH PRPHQW DIWHU WKH UHOHDVH RI WKH FRUSXV LWVHOI LW VWDUWV WR JHW ROG 0RUHRYHU HDFK LQGLYLGXDO¶V UHSHUWRLUH LV XQLTXH LQ JHQHUDO PRVW RI WKH OH[ LFRQ WKH PRUSKHPHV DQG WKH FRQVWUXFWLRQV DUH LQ FRPPRQ ZLWK RWKHU PHPEHUV RI WKH VDPH VSHHFK FRPPXQLW\ EXW HYHU\ VSHDNHU KDV D SURSHU ODQJXDJH VW\OH XVHV FRQVWUXFWLRQV LQ D VOLJKWO\ GLIIHUHQW PDQQHU HWF ,W LV ZKDW OLQJXLVWV XVXDOO\ FDOO µLGLROHFW¶ HYHU\ GLFWLRQDU\ LV ERXQG WR EH LQFRPSOHWH 7KHVH DUH WKH WKHRUHWLFDO OLQJXLVWLF OLPLWV 2XU DLP KHUH LV IRXQGDWLRQDO LH ZH ZDQW WR JLYH WKH ULJKW KLQWV WR EXLOG D FRQVWUXFWLYH GLFWLRQDU\ )URP D WKH

&RQVWUXFWLYH GLFWLRQDULHV



RUHWLFDO SRLQW RI YLHZ WKHUH DUH DW OHDVW WZR SDUWV LQ D FRQVWUXFWLYH GLFWLRQDU\ PRUSKHPHV DQG FRQVWUXFWLRQV )LUVW D FRQVWUXFWLYH GLFWLRQDU\ VKRXOG OLVW PRUSKHPHV DQG WKHLU SURSHUWLHV $V ZH KDYH SUHYLRXVO\ VHHQ PRUSKHPHV DUH GHILQHG E\ D PRUSK SRVVLEO\ HPSW\  D JUDPPDU FKDUDFWHU IRU OH[HPHV RU D WUDQVIHU IRU QRQOH[HPHV   DQG ILQDOO\ D FRQILJXUDWLRQ RI VHPDQWLF WUDLWV²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²VHH DJDLQ &KDSWHU  LI QHHGHG )URP WKH GHVFULSWLRQ JLYHQ DERYH LW VKRXOG EH FOHDU E\ QRZ WKDW D FRQVWUXF WLYH GLFWLRQDU\ GHVFULEHV IDU PRUH WKDQ D GLFWLRQDU\ LQ WKH XVXDO VHQVH²LH D ERRN WKDW OLVWV WKH ZRUGV RI D ODQJXDJH LQ DOSKDEHWLFDO RUGHU DORQJ ZLWK WKHLU PHDQLQJ²EXW UDWKHU WKH JUDPPDU RI WKH ODQJXDJH LQ D EURDG VHQVH PRUSKRORJ\ V\QWD[ OH[LFRQ DQG VHPDQWLFV²RQO\ SKRQRORJ\ DQG SKRQHWLFV DUH H[FOXGHG 1HYHUWKHOHVV ZH VWDUW RXU DQDO\VLV WR SURSRVH DQ RUJDQLVDWLRQ IRU D FRQVWUXF WLYH GLFWLRQDU\ E\ PDNLQJ D VWHS EDFN DQG ORRNLQJ PRUH FDUHIXOO\ WR WUDGLWLRQDO GLFWLRQDULHV WR XQGHUVWDQG KRZ WKH\ IDLO WR DGDSW WR D FRQVWUXFWLYH DSSURDFK

7UDGLWLRQDO GLFWLRQDULHV LQ D FRQVWUXFWLYH ZRUOG $ XVXDO GLFWLRQDU\ LV DQ RUGHUHG OLVW RI ZRUGV HDFK RQH ZLWK LWV DWWULEXWHV ,Q D QRUPDO GLFWLRQDU\ D ZRUG OLNH µZDON¶ FDQ EH OLVWHG DV D QRXQ RU D YHUE WUDQVLWLYH RU LQWUDQVLWLYH DFFRUGLQJ WR WKH PHDQLQJ $OVR HDFK HQWU\ IRU µZDON¶ XQLTXHO\ GHVFULEHV D SRVVLEOH PHDQLQJ DORQJ ZLWK D IHZ H[DPSOHV )LQDOO\ VRPH FRPPRQ SDWWHUQV RI XVDJH DUH OLVWHG DV ZHOO IRU H[DPSOH µZDON RQ DLU¶ µZDON RII¶ HWF 6RPH IRUPV OLNH µZDONV¶ RU µZDONLQJ¶ DUH QRW OLVWHG VLQFH WKH\ DUH FDQRQLFDO PRGLILFDWLRQV ZLWK D PHDQLQJ WKDW FDQ EH LPPHGLDWHO\ LQIHUUHG VHH H[DPSOH   LQ &KDSWHU  )URP D FRQVWUXFWLYH SHUVSHFWLYH ZH VHH WKDW µZDON¶ LV D PRUSK KDYLQJ D QXP EHU RI KRPRQ\PV RQH IRU HDFK HQWU\ LQ WKH GLFWLRQDU\²ZKHUH DQ HQWU\ GHVFULEHV D VLQJOH PRUSKHPH 0RUHRYHU HDFK PRUSKHPH KDV D QXPEHU RI DWWULEXWHV HL WKHU VWUXFWXUDO²HJ EHLQJ D QRXQ RU D YHUE WUDQVLWLYH RU LQWUDQVLWLYH HWF²RU



&KDSWHU )LYH

VHPDQWLFDO DV WKH GHVFULSWLRQ UHDOO\ LGHQWLILHV WKH VHPDQWLFDO WUDLWV WKDW FKDUDF WHULVH WKH PRUSKHPH DOWKRXJK QRW LQ D IRUPDO ZD\ 7KH FRPPRQ SDWWHUQV RI XVDJH DUH QRWKLQJ HOVH WKDQ JUDPPDWLFDOL]HG FRQVWUXFWLRQV ZKLFK KDYH EHFRPH VR µKDUGZLUHG¶ WR JDLQ DQ RXWVWDQGLQJ VWDWXV DQG PHDQLQJ VR WKH\ DUH UHSRUWHG LQ WKH GLFWLRQDU\ 6RPH RI WKHVH FRQVWUXFWLRQ DUH PRVWO\ LGLRPDWLF OLNH µZDON RQ DLU¶ DQG VRPH DUH VWLOO SURGXFWLYH OLNH µZDON RII¶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ρWUDQVIRUPDWLRQV WKDW GLVFULPLQDWH YDOLG UHVXOWV RI WKH DSSOLFDWLRQ RI FRQVWUXFWLRQV IURP WKH MXVW VWUXFWXUDOO\VRXQG RQHV ZKLFK GLG QRW WDNH WKHLU SODFH LQ WKH ODQJXDJH 8QIRUWXQDWHO\ WKLV SLFWXUH LV ODUJHO\ LQDGHTXDWH DQG XQVDWLVIDFWRU\ ,Q IDFW FRQVWUXFWLRQV LQ WKH DGSRVLWLRQDO SDUDGLJP DUH DEVWUDFW HQWLWLHV VHH YDOHQF\ LQ 6HFWLRQ  GHSHQGLQJ RQ WKHLU JRYHUQRU IRU D FRUUHFW LQVWDQFH 5HFDOOLQJ H[DP SOH  LQ &KDSWHU  DOWKRXJK LW LV SHUIHFWO\ FRUUHFW WR UHJDUG WKH PRUSKHPH µRSHQ¶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

&RQVWUXFWLYH GLFWLRQDULHV



DGSRVLWLRQ RQH FODVV ZKHUH WKH ILUVW DQG WKH VHFRQG DFWDQW DUH LQWURGXFHG E\ DQ ǫ DQG WKH WKLUG RQH E\ µWR¶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

$ PDWKHPDWLFDOO\ LQVSLUHG GLFWLRQDU\ $V HYLGHQW IURP WKH SUHYLRXV GLVFXVVLRQ D FRQVWUXFWLYH DGSRVLWLRQDO JUDPPDU IRU D QDWXUDO ODQJXDJH FDQQRW VHSDUDWH PRUSKHPHV IURP FRQVWUXFWLRQV 6R D GLFWLRQDU\ VKRXOG FRQWDLQ ERWK RI WKHP DQG VKRXOG GHVFULEH WKHP DV FRRUGLQDWHG HOHPHQWV DOORZLQJ WKH FRQVWUXFWLRQ RI DOO WKH ZHOOIRUPHG H[SUHVVLRQV RI WKH ODQ JXDJH $V DOUHDG\ VWDWHG LQ 6HFWLRQ  WKLV LV QRW SRVVLEOH ZLWKRXW FRQVLGHULQJ DOVR UHGXQGDQF\ ZKLFK LV HQFRGHG E\ ρWUDQVIRUPDWLRQV ,Q SULQFLSOH WKHVH LQJUHGLHQWV²PRUSKHPHV FRQVWUXFWLRQV DQG ρWUDQVIRUP DWLRQV²VXIILFH WR GHVFULEH DQG WR JHQHUDWH WKH ZKROH ODQJXDJH 6R D GLFWLRQDU\ FDQ EH DEVWUDFWO\ GHVFULEHG DV WKHLU FROOHFWLRQ DORQJ ZLWK DQ RUJDQLVDWLRQ SULQFL SOH DOORZLQJ IRU WKHLU LQVSHFWLRQ RQ QHHG ,Q IDFW ZH FDQ FRQFHLYH WKH FROOHFWLRQ RI RXU LQJUHGLHQWV DV D GDWDEDVH QR PDWWHU KRZ LQWHUQDOO\ UHSUHVHQWHG²DIWHU DOO FRPSXWHU VFLHQWLVWV KDYH GHYHO



&KDSWHU )LYH

RSHG D VHULHV RI YHU\ VRSKLVWLFDWHG WHFKQLTXHV WR VROYH WKH UHSUHVHQWDWLRQ SURE OHP²WKDW FDQ EH DFFHVVHG YLD D OLPLWHG QXPEHU RI µTXHULHV¶ VXSSRUWHG E\ DQ DSSURSULDWH LQGH[LQJ V\VWHP :KDW UHDOO\ PDWWHUV LV WR GHILQH ZKDW ZH ZDQW WR LQGH[ DV LW GHWHUPLQHV ZKDW ZH FDQ VHDUFK IRU ,Q WKLV VHQVH PRUSKHPHV DUH HDV\ HDFK PRUSKHPH LV GHVFULEHG E\ D PRUSK DQG D VHW RI DWWULEXWHV ,W LV UHDVRQDEOH WR VHDUFK IRU D PRUSK UHWULHYLQJ WKH VHW RI FRUUHVSRQGLQJ KRPRQ\PV RU WR VHDUFK IRU D VSHFLILF DWWULEXWH UHWULHYLQJ WKH VHW RI PRUSKHPHV KDYLQJ LW LQ WKHLU UHSUHVHQWDWLRQ  (YLGHQWO\ LQ WKLV YLHZ D PRUSKHPH LV D UHFRUG FRPSRVHG E\ D PRUSK DQG WKH OLVW RI LWV DWWULEXWHV $OVR WKH UHSUHVHQWDWLRQ  RI PRUSKHPHV LV QDWXUDO DQG FRKHUHQW ZLWK WKH WUHDWPHQW ZH PDGH RI WKHP DV GHSLFWHG LQ WKH SUHYLRXV FKDSWHUV 7R FRSH ZLWK VXSSOHWLRQ LW LV XVHIXO WR KDYH µFURVVUHIHUHQFHV¶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µPHDQLQJ¶ RI D PRUSKHPH LV QRW LQ WKH GRPDLQ RI WKH GLFWLRQDU\ FRPSLOHU $ VOLJKWO\ PRUH FRPSOH[ VLWXDWLRQ LV WKDW RI FRQVWUXFWLRQV LQ IDFW WKHUH LV D PLQRU DPELJXLW\ LQ WKH XVH ZH PDGH RI WKLV ZRUG DQG QRZ LW LV WLPH WR FODULI\ ,Q IDFW ZH XVHG WKH ZRUG µFRQVWUXFWLRQ¶ WR LGHQWLI\ WKUHH GLVWLQFW HQWLWLHV ,Q WKH ILUVW VHQVH D FRQVWUXFWLRQ LGHQWLILHV D IDPLO\ RI DGWUHHV ZKHUH WKH JRY HUQRU DQG WKH DGSRVLWLRQV DUH IL[HG DQG WKH WUHH VWUXFWXUH LV ULJLG :KDW PD\ YDU\ DUH WKH GHSHQGHQWV WKDW VKRXOG PDWFK WKH VSHFLILHG DWWULEXWHV SULPDULO\ JUDP PDU FKDUDFWHUV :H ZLOO QDPH WKHVH IRUPV DV EDVLF FRQVWUXFWLRQV $Q H[DPSOH LV D  ZKRVH DGWUHH LV VKRZQ LQ )LJXUH  µX RSHQV Y ZLWK Z ¶ +HUH WKH JRYHUQRU µRSHQV¶ DQG WKH DGSRVLWLRQV ǫ  ǫ DQG µZLWK¶ LQWURGXFLQJ WKH DFWDQWV X  Y DQG Z UHVSHFWLYHO\ DUH IL[HG ZKLOH WKH DFWDQWV PD\ EH DQ\ DGWUHH RQH OLNHV SURYLGHG LW LV D VWDWLYH LH LW KDV WKH O JUDPPDU FKDUDFWHU $V D EDVLF FRQVWUXFWLRQ LV DQ DGWUHH ODFNLQJ VRPH OHDYHV LW FDQ EH HDVLO\ UHSUHVHQWHG LQ WKH GDWDEDVH E\ D ORJLFDO WHUP ZLWK YDULDEOHV )RU H[DPSOH WKH WHUP UHSUHVHQWLQJ WKH EDVLF FRQVWUXFWLRQ RI D LV with(ǫ(ǫ(opens, X), Y), Z)

&RQVWUXFWLYH GLFWLRQDULHV



LH WKH OLQHDULVHG DGWUHH ZKHUH WKH DFWDQWV DUH VXEVWLWXWHG ZLWK WKH X  Y DQG Z YDULDEOHV DQG WKH DGSRVLWLRQV DUH IXQFWLRQ V\PEROV ,Q WKH VHFRQG VHQVH D FRQVWUXFWLRQ LGHQWLILHV D IDPLO\ RI DGWUHHV ZKRVH JRY HUQRU DQG GHSHQGHQWV PD\ YDU\ DOWKRXJK WKH\ KDYH VSHFLILF JUDPPDU FKDUDF WHUV RU VSHFLILF DWWULEXWHV  EXW WKH DGSRVLWLRQV DQG WKH WUHH VWUXFWXUH DUH IL[HG :H FDOO JHQHUDO FRQVWUXFWLRQV WKHVH IRUPV ,W LV REYLRXV WKDW EDVLF FRQVWUXF WLRQV DUH MXVW SDUWLDO LQVWDQFHV RI JHQHUDO FRQVWUXFWLRQ DQG VR DQ\ DPELJXLW\ LV LPPHGLDWHO\ VROYHG $Q H[DPSOH RI JHQHUDO FRQVWUXFWLRQ ZKHUH WKH DGSR VLWLRQ KDV D IL[HG YDOXH LV VKRZQ LQ )LJXUH  ZKLFK LOOXVWUDWHV WKH µJHQHULF¶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lLQHQ   IRU H[DPSOH LQ WKH LPSOHPHQWDWLRQ RI WKH 3URORJ ODQJXDJH VHH %DDGHU DQG 6LHNPDQQ   ,W LV UHDVRQDEOH WR EH FXULRXV DERXW WKH UHODWLRQ RI WKH PDWKHPDWLFDO PRGHO LQ $SSHQGL[ % ZLWK WKH SURSRVHG UHSUHVHQWDWLRQ RI WKH GLFWLRQDU\ LQ WKLV UHVSHFW LW LV ZRUWK QRWLFLQJ WKDW ZKDW KDYH EHHQ FDOOHG µJHQHUDO FRQVWUXFWLRQV¶ DUH H[ DFWO\ WKH VDPH WKLQJ DV µJUDPPDU FRQVWUXFWLRQV¶ LQ WKH IRUPDO PRGHO²ZH SUHIHU WR UHWDLQ GLIIHUHQW QDPHV WR GLVWLQJXLVK WKH FRQWH[WV $OVR PRUSKHPHV DUH MXVW WKH DWRPV RI WKH IRUPDO PRGHO DQG ρ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



&KDSWHU )LYH

$IWHU DQ H[WHQVLYH DQDO\VLV ZH KDYH QRW EHHQ DEOH WR ILQG DQ\ DEVWUDFW FRQ VWUXFWLRQ ZKLFK QDWXUDOO\ RFFXUV LQ WKH VWXG\ RI OLQJXLVWLFV DQG WKDW FDQQRW EH UHGXFHG WR D ILQLWH IDPLO\ RI JHQHUDO FRQVWUXFWLRQV VR ZH LQGXFH WKDW GHILQLQJ DEVWUDFW FRQVWUXFWLRQV SUHFLVHO\ DV ILQLWH IDPLOLHV RI JHQHUDO FRQVWUXFWLRQV LV D JRRG GHILQLWLRQ ZKLFK FRYHUV WKH JHQHUDO FDVH %HLQJ D IDPLO\ RI JHQHUDO FRQVWUXFWLRQV DQ DEVWUDFW FRQVWUXFWLRQ α FDQ EH LPPHGLDWHO\ UHSUHVHQWHG LQ WKH GDWDEDVH DV D TXHU\ VSHFLILFDOO\ DV WKH ORJLFDO WHUP ǫ(C1 , . . . , Cn ) ZKHUH C1  « Cn DUH WKH WHUPV UHSUHVHQWLQJ WKH JHQHUDO FRQ VWUXFWLRQV ZKLFK DUH PHPEHUV RI α  ,Q IDFW SDWWHUQ PDWFKLQJ ZLOO SURGXFH DV D UHVXOW H[DFWO\ WKH LQVWDQFHV RI C1  « Cn LQ WKH GDWDEDVH WKXV UHGXFLQJ WKH SUREOHP RI UHSUHVHQWLQJ DEVWUDFW FRQVWUXFWLRQV WR WKH DOUHDG\ VROYHG SUREOHP RI UHSUHVHQWLQJ DQG VHDUFKLQJ IRU JHQHUDO FRQVWUXFWLRQV ,Q WKH VDPH OLQH RQH FDQ HDVLO\ UHSUHVHQW ρWUDQVIRUPDWLRQV ,Q IDFW D ρ WUDQVIRUPDWLRQ VHH 6HFWLRQ  LI QHHGHG PDSV DGWUHHV PDWFKLQJ D IL[HG SDWWHUQ LQWR DGWUHHV KDYLQJ D VLPLODU VWUXFWXUH WKH LGHD EHLQJ WKDW WKH SDWWHUQ LQGLYLGX DWHV WKH µPLVWDNHV¶ DQG WKH UHVXOW LV D µFRUUHFWHG¶ DGWUHH WKH SDUDPHWULF SDUWV RI WKH SDWWHUQ DUH XVHG WR LQVWDQWLDWH WKH UHVXOW ,I ZH UHSUHVHQW D ρWUDQVIRUPDWLRQ DV D SDLU RI ORJLFDO WHUPV WKH ILUVW RQH IRU WKH SDWWHUQ DGWUHH WKH VHFRQG RQH IRU WKH UHVXOWLQJ DGWUHH²ZLWK WKH DGGLWLRQDO FDUH WR XVH WKH VDPH YDULDEOHV ZKHUH QHHGHG²WKH DSSOLFDWLRQ RI D ρWUDQVIRUPDWLRQ WR DQ DGWUHH A FDQ EH GHVFULEHG DV IROORZV ILUVW ZH FKHFN WKDW A PDWFKHV WKH SDWWHUQ RI WKH WUDQVIRUPDWLRQ²WKLV RSHUDWLRQ LV MXVW PDWFKLQJ WZR ORJLFDO WHUPV LI WKH PDWFK LV SRVVLEOH ZH ZLOO KDYH DQ DVVLJQPHQW RI WKH YDULDEOHV LQ WKH SDWWHUQ PDNLQJ LW HTXDO WR A WKHQ WKH DVVLJQPHQW LV DSSOLHG WR WKH UHVXOW SDUW RI WKH WUDQVIRUPDWLRQ \LHOGLQJ WKH B DGWUHH ZKLFK LV WKH UHVXOW RI WKH DSSOLFDWLRQ RI WKH ρWUDQVIRUPDWLRQ WR A 3OHDVH FRPSDUH WKLV SURFHGXUH ZLWK H[DPSOHV  DQG  LQ &KDSWHU  3OHDVH QR WLFH WKDW DOVR WUDQVIHUV FDQ EH UHSUHVHQWHG DORQJ WKH VDPH OLQH VHH )LJXUH  6LQFH D ρWUDQVIRUPDWLRQV FDQ EH UHSUHVHQWHG DV D SDLU RI WHUPV (P, R) LW FDQ EH PRUH HIILFLHQWO\ UHSUHVHQWHG E\ WKH VLQJOH WHUP ǫ(P, R) ZKLFK VXLWV WKH IRUPDW RI RXU GLFWLRQDU\ DV GHVLJQHG VR IDU $QG RI FRXUVH WKH TXHU\ PHFKDQLVP EDVHG RQ WHUP PDWFKLQJ DQG XVHG IRU VHDUFKLQJ DPRQJ FRQVWUXFWLRQV ZRUNV DOVR WR VHDUFK IRU ρWUDQVIRUPDWLRQV +HQFH XVLQJ D GDWDEDVH DV RXU GLFWLRQDU\ ZKHUH PRUSKHPHV DUH UHSUHVHQWHG DV UHFRUGV FRPSRVHG E\ WKH PRUSK DQG WKH DWWULEXWHV DQG FRQVWUXFWLRQV DQG ρ WUDQVIRUPDWLRQV DUH UHSUHVHQWHG DV ORJLFDO WHUPV DFFRUGLQJ WR WKH OLQHDULVHG IRUP RI WKH LQYROYHG DGWUHHV SURYLGHV XV ZLWK SUHFLVHO\ WKH RUJDQLVDWLRQ ZH ZDQW IRU D FRQVWUXFWLYH GLFWLRQDU\ RYHUFRPLQJ WKH GLIILFXOWLHV ZH KDYH IRXQG LQ D PRUH WUDGLWLRQDO DSSURDFK 7KH NH\ DVSHFW EHKLQG WKLV RUJDQLVDWLRQ LV WKDW PDWFKLQJ

&RQVWUXFWLYH GLFWLRQDULHV



RI ORJLFDO WHUPV LV FRPSXWDEOH DQG UHDVRQDEO\ HIILFLHQW LQ SUDFWLFH $OVR WKH PRUSKHPLF OHYHO RI WKH ODQJXDJH FDQ EH UHSUHVHQWHG VLQFH WUDQVIHU VKDUH WKH VDPH UHSUHVHQWDWLRQ DQG VHDUFKLQJ VWUDWHJLHV DV ρWUDQVIRUPDWLRQV 2QH PD\ EH WHPSWHG WR VOLJKWO\ H[WHQG WKH GHILQLWLRQ RI JHQHUDO FRQVWUXFWLRQV DOORZLQJ IRU YDULDEOH DGSRVLWLRQV $QG WKH UHDGHU PD\ ZRQGHU ZK\ ZH KDYH QRW SURSRVHG VXFK DQ REYLRXV JHQHUDOLVDWLRQ LQ WKH ILUVW SODFH VLQFH LW VHHPV WR UHGXFH WKH QXPEHU RI FRQVWUXFWLRQV DQG ρWUDQVIRUPDWLRQV ZH PD\ QHHG WR UHSUHVHQW²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



&KDSWHU )LYH

2Q WKH RWKHU VLGH WKH UHIHUHQFH GLFWLRQDU\ LV ERXQG WR EH KXJH D QDWXUDO ODQJXDJH KDV KXQGUHGV RI WKRXVDQGV PRUSKHPHV DQG JHQHUDO FRQVWUXFWLRQV DUH D FRPELQDWLRQ RI DGSRVLWLRQV YDOHQF\ DQG JUDPPDU FKDUDFWHUV ZLWK DQ HYLGHQW FRPELQDWRULDO H[SORVLRQ²ZKLFK FDQ RQO\ JURZ ZKHQ FRQVLGHULQJ DOVR VHPDQWL FDO WUDLWV DQG WKH RWKHU DWWULEXWHV RI PRUSKHPHV $ URXJK HVWLPDWH IRU D ODQJXDJH OLNH (QJOLVK LV DERXW D WKRXVDQG RI FRQVWUXFWLRQV 7KHVH IDFWV DUH QRW VXUSULVLQJ DV QR RQH LV XQDZDUH RI WKH UHODWLRQV DPRQJ PRUSKHPHV DQG DPRQJ FRQVWUXFWLRQV²VR WKH µUHDOO\ GLIIHUHQW¶ PRUSKHPHV DQG FRQVWUXFWLRQV DUH IDU OHVV :H VSHQW WKH HQWLUH &KDSWHU  WR VWXG\ WKH UHODWLRQV DPRQJ FRQVWUXFWLRQV²WKH\ DUH H[DFWO\ WKH τWUDQVIRUPDWLRQV²DQG WKH ILUVW SDUW RI WKLV FKDSWHU WR VWXG\ WKH UHODWLRQV DPRQJ PRUSKHPHV²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τWUDQVIRUPDWLRQV DUH DSSOLHG WR ODUJH IDPLOLHV RI DGWUHHV FRPLQJ IURP GLIIHUHQW JHQHUDO FRQVWUXFWLRQV ZH REWDLQ D VLJQLILFDQW FXW LQ WKH QXPEHU RI FRQVWUXFWLRQV ZH QHHG 7KH VDPH KROGV IRU PRUSKHPHV WUDQVIHUHQFH DOORZV WR FRQVLGHU D VLQJOH PRUSKHPH DQG WKH µFORXG¶ RI PRUSKHPHV LW JHQHUDWHV $V IDU DV WUDQVIRUPDWLRQV DUH ZLGHO\ DSSOLHG DQG RI JHQHUDO YDOLGLW\ PRVW RI WKH GLFWLRQDU\ FDQ EH UHGXFHG WR D IHZ WKRXVDQG RI EDVLF PRUSKHPHV DQG D QXPEHU RI IXQGDPHQWDO FRQVWUXF WLRQV²WKHLU QXPEHU LV KDUG WR HVWLPDWH EXW QR PRUH WKDQ D IHZ KXQGUHGV RI JHQHUDO FRQVWUXFWLRQV 6R D SUDFWLFDO GLFWLRQDU\ ZKLFK LV DOVR XVHIXO DQG VLJQLILFDQW WR XQGHUVWDQG WKH QDWXUH RI D ODQJXDJH PXVW UHSUHVHQW EDVLF PRUSKHPHV WKH IXQGDPHQWDO FRQ VWUXFWLRQV WKH ρWUDQVIRUPDWLRQV WR FKHFN WKH YDOLGLW\ RI WKH JHQHUDWHG H[SUHV VLRQV DQG DOVR D QXPEHU RI τWUDQVIRUPDWLRQV DQG WUDQVIHUHQFHV :H DOUHDG\ NQRZ KRZ WR UHSUHVHQW DQG WR LQGH[ LQ D GDWDEDVH WKH PRUSKHPHV WKH FRQVWUXFWLRQV DQG WKH ρWUDQVIRUPDWLRQV 6R ZH KDYH WR DQDO\VH KRZ WR UHS UHVHQW WUHH WUDQVIRUPDWLRQV DQG JHQHUDO WUDQVIHUHQFHV LQ D ZD\ WKDW PDNH WKHP VXLWDEOH IRU HIILFLHQW VHDUFKLQJ $V VDLG DW WKH EHJLQQLQJ RI &KDSWHU  τWUDQVIRUPDWLRQV DQG WUDQVIHUHQFHV DUH LQ IDFW LQVWDQFHV RI WUHH WUDQVIRUPDWLRQV LQ JHQHUDO RSHUDWLQJ DW GLIIHUHQW

&RQVWUXFWLYH GLFWLRQDULHV



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²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¶V UHSUHVHQWDWLRQ JHQHUDOLVHV WKH RQH RI ρ WUDQVIRUPDWLRQV ,Q IDFW ρWUDQVIRUPDWLRQV²QRW VXUSULVLQJO\²FDQ EH VHHQ DV WUHH WUDQVIRUPDWLRQV ZKRVH UHSUHVHQWDWLRQ LV D VLQJOHWRQ VHW $QG RI FRXUVH LQGH[LQJ DQG VHDUFKLQJ IRU WUDQVIRUPDWLRQV LV D VLPSOH DQG HYLGHQW JHQHUDOLVDWLRQ RI WKH FRUUHVSRQGLQJ RSHUDWLRQV RQ ρWUDQVIRUPDWLRQV )RU H[DPSOH WKH DFWLYHWRSDVVLYH WUDQVIRUPDWLRQ IRU D ELYDOHQW YHUE FDQ EH FRGHG DV WKH VHW T RI SDLUV (Pa , Ra ) ZKHUH Pa DQG Ra DUH DV LQ )LJXUH  ZLWK a UDQJLQJ RYHU WKH FODVV RI DGSRVLWLRQV²FRPSDUH ZLWK )LJXUHV  DQG ²DQG X  Y DQG V DUH ORJLFDO YDULDEOHV 2I FRXUVH WKH GHSLFWHG WUDQVIRUPDWLRQV KDV WR EH FRUUHFWHG E\ VXLWDEOH ρ WUDQVIRUPDWLRQV WR SXW WKH µHVVH¶ YHUEDQW LQ WKH FRUUHFW WHQVH²ZH KDYH QRW LQ GLFDWHG WKH VHPHPHV QRW WR EXUGHQ WKH DOUHDG\ FRPSOH[ SLFWXUH²DQG LQ VRPH FDVHV VHH HJ   )LJXUH  WR FRQVLGHU VXSSOHWLRQV 6XPPDULVLQJ WKH HQWLWLHV FRPSRVLQJ WKH GLFWLRQDU\ ZKLFK LV D GDWDEDVH DUH UHSUHVHQWHG DV LQ 7DEOH  DQG WKH VHDUFKLQJ DQG LQGH[LQJ RSHUDWLRQV DUH QDWX UDOO\ UHGXFHG WR SDWWHUQ PDWFKLQJ RI ILUVWRUGHU ORJLFDO WHUPV



&KDSWHU )LYH

q
A
→A
E\ A
E A A
Aq

A
→A X
ǫ A Xact
I22 A A
Aq

A
q
←A

A
ǫ A
→
aA
I21 A

I2 A A

A
q

2 Aq
A
A HVVH = Ra {
→A
→ Y Y ǫA I2aux ǫ 2 A
A
I Yact Yact
1 A
A > YauxA
A V
q A X 2
A Iact  Xact
→A Yaux
a + GA
I22 > YauxA
A
Aq
A
→A Y 
ǫ A Yact
I21 A A
A
V X I2act Xact

△

Pa =

△

△

△

△

△

)LJXUH  5HSUHVHQWLQJ WUHH WUDQVIRUPDWLRQV

&RQVWUXFWLYH GLFWLRQDULHV



7DEOH  5HSUHVHQWDWLRQ RI DQ DGSRVLWLRQDO JUDPPDU 0RUSKHPH

M(m, a1 , . . . , an )

&RQVWUXFWLRQ

C(c)

7UDQVIRUPDWLRQ ρ τ DQG WUDQVIHU

T(τ(p, r))

m = PRUSK a1 , . . . , an = DWWULEXWHV c = ORJLFDO WHUP FRUUHVSRQGLQJ WR WKH OLQHDULVHG DGWUHH τ = QDPH RI WKH WUDQVIRUPDWLRQ p = SDWWHUQ r = UHVXOW WKHUH DUH DV PDQ\ WHUPV ZLWK WKH VDPH τ DV WKH QXPEHU RI FRPSRQHQWV RI WKH WUDQVIRUPDWLRQ

Chapter Six Discourse and beyond :K\ WKHUH LV PRUH WKDQ RQH VLQJOH KXPDQ ODQJXDJH LQ WKH ZRUOG LI OHDUQLQJ WR VSHDN D ODQJXDJH LV D QDWXUDO IDFW FDUYHG LQ KXPDQ EHLQJV" $IWHU GHDOLQJ ZLWK PRUSKRV\QWD[ DQG VHPDQWLFV ZH VKRXOG ILQDOO\ SXW QDWXUDO ODQJXDJHV LQWR XVH WKLV LV WKH UHDOP RI SUDJPDWLFV 8VXDOO\ ZH KDYH XVHG WKH WHUP µODQJXDJH¶ UHIHUULQJ WR µQDWXUDO ODQJXDJHV¶ WDNLQJ WKLV ODVW H[SUHVVLRQ DV JUDQWHG +RZHYHU WKLV LV IDU IURP EHLQJ WUXH µQDW XUDO ODQJXDJH¶ DV ZHOO DV RWKHU FRPPRQ H[SUHVVLRQV²VXFK DV µPRWKHU WRQJXH¶ DQG µQDWLYH VSHDNHU¶ IRU LQVWDQFH²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²DQ DFWXDO XWWHUDQFH²FRQVWUXHV D VFHQH LH VRPH WKLQJ WKDW JRHV EH\RQG WKH VWUDLJKWIRUZDUG SHUFHSWXDO DQG VHQVRU\PRWRU FRJQL WLYH UHSUHVHQWDWLRQ 6SHHFK DFW WKHRU\ SLRQHHUHG E\ $XVWLQ JLYHV DQ H[SODQDWLRQ RI WKLV YHU\ LPSRUWDQW IXQGDPHQWDO SURSHUW\ RI QDWXUDO ODQJXDJHV :KHQ D VLQJOH OLQJXLVWLF DFW LV SHUIRUPHG HDFK OLQJXLVWLF DFW VD\V VRPHWKLQJ FRQVWDWLYH DQG GRHV VRPH WKLQJ SHUIRUPDWLYH DW WKH VDPH WLPH $XVWLQ    :LWKLQ WKH DGSRVLWLRQDO SDUDGLJP WKLV µGRLQJ WKLQJV ZLWK ZRUGV¶ LV PDSSHG LQWR WKH DGWUHH UHSUHVHQWD WLRQ WKURXJK WKH LQGLFDWRUV RI WKH LQIRUPDWLRQ SURPLQHQFH WUDMHFWRU\ %XW DGWUHHV RQO\ VDWLVI\ WKH QHHG WR UHSUHVHQW ZKDW LV DFWXDOO\ VDLG WKH ORFXWLRQDU\ IDFHW LQ $XVWLQ¶V WHUPV  QRW ZKDW LV UHDOO\ PHDQW LH WKH LOORFXWLRQDU\ IDFHW QRU ZKDW LV DFWXDOO\ EHKDYLRXUDOO\ SHUIRUPHG WKH SHUORFXWLRQDU\ IDFHW 



&KDSWHU 6L[

,Q RWKHU WHUPV HDFK VSHHFK DFW KDV WKUHH IDFHWV WKH ORFXWLRQDU\ RQH EHLQJ SURSHUO\ OLQJXLVWLF LQ QDWXUH ZKLOH WKH QRQORFXWLRQDU\ RQHV²WKH LOORFXWLRQDU\ DQG WKH SHUORFXWLRQDU\²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¶V DQG DVVHV VRU¶V ZRUN" 7KLV FKDSWHU DLPV WR DQVZHU WKHVH TXHVWLRQV UHIHUULQJ WR WKH VHPLQDU PHQWLRQHG DERYH DQG WKH ILUVW DQDO\VHV RI WUDQVFULSWV DOUHDG\ GRQH 7KLV H[SHULHQFH FDQ EH VHHQ DV WKH ILUVW UHDOZRUOG DSSOLFDWLRQ RI FRQVWUXF WLYH DGSRVLWLRQDO JUDPPDUV 7KH UHVHDUFK SURJUDP LV WR VHW XS D IUDPHZRUN IRU GLUHFW DSSOLFDWLRQ RI &RQVWUXFWLYH &RQYHUVDWLRQDO $QDO\VLV &R&$/ VXLWDEOH IRU WKHUDSLVWV LQ SDUWLFXODU WKHUDSHXWLF DVVHVVRUV 

'LVFRXUVH DQG EH\RQG



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


&KDSWHU 6L[

1HYHUWKHOHVV D SDUW RI SUDJPDWLFV FDQ EH IRXQG LQ DGWUHHV PRUH SUHFLVHO\ LQ LQIRUPDWLRQ SURPLQHQFH DV DOUHDG\ PHQWLRQHG LQ   ,Q SDUWLFXODU VSRNHQ HP SKDVLV SXW LQ EROG LQ  FDQ FKDQJH WKH WUDMHFWRU\ RI LQIRUPDWLRQ SURPLQHQFH )LJXUH   EXW DW WKH VDPH WLPH LW JLYHV DGGLWLRQDO SUDJPDWLF LQIRUPDWLRQ D ,¶YH VHHQ 0DU\ ZLWK 3DXO QR HPSKDVLV E ,¶YH VHHQ 0DU\ ZLWK 3DXO HJ QRW /L]D F ,¶YH VHHQ 0DU\ ZLWK 3DXO HJ QRW ZLWK -RKQ

q q q
A
A
A
→A
→A
→A
ǫ2 A
ǫ2 A
ǫ2 A
I2 A
I2 A
I2 A
q A
q A A q

A
A
A
→A
←A
↔A ,·YH VHHQ ,·YH VHHQ ,·YH VHHQ ZLWK A ZLWK A 2 2


ZLWK A I21 I I 1 1
A>Y A
A>Y A
A>Y A
A
A
A

△

△

△

3DXO

0DU\

3DXO

0DU\

3DXO

0DU\

O

Y

O

Y

O

Y

)LJXUH  +RZ HPSKDVLV LV PDSSHG LQWR LQIRUPDWLRQ SURPLQHQFH ,Q IDFW ZKLOH LQ D  ZKLFK LV WKH XQPDUNHG IRUP WKHUH LV QR SDUWLFXODU DVVXPSWLRQ EHOLHI RU RWKHU PHQWDO VWDWH LQ E LW FDQ EH DVVXPHG WKDW WKH VSHDNHU H[SHFWHG WR VHH VRPHRQH HOVH VD\ /L]D ZLWK 3DXO EXW WKHQ LW UHYHDOV WKDW LW ZDV 0DU\ WR EH ZLWK KLP $QDORJRXVO\ LQ F 0DU\ ZDV H[SHFWHG WR EH ZLWK VRPHRQH HOVH VD\ /L]D  QRW 3DXO 7KLV DVVXPSWLRQV DQG FKDQJHV RI EHOLHIV DUH FRPPXQLFDWHG WR WKH OLVWHQHU E\ HPSKDVLV²LQ RWKHU ZRUGV WKH VSHDNHU DVVXPHV WKDW WKH OLVWHQHU UHFHLYHV KLV LOORFXWLRQV +RZHYHU WKH WUDMHFWRU\ RI LQIRUPDWLRQ SURPLQHQFH LV WKH WLS RI WKH LFHEHUJ WKH LOORFXWLRQV EHKLQG WKH LQGLFDWRU FDQQRW EH FDSWXUHG FRPSOHWHO\ E\ DGWUHHV :H QHHG DQRWKHU OHYHO RI DEVWUDFWLRQ LQ RUGHU WR GHDO ZLWK SUDJPDWLF SKHQRPHQD

 3UDJPDWLF DGSRVLWLRQDO WUHHV ,OORFXWLRQ FDQ EH H[SUHVVHG OLQJXLVWLFDOO\ IRU DQDO\WLF SXUSRVHV EXW WKH YHU\ ZRUG LQJ ZH FKRRVH LV DUELWUDU\ LQ RWKHU ZRUGV WR HOLFLW WKHVH LQIRUPDWLRQ LV QRW QHX

'LVFRXUVH DQG EH\RQG



WUDO EXW RQ WKH FRQWUDU\ LV IXOO RI FKRLFHV RI KRZ FRJQLWLYHO\ DQG OLQJXLVWLFDOO\ WKH VFHQH LV SHUFHLYHG )RU WKLV UHDVRQ LOORFXWLRQ VKRXOG EH UHSUHVHQWHG DV SDFNHG KLGGHQ LQIRUPDWLRQ WR EH HOLFLWHG RQO\ ZKHQ UHDOO\ QHHGHG :H ZLOO LQGLFDWH SUDJPDWLF LQIRUPDWLRQ²KLGGHQ XQGHU WKH DGWUHH²ZLWK ODPEGDV λ   p
←A
ǫA

λ1 AA

△

△

loc1 illoc1 I{λ λ )LJXUH  3UDJPDWLF DEVWUDFW DGWUHH DW WXUQ  /HW XV LPDJLQH WKDW D VSHDNHU VWDUWV D FRQYHUVDWLRQ ZH ZLOO LQGLFDWH ZKDW LV PHDQW LQ WXUQ 1 ZLWK illoc1 DQG ZKDW LV DFWXDOO\ VDLG ZLWK loc1 )LJXUH   :KDW VDLG ORFXWLRQDU\ IDFHW LH loc1 LV JRYHUQHG E\ ZKDW LV PHDQW LOORFX WLRQDU\ IDFHW LH illoc1  LQWXLWLYHO\ KXPDQV VD\ VRPHWKLQJ OHDG E\ VRPHWKLQJ WKH\ PHDQ 1RUPDOO\ ZKDW LV LQWHQGHG LV PRUH SURPLQHQW WKDQ ZKDW LV DFWXDOO\ VDLG WKHUHIRUH WKH ORFXWLRQLOORFXWLRQ ZLOO EH JRYHUQPHQW →  ,I WKH FRQWUDU\ LV WUXH LH LI WKH ORFXWLRQDU\ IDFHW LV PRUH SURPLQHQW ZRUG LQJ LV IRUFHG WR EH LQWHUSUHWHG LQ LWV EDVLF VHQVH WKLV LV WKH FDVH RI OLWHUDOLVP ZKLFK LV D PLQRULW\ SKHQRPHQRQ LQ DEVROXWH WHUPV ,Q FDVHV RI OLWHUDOLVP WKH ORFXWLRQLOORFXWLRQ UHODWLRQ ZLOO EH RI GHSHQGHQF\ ←  7KH ODPEGD RI WKH PRVW SURPLQHQW IDFHW ZLOO EH SURPRWHG DV WKH ODPEGD RI WKH SUDJPDWLF DGWUHH²D VRUW RI ³DGSRVLWLRQDO´ SUDJPDWLF FKDUDFWHU HYHQ LI WKH ³DGSRVLWLRQ´ LV DOZD\V DQ HS VLORQ WKH LOORFXWLRQDU\ LQIRUPDWLRQ EHLQJ OLQJXLVWLFDOO\ LPSOLFLW %\ FRQYHQWLRQ HYHU\ SKUDVDO FRQVWUXFWLRQ LH DGWUHH JRYHUQHG E\ D YHU EDQW FDQ EH YHKLFOH RI SUDJPDWLF LQIRUPDWLRQ lambda  $ GLUHFW OLQJXLVWLF DFW RFFXUV ZKHQ WKH WZR ODPEGDV EHORQJLQJ UHVSHFWLYHO\ WR ORFXWLRQ DQG LOORFXWLRQ FRLQFLGH RWKHUZLVH WKH OLQJXLVWLF DFW ZLOO EH LQGLUHFW /HW XV VXSSRVH WKDW WKH VSHDNHU KDV UHTXHVWHG D OLQJXLVWLF DFW²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loc2 ? = illoc1  7KH QH[W WXUQV DUH VLPLODU



&KDSWHU 6L[

q
A
← ǫA
λ2 A A


△

△

loc2 ? = illoc1 illoc2 I{λ λ )LJXUH  3UDJPDWLF DEVWUDFW DGWUHH DW WXUQ 

2I FRXUVH HDFK WXUQ FDQ EH IRUPHG E\ PRUH WKDQ RQH ORFXWLRQDU\ DFW²LH SKUDVDO FRQVWUXFWLRQV VHHQ DW WKH SUDJPDWLF OHYHO²DQG WKH FRUUHVSRQGHQW LOORFX WLRQDU\ IDFHWV FDQ FKDQJH ZLWKLQ WKH VDPH WXUQ ,Q VXFK FDVHV WKH OLVWHQHU FDQ VDWLVI\ WKH ODVW LOORFXWLRQDU\ IDFHW RU D SUHYLRXV RQH²RU QR RQH :KDW LV LPSRU WDQW WR QRWH LV WKDW SUDJPDWLFV LV VLPSO\ EXLOW XSRQ WKH VDPH UXOHV ZH KDYH VHHQ LQ WKH SUHYLRXV FKDSWHUV )LJXUH  

q
A
↔ ǫA
λ A Aq

A
↔ ... ǫA
λ A λn A q
A
A A
← ǫA A
λ2 A Aq A

A
← loc2 ? = illoc1 illoc2 ǫA
A λ I{λ λ 1
A

△

△

△

△

△

loc1 I{λ

illoc1 λ

)LJXUH  +RZ WXUQV DUH UHSUHVHQWHG )URP D IRUPDO SRLQW RI YLHZ QRWKLQJ FKDQJHV ODPEGDV DUH RQO\ IXUWKHU GHF RUDWLRQV RI H[LVWLQJ DGWUHHV²KLGGHQ E\ GHIDXOW LQ FDVH RI LOORFXWLRQV PDSSHG RQWR YHUEDQWV LQ FDVH RI ORFXWLRQV 7KHUHIRUH ZKDW ZH QHHG QRZ LV D WD[RQRP\

'LVFRXUVH DQG EH\RQG



RI LOORFXWLRQ VR WKDW ZH FDQ DQVZHU WKH IROORZLQJ TXHVWLRQ KRZ PDQ\ LQVWDQFHV RI ODPEGDV DUH WKHUH"

 $ WD[RQRP\ RI SUDJPDWLF FKDUDFWHUV 2XU DLP LV WR ODEHO HDFK SKUDVH LH SKUDVDO FRQVWUXFWLRQ JRYHUQHG E\ D YHU EDQW ZLWK WKUHH ODPEGDV RQH IRU ORFXWLRQ RQH IRU LOORFXWLRQ DQG RQH RI WKH ORFXWLRQLOORFXWLRQ DGWUHH E\ SURPRWLRQ RI WKH PRVW SURPLQHQW²W\SLFDOO\ WKH LOORFXWLRQDU\ ODPEGD ,W LV LPSRUWDQW WR XQGHUOLQH WKDW RXU FRQWH[W LV QRW RQO\ WKHRUHWLFDO EXW DOVR SUDFWLFDO DQG DSSOLFDWLYH WKH ODEHOOLQJ VKRXOG EH HDV\ WR EH SHUIRUPHG E\ D WUDLQHG WKHUDSLVW RQ WKH WUDQVFULSW RI D FRQYHUVDWLRQ ZLWK FOHDU LQGLFDWLRQV RQ KRZ WR SURFHHG ZLWKRXW SUREOHPV RI VXEMHFWLYLW\ ,Q RWKHU ZRUGV WKH WD[RQRP\ VKRXOG EH SUHFLVH DQG FOHDU EH\RQG LQGLYLGXDO¶V RSLQLRQV RQ RQH KDQG DQG SUDFWLFDO HQRXJK WR EH XVHG ZLWK WKH DSSURSULDWH HIIRUW $ UHOHYDQW SDUW RI WKH SKLORVRSKLFDO LQYHVWLJDWLRQ E\ 6HDUOH LQ WKH ODVW IRXU GHFDGHV LV GHYRWHG WR WKH GHILQLWLRQ DSSOLFDWLRQ DQG UHILQHPHQW RI KLV WD[RQRP\ RI LOORFXWLRQ DQG LWV FRQVHTXHQFHV DW SKLORVRSKLFDO FRJQLWLYH OLQJXLVWLF DQG VR FLDO OHYHOV  ,Q RXU SHUVSHFWLYH 6HDUOH¶V WD[RQRP\ LV DW D SUDJPDWLF OHYHO ZKDW 7HVQLqUH¶V WD[RQRP\ LV DW D V\QWDFWLF OHYHO D XVHIXO VHW RI FKDUDFWHUV LQ RUGHU WR ODEHO ORFXWLRQ LOORFXWLRQ DQG WKHLU UHODWLRQV

'LUHFWLRQV RI ILW :H FDQ GHVFULEH LOORFXWLRQ DV WKH FROOHFWLRQ RI LQWHQWLRQDO VWDWHV UHODWHG WR WKH ORFXWLRQ 6HDUOH LQVLVWV RQ WKH IDFW WKDW ³LQ JHQHUDO EHOLHIV GHVLUHV DQG VR RQ DUH QRW DWWLWXGHV WR SURSRVLWLRQV ,I , EHOLHYH WKDW :DVKLQJWRQ ZDV WKH ILUVW SUHVLGHQW P\ DWWLWXGH LV WR :DVKLQJWRQ DQG QRW WR WKH SURSRVLWLRQ´ 6HDUOH   7KLV LV D YHU\ LPSRUWDQW SRLQW EHFDXVH LW VWDWHV WKDW WKH SURSRVLWLRQ²LQ RXU WHUPV RQH RU PRUH SKUDVDO FRQVWUXFWLRQV VRPHKRZ OLQNHG WRJHWKHU²VKRXOG EH DQDO\VHG WR ILQG WKH H[SUHVVLRQV RI UHIHUHQFH LH WKH VWDWLYHV DQG WKHLU SUHGLFDWLRQV LH YHUEDQWV  ,Q SDUWLFXODU WKHUH DUH SDUWLFXODU YHUEDQWV ZKRVH SUDJPDWLF UROH LV WKHLU UHVSRQVLELOLW\ WR ILW ZKDW $XVWLQ FDOOHG WKH ³LOORFXWLRQDU\ IRUFH´ WR WKH ZRUOG /HW XV LPDJLQH WKDW WKH ZRUOG LH WKH REMHFW RI D SHUVRQ¶V SHUFHSWLRQ WKURXJK VHQVHV DQG PLQG SHUWDLQLQJ WR SKHQRPHQD RU ILFWLRQ DV ZHOO VWDQGV EHORZ XV ZKLOH PLQG LH WKH LOORFXWLRQDU\ IRUFH WKDW GULYHV RXU PHQWDO VWDWHV DQG VR WKH SURSRVLWLRQDO ORFXWLRQ VWDQGV DERYH XV  7KHUH DUH WZR EDVLF GLUHFWLRQV EH



&KDSWHU 6L[

WZHHQ WKH ZRUOG DQG WKH PLQG HLWKHU GRZQZDUG PLQGWRZRUOG RU XSZDUG ZRUOGWRPLQG  7KXV WKH DLP RI D EHOLHI LV WR EH WUXH DQG LW IDLOV LI LW LV IDOVH ,QVRIDU DV LW LV WUXH ZH FDQ VD\ WKDW WKH EHOLHI PDWFKHV RU ILWV RU DFFXUDWHO\ UHSUHVHQWV WKH ZRUOG ,W KDV WKH PLQGWRZRUOG GLUHFWLRQ RI ILW ↓ 'HVLUHV DQG LQWHQWLRQV RQ WKH RWKHU KDQG DUH QRW VXSSRVHG WR UHSUHVHQW KRZ WKH ZRUOG LV EXW KRZ ZH ZRXOG OLNH LW WR EH LQ WKH FDVH RI GHVLUHV RU KRZ ZH LQWHQG WR PDNH LW EH LQ WKH FDVH RI LQWHQWLRQV  :H FDQ VD\ LQ VXFK FDVHV WKDW WKH LQWHQWLRQ DQG WKH GHVLUH KDYH WKH ZRUGWRPLQG GLUHFWLRQ RI ILW ↑ 6HDUOH  ± HPSKDVLV LQ WKH RULJLQDO 

2I FRXUVH EHOLHIV GHVLUHV DQG LQWHQWLRQV GR QRW H[KDXVW DOO WKH SRVVLEOH PHQ WDO VWDWHV 0RVW HPRWLRQDO VWDWHV VXFK DV SULGH VKDPH ZRUU\ DQ[LHW\ JUDWLWXGH ORYH IHDU HQWKXVLDVP GLVJXVW DQG VR RQ SUHVXSSRVH WKH H[LVWHQFH RI WKH ILW 7KXV LI , DP SURXG WKDW , KDYH D ELJ QRVH RU , DP DVKDPHG WKDW , KDYH D ELJ QRVH LQ ERWK FDVHV WKH IDFW WKDW , KDYH D ELJ QRVH LV VLPSO\ WDNHQ IRU JUDQWHG 7KDW LV LW LV QRW WKH DLP RI WKH LQWHQWLRQDO VWDWH WR UHSUHVHQW WKH IDFW WKDW , KDYH D ELJ QRVH PLQGWRZRUOG ↓  QRU LV LW LWV DLP WR EULQJ LW DERXW WKDW , KDYH D ELJ QRVH ZRUOGWRPLQG ↑  ,Q WKHVH VWDWHV ZH VLPSO\ SUHVXSSRVH WKDW , KDYH D ELJ QRVH 6HDUOH   HPSKDVLV LQ WKH RULJLQDO 

6HDUOH  SURSRVHV WR LQGLFDWH WKH SUHVXSSRVHG GLUHFWLRQ RI ILW ZLWK ³3UH VXS )LW´ RU ³3UHVXS´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l  7KH GHILQLWLRQ LV WKDW DQ XWWHUDQFH LV D GHFODUDWLRQ LI WKH VXFFHVVIXO SHUIRU PDQFH RI WKH VSHHFK DFW LV VXIILFLHQW WR EULQJ DERXW WKH ILW EHWZHHQ ZRUGV >LH PLQG DXWKRUV¶ QRWH@ DQG ZRUOG WR PDNH WKH SURSRVLWLRQDO FRQWHQW WUXH 'HFODUDWLRQV WKXV KDYH WKH GRXEOH GLUHFWLRQ RI ILW l >@ ,I VRPHERG\ VD\V ³7KH PHHWLQJ LV DGMRXUQHG´ ³, SURQRXQFH \RX KXVEDQG DQG ZLIH´ ³:DU LV GHFODUHG´ RU ³@ )DLU\ VWRULHV E\ WKH ZD\ DUH IXOO RI GHFODUDWLRQV SHUIRUPHG E\

'LVFRXUVH DQG EH\RQG



ZLWFKHV ZL]DUGV PDJLFLDQV DQG VR IRUWK :H RUGLQDU\ KXPDQV GR QRW KDYH WKH DELOLW\ WR SHUIRUP VXSHUQDWXUDO GHFODUDWLRQV EXW ZH GR KDYH D TXDVL PDJLFDO SRZHU QRQHWKHOHVV RI EULQJLQJ DERXW FKDQJHV LQ WKH ZRUOG WKURXJK RXU XWWHUDQFHV DQG ZH DUH JLYHQ WKLV SRZHU E\ D NLQG RI KXPDQ DJUHHPHQW >@ :KHQ WKH FKDLUPDQ VD\V ³7KH PHHWLQJ LV DGMRXUQHG´ KH SHUIRUPV D OLQJXLVWLF DFW EXW WKH IDFW KH FUHDWHV WKDW WKH PHHWLQJ LV DGMRXUQHG LV QRW D OLQJXLVWLF IDFW 6HDUOH  ± 

6HDUOH¶V VWURQJ WKHVLV LV WKDW 'HFODUDWLRQV DUH WKH PDLQ LQVWUXPHQW LQ RXU FRQ VWUXFWLRQ RI VRFLDO UHDOLW\ RXU PDNLQJ RI WKH VRFLDO ZRUOG 6HDUOH    7DEOH  VXEVXPHV 6HDUOH¶V UHIOHFWLRQV DERXW WKH UHVSRQVLELOLW\ RI WKH LOORFXWRU\ IDFHW RI SUHGLFDWLRQ LQ RXU OLQJXLVWLF SURSRVLWLRQV  7KH WD[RQRP\ SURSRVHG E\ 6HDUOH WR FRPSUHKHQG DOO WKH SRVVLEOH W\SHV RI VSHHFK DFWV DORQJ WKHLU LOORFXWLRQDU\ IDFHW KDV ILYH HOHPHQWV DVVHUWLYHV ↓ A  GLUHFWLYHV ↑ D  FRPPLVVLYHV ↑ C  H[SUHVVLYHV = E  'HFODUDWLRQV l D  ,Q FRQVWUXFWLYH DGSRVLWLRQDO JUDPPDUV HDFK HOHPHQW RI WKLV WD[RQRP\ LV D SUDJPDWLF FKDUDFWHU ZKLFK ODEHOV WKH DFWLYH YHUEDQW RI WKH FRUUHVSRQGLQJ SKUDVDO FRQVWUXFWLRQ ORFXWLRQDU\ FKDUDFWHU λloc DQG LWV LOORFXWLRQDU\ JRYHUQRU LOORFXWLRQDU\ FKDUDFWHU λilloc  DV DOUHDG\ VKRZQ LQ )LJXUH  ZKLFK LOOXVWUDWHV WKH SUDJPDWLF DEVWUDFW DGWUHH ,Q WKH VHTXHO ZH ZLOO H[SODLQ GLUHFW DFWV EHIRUH DV WKH\ DUH VLPSOHU WKDQ LQGLUHFW RQHV ,Q IDFW GLUHFW VSHHFK DFWV KDYH WKH VDPH YDOXH LQ ERWK ODPEGDV λilloc = λloc  7DEOH  6HDUOH¶V GLUHFWLRQV RI ILW

GLUHFWLRQ RI ILW PLQGWRZRUOG

V\PERO ↓

ZRUOGWRPLQG

↑

PLQGZRUOG SUHVXSSRVHG

=

PLQG ZRUOG

l

LQWHQWLRQDO VWDWHV EHOLHIV YLVXDO H[SHULHQFH UHPHPEHULQJ LQWHQWLRQV GHVLUHV SULGH DVKDPH JUDWLWXGH HWF QRQH



&KDSWHU 6L[

$VVHUWLYHV $VVHUWLYHV DUH WKH ILUVW W\SH LQ 6HDUOH¶V WD[RQRP\ DQG WKH\ JLYH DQ DFFRXQW RI PLQGWRZRUOG ↓ GLUHFWLRQ RI ILW )RU WKLV UHDVRQ WKHLU V\PERO LV WKH IROORZLQJ RQH ↓ A  DQG WKHLU SURWRW\SLFDO YHUEDQW LV DVVHUW $VVHUWLYHV FRPSUHKHQG VWDWH PHQWV GHVFULSWLRQV DVVHUWLRQV DQG VR RQ 7KH\ DUH SURMHFWHG RQ WKH RQJRLQJ VWLOO LQ SURJUHVV RU ILQLVKHG WKH µ\HW¶  (DFK SUDJPDWLF FKDUDFWHU KDV DQ H[DFW DQDORJXH LQ LQWHQWLRQDO VWDWHV FRUUH VSRQGLQJ WR DVVHUWLYHV DUH EHOLHIV 7KHUHIRUH WKHLU HVVHQWLDO IHDWXUH LV WR EH WUXH RU IDOVH DQG WKHLU LOORFXWLRQDU\ FRQWHQW LV WKH SURSRVLWLRQ LWVHOI ,Q RWKHU ZRUGV WKH VSHDNHU KDV HYLGHQFH UHDVRQV HWF IRU WKH WUXWK RI WKH SURSRVLWLRQ DQG KH FRPPXQLFDWHV WKLV EHOLHI WR WKH OLVWHQHU DV ZHOO 7KHUH LV QR DWWHPSW WR FRQYLQFH WKH OLVWHQHU WR DGRSW WKH VSHDNHU¶V EHOLHI ³7KXV µ, DP VLPSO\ VWDWLQJ WKDW p DQG QRW DWWHPSWLQJ WR FRQYLQFH \RX¶ LV DFFHSWDEOH´ 6HDUOH    D , ZRQ WKH UDFH , DP WHOOLQJ WKDW , ZRQ WKH UDFH /HW VXSSRVH WKDW D FKDPSLRQ LQ )RUPXOD  UDFLQJ LV JLYLQJ DQ LQWHUYLHZ  D   7KHUH DUH WZR SUDJPDWLF DFWDQWV WKH ILUVW DFWDQW LV WKH VSHDNHU S LQ WKLV FDVH WKH FKDPSLRQ ZKLOH WKH VHFRQG DFWDQW LV WKH VSHDNHU¶V EHOLHI (Y, S) ZKHUH KHUH Y VWDQGV IRU WKH EHOLHI  6SHDNHU DVVHUWV WKDW VSHDNHU¶V EHOLHI H[LVWV

q
A
←A
WKDW ↓A A A
q
A A
→ A A ǫ
Y A A A Aq q

A
A
→A
→ H[LVWV A ·V
Y A
↓A A Ix A A



△

△

△

△

△

VSHDNHU

EHOLHI

VSHDNHU

DVVHUWV

X=S>A

Y

X=S

↓A

)LJXUH  $EVWUDFW SUDJPDWLF DGWUHH IRU DVVHUWLYHV

'LVFRXUVH DQG EH\RQG



([DPSOH  LV D SRVVLEOH ZRUGLQJ IRU WKH DEVWUDFW SUDJPDWLF DGWUHH IRU DVVHUWLYHV )LJXUH   7KH LOORFXWLRQ VWDQGV DW WKH ULJKW RI WKH DGWUHH VSHDNHU DVVHUWV  DQG WKH DGSRVLWLRQ ZDV ER[HG DV LW GRHV QRW PDNH VHQVH WR JHW LW H[SOLFLW 2Q WKH OHIW VLGH WKHUH LV WKH ORFXWLRQDU\ SDUW ZKHUH WKH PRUSKRV\QWDFWLF YD OHQF\ ZDV OHIW XQGHUVSHFLILHG Ix  DV WKH WZR SUDJPDWLF DFWDQWV RI DVVHUWLYHV DUH FRPSOHWHO\ LQGHSHQGHQW IURP WKH DFWXDO PRUSKRV\QWDFWLF UHDOLVDWLRQV SHUIRUPHG E\ ORFXWLRQ 7KLV LPSRUWDQW IDFW LV HDV\ WR VKRZ WKURXJK DQ H[DPSOH  , WHOO \RX ZKDW , IRXQG LQ WKH OLEUDU\ )RU LQVWDQFH  LV FOHDUO\ DQ DVVHUWLRQ DQG LWV ORFXWLRQ LV JRYHUQHG E\ WKH WULYDOHQW YHUEDQW WHOO , LV WKH ILUVW DFWDQW ZKDW , IRXQG LQ WKH OLEUDU\ WDNHQ DV D ZKROH LV WKH VHFRQG DFWDQW ZKLOH ILQDOO\ \RX LV WKH WKLUG RQH

q
A
← A WKDW
 A ↓ q
A A A
A A
← ǫA A
I2 A A
2 Aq A
A A A
→ WKH UDFH ǫ A (Y, S)
I21 A Aq A

A ZRQ , →A
X = S I2 {↓ A
 A ↓A
A

△

△  △

{

p
←A
ǫA

p ↓ A AA
←A A
ǫA A 2 AA

I2 AAp
→A A A WKH UDFH
ǫ A 2 A
AA I (Y, S)
1 A

△

,

S

ZRQ

↓A

   VSHDNHU DVVHUWV  X=S ↓A

△

DVVHUW

(↓ A, S)

)LJXUH  3UDJPDWLF DGWUHH RI WKH DVVHUWLYH , ZRQ WKH UDFH )LJXUH  VKRZV KRZ WR LQVWDQWLDWH WKH DEVWUDFW SUDJPDWLF DGWUHH IRU WKH DV VHUWLYH D  :KLOH RQ WKH OHIW DGWUHH VRPH PRUSKRV\QWDFWLF LQIRUPDWLRQ ZDV SURYLGHG LQ RUGHU WR KHOS WKH UHDGHU LQ HVWDEOLVKLQJ WKH EULGJH EHWZHHQ FRQVWUXF WLYH PRUSKRV\QWD[ DQG SUDJPDWLFV RQ WKH ULJKW RQO\ WKH SUDJPDWLF ODEHOV ZHUH PDGH H[SOLFLW LQ SDUWLFXODU (↓ A, S) LQGLFDWHV LQ D FRPSDFW ZD\ WKDW LOORFXWLRQ LV SHUIRUPHG E\ S



&KDSWHU 6L[

'LUHFWLYHV 7KH DLP RI GLUHFWLYHV LV WR WU\ WR JHW RWKHU SHRSOH WR GR WKLQJV 7KH VSHDNHU ZKR VD\V WKH XWWHUDQFH LV QRW VDWLVILHG RI WKH ZRUOG DV LW LV VR LW WULHV WR FKDQJH LW 7KHUHIRUH GLUHFWLYH GLUHFWLRQ RI ILW LV ZRUOGWRPLQG ↑ 3URWRW\SLFDO H[DPSOHV RI GLUHFWLYHV DUH RUGHUV FRPPDQGV UHTXHVWV EXW DOVR GHVLUHV ZDQWV ZLVKHV DQG VR RQ 7KHLU V\PERO LV ↑ D  DQG WKHLU SURWRW\SLFDO YHUEDQW LV direct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²WKLV LV YDOLG IRU DQ\ SUDJPDWLF FKDUDFWHU QRW RQO\ GLUHFWLYHV DV LQ    /L]D RUGHUHG 3DXO WR OHDYH ,Q VXFK FDVHV WKH LOORFXWLRQDU\ SDUW RI WKH DGWUHH FDQ EH UHQGHUHG H[SOLFLWO\ DV LQ )LJXUH 

&RPPLVVLYHV 'LUHFWLYHV DQG FRPPLVVLYHV VKDUH WKH SURSHUW\ RI KDYLQJ DQ XSZDUG GLUHFWLRQ RI ILW ↑ DQG IRU WKLV UHDVRQV WKH\ DUH FDOOHG FROOHFWLYHO\ PRWLYDWRUV 6HDUOH    8QOLNH DVVHUWLYHV WKH\ DUH ERWK SURMHFWHG WR WKH IXWXUH WKH µQRW \HW¶  +RZHYHU ZKLOH GLUHFWLYHV DUH WU\LQJ WR FKDQJH WKH ZRUOG WKURXJK RWKHUV FRPPLVVLYHV UHO\ RQ WKH VSHDNHU KLPVHOI 7\SLFDO FRPPLVVLYHV DUH SURPLVHV YRZV DQG SOHGJHV 7KHLU LQWHQWLRQDO VWDWH LV SXUH LH LW LV LQWHQWLRQ 7KH FRQ YHQWLRQDO V\PERO IRU FRPPLVVLYH LV ↑ C  DQG WKH SURWRW\SLFDO YHUEDQW LV FRPPLW

'LVFRXUVH DQG EH\RQG



q
A
← ǫA
↑D A
q A
A A
→ A ǫA
Ix A A
Aq A
A A
↔ A UHTXHVW ǫA x A
A I Z A
Aq
A
→ WRBGR UHFHLYHU A
↑D A Ix Y=R
A

△

△

△

△

△

VSHDNHU

GLUHFWV

X=S

↑D

)LJXUH  $EVWUDFW SUDJPDWLF DGWUHH IRU GLUHFWLYHV

q
A
← ǫA
↑D A A q

A A
← A ǫA
I2 A A
2 Aq A
A A
← A WKH UDFH ǫA A (Z, R)
I21 A
A A

△

\RX

R

ZLQ

↑D

△

GLUHFW

(↑ D, S)

)LJXUH  3UDJPDWLF DGWUHH RI WKH GLUHFWLYH :LQ WKH UDFH



&KDSWHU 6L[

p
←A
ǫA

↑ D AA
A
A AA



△

△

3DXO WR OHDYH

/L]D RUGHUHG

(Z, R)

(↑ D, S)

)LJXUH  3UDJPDWLF DGWUHH RI WKH GLUHFWLYH /L]D RUGHUHG 3DXO WR OHDYH

([DPSOH  LV D SRVVLEOH ZRUGLQJ RI FRPPLVVLYHV )LJXUH   WKH DQDORJLHV DQG GLIIHUHQFHV ZLWK GLUHFWLYHV DUH TXLWH FOHDU  6SHDNHU SURPLVHV WKDW VSHDNHU ZLOO GR WKH SURPLVH

q
A
← ǫA
↑C A
q A
A A
→ A ǫA
Ix A A
Aq A
A A
↔ A SURPLVH ǫA x A
A I Z
A Aq
A
→ VSHDNHU ZLOOBGR A
↑C A Y=S Ix
A

△

△

△

△

△

VSHDNHU SURPLVHV

X=S

↑C

)LJXUH  $EVWUDFW SUDJPDWLF DGWUHH IRU FRPPLVVLYHV ,I ZH H[SDQG WKH VFHQH DURXQG WKH )RUPXOD  UDFLQJ VWDWHG EHIRUH LQ F LV UHSRUWHG ZKDW WKH FKDPSLRQ VD\V LQ KLV FDU EHIRUH WKH VWDUW )LJXUH   F ,¶OO ZLQ WKH UDFH , SURPLVH P\VHOI WR ZLQ WKH UDFH

'LVFRXUVH DQG EH\RQG



q
A
← ǫA
↑C A
q A A
A A
← ǫA A
I2 A A
2 Aq A
A A
← WKH UDFH ǫA 2 A A
I (Z, S) A
1 A

△

,

S

△

△

·OO ZLQ

FRPPLW

↑C

(↑ C , S)

)LJXUH  3UDJPDWLF DGWUHH RI WKH FRPPLVVLYH ,¶OO ZLQ WKH UDFH

,W LV LPSRUWDQW WR QRWH WKDW D FRPPLVVLYH LV DOZD\V UHIHUUHG WR WKH VSHDNHU S SURSHUO\ WKH SXUH LQWHQWLRQ LV QRW GLUHFWHG WR RWKHUV ,Q F  WKH FKDPSLRQ LV QRW QHFHVVDULO\ HQWDQJOLQJ KLPVHOI ZLWK DQ DQVZHU WR KLV WHDP OHDGHU¶V GLUHF WLYH²HYHQ LI VXFK D VFHQDULR LV QRW RQO\ SRVVLEOH EXW DOVR UHDOLVWLF ,Q VXFK D FDVH WKH LQWHQWLRQ LV QR PRUH SXUH HYHQ LI WKH SUDJPDWLF FKDUDFWHU UHPDLQV ↑ C  ,Q IDFW PRVW XWWHUDQFHV GR QRW OLYH LQ LVRODWLRQ EXW LQ FRQYHUVDWLRQV ZKHUH D FRP SOH[ DUFKLWHFWXUH RI LPSOLFDWLRQV SUHVXSSRVLWLRQV DVVXPSWLRQV DUH FRQWLQXDOO\ QHJRWLDWHG DPRQJ WKH DFWRUV RI WKH FRQYHUVDWLRQ LWVHOI

([SUHVVLYHV 6SHDNHUV XVH H[SUHVVLYHV ZKHQ WKH UHODWLRQ PLQGZRUOG LV WDNHQ DV JUDQWHG LV SUHVXSSRVHG DQG VRPH IHHOLQJ DWWLWXGH RU HPRWLRQ DERXW D VWDWH RI DIIDLUV LV QHHGHG WR EH H[SUHVVHG 7KH FRQYHQWLRQDO V\PERO RI H[SUHVVLYH LV = E  DQG LW FRYHUV WKH ZKROH UDQJH RI LQWHQWLRQDO VWDWHV ZKHUH WKH HPRWLRQDO SDUW LV UHOHYDQW 6HDUOH¶V H[DPSOHV DUH JUHHWLQJV FRQJUDWXODWLRQV DQG DSRORJLHV EXW WKH OLVW FDQ EH H[WHQGHG HDVLO\ IROORZLQJ FXOWXUDO FRQWH[WV WLPH DJH SHUVRQDOLW\ RI VSHDNHUV DQG VR RQ 7KH SURWRW\SLFDO YHUEDQW LV H[SUHVV  6SHDNHU H[SUHVVHV VSHDNHU¶V HPRWLRQ RQ UHFHLYHU )LJXUH  VKRZV WKH SUDJPDWLF DGWUHH RI D SRVVLEOH DEVWUDFW ZRUGLQJ RI H[SUHVVLYHV   /LNH FRPPLVVLYHV WKH LQWHQWLRQDO VWDWH RI H[SUHVVLYHV VWDQGV



&KDSWHU 6L[

LQ WKH VSHDNHU EXW XQOLNH FRPPLVVLYHV²DQG OLNH GLUHFWLYHV²WKH WKLUG DFWDQW LV WKH UHFHLYHU R RI WKH VSHDNHU¶V HPRWLRQ (Y, S) 6RPHWLPHV (Y, S) LV QRW HQWLUHO\ NQRZQ HYHQ E\ WKH VSHDNHU KLPVHOI WKLV LV SDUW RI WKH UHDVRQ ZKLOH KXPDQ EHLQJV DUH LQWURVSHFWLYH DQG KHQFH ZK\ SV\FKRORJLVWV DQG WKHUDSLVWV LQ JHQHUDO GR H[LVW LQ DQ\ KXPDQ VRFLHW\²FDOO WKHP VKDPDQV UDEELV SULHVWV RU ZKDWHYHU 

q
A
← ǫA
=E A AA q


A A ←A
RQ A
Ix A A AAq AA


A A
→A A UHFHLYHU
I·Vx A A R
A AAq
A
A
→ VSHDNHU HPRWLRQ ǫA S Ix = Y
= E A AA



△

△

△

△

△

VSHDNHU H[SUHVVHV

X=S

=E

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³RWKHU´ PHQWDO VWDWHV GLIIHUHQW IURP EHOLHIV GHVLUHV DQG LQWHQWLRQV²'HFODUDWLRQV KDYLQJ QR LQWHQWLRQDO VWDWHV DW DOO 1RQHWKHOHVV WKHLU

'LVFRXUVH DQG EH\RQG



q
A
←A
=ǫE A
A A q

A A
←A A
IRU A A
E A A Aq
A
A A
←A A WKHLU KHOS
ǫ2 A A (Y, S)
I2 A A
A A

△

△

△

△

P\ WHDP

, WKDQN

H[SUHVV

R

(Y, S)

(= E, S)

)LJXUH  3UDJPDWLF DGWUHH RI WKH H[SUHVVLYH , WKDQN P\ WHDP IRU WKHLU KHOS

LPSRUWDQFH FDQQRW EH SXW EHORZ DVVHUWLYHV GLUHFWLYHV RU FRPPLVVLYHV 0RUH RYHU H[SUHVVLYHV DUH YHU\ LPSRUWDQW IRU WKHUDSLVWV DV WKH\ SHUPLW WR FRORXU WKH SUDJPDWLF SLFWXUH ZLWK D IXOO SDOHWWH RI HPRWLRQV

'HFODUDWLRQV 6HDUOH  GHYRWHV PRVW RI KLV UHIOHFWLRQV RQ 'HFODUDWLRQV EHFDXVH WKH\ FUH DWH HVWDEOLVK DQG WUDQVIRUP VRFLDO UHDOLW\ 7KHLU GLUHFWLRQ RI ILW LV ERWK PLQG WRZRUOG DQG ZRUOGWRPLQG LH PLQG ZRUOG l DQG KHQFH WKHLU V\PERO LV WKH IROORZLQJ l D  :KDW 'HFODUHG LV D UHDOLW\ EXLOW RYHU WKH SK\VLFDO RQH 2XU VHQVH WKDW WKHUH LV DQ HOHPHQW RI PDJLF D FRQMXULQJ WULFN D VOHLJKW RI KDQG LQ WKH FUHDWLRQ RI LQVWLWXWLRQDO IDFWV RXW RI EUXWH IDFWV GHULYHV IURP WKH QRQSK\VLFDO QRQFDXVDO FKDUDFWHU RI WKH UHODWLRQ RI WKH ; DQG < WHUPV LQ WKH VWUXFWXUH ZKHUH ZH VLPSO\ FRXQW ; WKLQJV DV < WKLQJV ,Q RXW WKRXJK HVW PHWDSK\VLFDO PRRG ZH ZDQW WR DVN µ%XW LV DQ ; UHDOO\ D <"¶ )RU H[ DPSOH DUH WKHVH ELWV RI SDSHU UHDOO\ PRQH\" ,V WKLV SLHFH RI ODQG UHDOO\ VRPHERG\¶V SULYDWH SURSHUW\" ,V PDNLQJ QRLVHV WKURXJK WKH PRXQW UHDOO\ JHWWLQJ PDUULHG " >@ :H GR QRW KDYH WKLV VHQVH RI JLGGLQHVV ZKHUH WKH DJHQWLYH IXQFWLRQ LV SHUIRUPHG HQWLUHO\ LQ YLUWXH RI SK\VLFDO IHDWXUHV 7KLV ZH GR QRW KDYH DQ\ PHWDSK\VLFDO GRXEWV DERXW ZKHWKHU RU QRW WKLV LV UHDOO\



&KDSWHU 6L[ D VFUHZGULYHU RU WKLV LV UHDOO\ D FDU EHFDXVH WKH VKHHU SK\VLFDO IHDWXUHV RI WKH REMHFWV LQ TXHVWLRQ HQDEOH WKHP WR IXQFWLRQ DV VFUHZGULYHUV RU FDUV 6HDUOH  

'HFODUDWLRQV DUH VSHFLDO LQ PDQ\ ZD\V )LUVW WKHUH LV QR LQWHQWLRQDO VWDWH EHFDXVH WKH 'HFODUDWLRQ LV SHUIRUPDWLYH LQVWHDG RI SRVLQJ DQ LQWHQW WKH VSHDNHU SHUIRUPV DQ DFW 'HFODUDWLRQV OLYH LQ WKH µKHUH DQG QRZ¶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¶ &KDPSLRQVKLS :'& UHFRJQLVHG E\ D VHW RI 'HFODUDWLRQV  ZKLOH WKH VSHDNHU S LV WKH RIILFLDO UHIHUHH LQ WKLV UDFH ± VWDWXV JLYHQ E\ DQRWKHU 'HFODUDWLRQ 7KH UHFHLYHU R VKRXOG EH WKH GULYHU ZKR DFWXDOO\ ZRQ WKH UDFH DQG WKURXJK WKH VSHDNLQJ RI H KH DFTXLUHV WKH QHZ VRFLDO VWDWXV S EHFRPLQJ WKH ZLQQHU RI WKH UDFH $OO FRPSRQHQWV RI C DUH QHHGHG LQ RUGHU WR DFWLYDWH WKH 'HFODUDWLRQ IRU LQVWDQFH LI WKH VSHDNHU LV QRW WKH RIILFLDO UHIHUHH EXW D FKDPSLRQ¶V IDQ WKH 'HFODUDWLRQ IDLOV  l D 'HFODUDWLRQV OLYH ZLWKLQ LQVWLWXWLRQV IRU LQVWDQFH ZLWKLQ KLV IDPLO\ KH LV WKH IDWKHU IRU KLV FKLOGUHQ DQG WKH KXVEDQG IRU KLV ZLIH  ZKLOH IRU KLV ROG JRRG IULHQGV RI KLV FROOHJH KH LV VLPSO\ DQ DOXPQXV ,QVWLWXWLRQV DUH VRFLDO UHDOLWLHV ZKLFK FROOHFWLYHO\ IRUP D VRFLHW\ ZLWKLQ WKHLU VRFLHW\ LQVWLWXWLRQV KHOG GHRQWLF SRZHUV VRPHRQH KDV VRPH ULJKW WR GR WKLQJV LQ KROGLQJ WKH VWDWXV S DQG VRPH REOLJDWLRQV DV ZHOO )RU H[DPSOH UHOLJLRQ DV VXFK LV QRW DQ LQVWLWXWLRQ ZKLOH WKH &DWKROLF &KXUFK LV

'LVFRXUVH DQG EH\RQG



7KHUH LV D WHVW WR XQGHUVWDQG LI D DFWLYDWLQJ FRQWH[W SHUWDLQV WR DQ LQVWLWXWLRQ ³,I SHRSOH GR QRW QRZ EHOLHYH LW DQG GLG QRW LQ WKH SDVW EHOLHYH LW ZRXOG LW VWLOO EH WUXH" ,Q WKH FDVH RI D UHFHVVLRQ LI SHRSOH GLGQ¶W EHOLHYH WKDW LW ZDV D UHFHVVLRQ LW ZRXOG VWLOO EH D UHFHVVLRQ´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¶V ILFWLRQDO SOD\ VXFK DV ³2ND\ ,¶OO EH $GDP \RX EH (YH DQG ZH¶OO OHW WKLV EORFN EH WKH DSSOH´ D FUXFLDO FDSDFLW\ IRU VDQH JURZLQJ DV SRLQWHG RXW E\ 5DNRF]\ DQG 7RPDVHOOR 6HDUOH     6SHDNHU 'HFODUHV µWKH 5HFHLYHU KDV WKH 'HFODUHG 6WDWXV¶

q
A
←  A
lDA
q A
A A
← A ǫA
Ix A A Aq
A
A A VWDWXV
→ A ǫA S
Ix A A
A Aq
A UHFHLYHU KDV
→ ǫA Y=R Ix
lD A
A VSHDNHU 'HFODUHV

X=S

lD

)LJXUH  $EVWUDFW SUDJPDWLF DGWUHH IRU 'HFODUDWLRQV ([DPSOH  LV D SRVVLEOH ZRUGLQJ IRU 'HFODUDWLRQV ,QVWLWXWLRQV DUH QRW RQO\ JRYHUQPHQWDO RU HFRQRPLF ORFDO VSRUWLQJ FOXEV VFKRROV SULYDWH SURSHUW\



&KDSWHU 6L[

IULHQGVKLS IDPLO\ DUH DOO YDOLG LQVWLWXWLRQV DV WKH WHVW IRU WKH DFWLYDWLQJ FRQWH[W LV SDVVHG²LH WKH REMHFW QDPHG KDV GHRQWLF SRZHUV  )DWKHU
q
A
← ǫA
lD A
q A
A A
→ A ǫA
I2 A A
2 Aq A

A A

← A ǫA

I2 A A
q
1 A Aq
A
A
△

EODFN

VKHHS

A

O

)LJXUH  3UDJPDWLF DGWUHH RI «EODFN VKHHS« ,Q  WKH VSHDNHU S LV D IDWKHU ZKR 'HFODUHV WR WKH UHFHLYHU R KLV VRQ WKDW KH RZQV WKH VWDWXV S RI EHLQJ WKH EODFN VKHHS RI WKH IDPLO\²FRXQWLQJ DV D ZKROH XQGHU D SUDJPDWLF SRLQW RI YLHZ )LJXUH   ,Q  WKH LQVWLWXWLRQ ZLWKLQ WKH DFWLYDWLQJ FRQWH[W C LV YDOLG DQG LW LV WKH IDPLO\ XQOLNH RWKHU H[DPSOHV LQ  WKH UHOHYDQW LQVWLWXWLRQ LV VDLG H[SOLFLWO\ 2I FRXUVH D IDWKHU FDQ 'HFODUH LW VXFFHVVIXOO\ EHFDXVH KH RZQV D SURSHU VWDWXV LQ WKH IDPLO\ ,I WKH VSHDNHU ZHUH D VRQ¶V IULHQG IRU LQVWDQFH  ZRXOG EH VLPSO\ DQ DVVHUWLYH ↓ A  2XU FODLP LV WKDW &RQVWUXFWLYH &RQYHUVDWLRQDO $QDO\VLV FDQ KHOS D WKHUDSLVW LQ PDNLQJ H[SOLFLW WKH LQVWLWXWLRQV DQG UHODWHG 'HFODUDWLRQV WKDW UXOHV SDWLHQW¶V OLIH TXLWH RIWHQ KLP EHLQJ XQDZDUH RI WKHP

'LVFRXUVH DQG EH\RQG



7DEOH  7KH SUDJPDWLF FKDUDFWHUV W\SH RI LOORFXWLRQ DVVHUWLYH GLUHFWLYHV FRPPLVVLYHV H[SUHVVLYHV 'HFODUDWLRQV

YHUEDQW

V\PERO

DVVHUW GLUHFW FRPPLW H[SUHVV 'HFODUH

↓A ↑D ↑C =E lD

LQWHQWLRQDO VWDWH EHOLHIV GHVLUHV LQWHQWLRQ PDQ\ QRQH

GLUHFWLRQ RI ILW PLQGWRZRUOG ZRUOGWRPLQG ZRUOGWRPLQG 3UHVXS PLQG ZRUOG

SUDJPDWLF DFWDQWV S; (Y, S) S; R; (Z, R) S; S; (Z, S) S; (Y, S); R S; (S, R)

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↓ A  :K\ KDYH \RX VWLOO WR ILQLVK \RXU KRPHZRUN" ↑ D  2Q ZKDW , KDYH P\ PLQG IL[HG WRGD\" ↑ C  +RZ VKRXOG , IHHO DERXW WKDW" = E 8QWLO QRZ ZH KDYH VHHQ GLUHFW DFWV LH ZKHUH WKH SUDJPDWLF FKDUDFWHU RI WKH LOORFXWLRQ LV WKH VDPH RI WKH SUDJPDWLF FKDUDFWHU RI WKH ORFXWLRQ λilloc = λloc  ,Q WUXWK UHDOZRUOG VSHHFK DFWV DUH RIWHQ LQGLUHFW )RU LQVWDQFH W\SLFDO LQGLUHFW DFWV DUH FRPPLVVLYHV PDVNHG DV GLUHFWLYHV DQG YLFH YHUVD  , SURPLVH \RX¶OO GR LW  , UHTXHVW P\VHOI WR EH EUDYH



&KDSWHU 6L[

q
A
→ ǫA
↑D A A q

A
← ǫ A , SURPLVH
I2 A (↑ C , S)
2 Aq
A LW
← A (Z, R)
ǫ2 A I1
A

△

\RX

R

q
A
→ ǫA
↑D A
A

, SURPLVH
(↑ C , S)


△

{

△

\RX·OO GR LW

△

(↑ D, S)

·OO GR

(↑ D, S)

)LJXUH  $GWUHHV RI WKH LQGLUHFW GLUHFWLYH , SURPLVH \RX¶OO GR LW

q
A
→ ǫA
↑C A AA q


A
→ , UHTXHVW ǫA
I2 A (↑ D, S) 2 AAq


A EUDYH
→ ǫA (Z, S)
I2 A 1 AA



△

△

△

P\VHOI

WR EH

S

(↑ C , S)

q
A
→ ǫA
↑C A AA



, UHTXHVW
(↑ D, S)



△

{

△

WR EH EUDYH

(↑ C , S)

)LJXUH  $GWUHHV RI WKH LQGLUHFW FRPPLVVLYH , UHTXHVW P\VHOI WR EH EUDYH

'LVFRXUVH DQG EH\RQG



7KH JRYHUQRU , SURPLVH RI  LV SURWRW\SLFDO RI FRPPLVVLYHV EXW WKH LQ QHU VWUXFWXUH RI WKH GHSHQGHQW \RX¶OO GR LW UHYHDO WKH VWURQJHU SUDJPDWLF FKDUDF WHU RI GLUHFWLYH )LJXUH   ,Q IDFW  VHHPV OLNHO\ WR EH D VRUW RI PHQDFH WKH ILQDO SUDJPDWLF FKDUDFWHU ZLOO EH GLUHFWLYH  :K\ VKRXOG , EH DQJU\ ZLWK KLP" = E {↑ D  , ZRQGHU LI , DP DVKDPHG WR IROORZ KHU = E {↓ A

q
A
←A
↑ "D A AA



WHOOBPH ZK\
(↑ D, S)



△

q
A
←A
LI A ↓A AA



, ZRQGHU
(↓ A, S)

△





△

△

VKRXOG , EH DQJU\ ZLWK KLP

, DP DVKDPHG WR IROORZ KHU

(= E, S)

(= E, S)

)LJXUH  7ZR H[DPSOHV RI LQGLUHFW DFWV HQFDSVXODWLQJ H[SUHVVLYHV ,Q SULQFLSOH DQ\ SUDJPDWLF FKDUDFWHU FDQ EH XQGHU GLVJXLVH /HW XV SUHVHQW WZR H[DPSOHV RI H[SUHVVLYHV  LV D UHTXHVW ↑ D WR WKH OLVWHQHU DERXW D IHHOLQJ RI DQJHU ZKLFK LV DQ H[SUHVVLYH = E  0RUHRYHU  HQFDSVXODWHV WKH DVKDPH = E LQWR D EHOLHI WKURXJK WKH JRYHUQRU , ZRQGHU VR WKDW WKH ILQDO SUDJPDWLF FKDUDFWHU LV DVVHUWLYH ↓ A )LJXUH   $JDLQ XQOLNH WKH RWKHUV W\SHV 'HFODUDWLRQV VHHP QRW WR EH VXLWDEOH IRU PDVTXHUDGH RU LQGLUHFWQHVV

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



&KDSWHU 6L[

$ FOLHQWWKHUDSLVW LQWHUDFWLRQ IUDJPHQW 7KH IUDJPHQW RI WKH LQWHUDFWLRQ LV  WXUQV ORQJ ZKLFK PHDQV OHVV WKDQ D PLQXWH RI FRQYHUVDWLRQ )LQQ    /HW XV FRQVLGHU WKDW D FOLHQWWKHUDSLVW LQWHUDFWLRQ QRUPDOO\ ODVWV DSSUR[LPDWHO\  PLQXWHV WKHUHIRUH RXU GDWD DUH YHU\ OLPLWHG 1RQHWKHOHVV VRPH XVHIXO LQIRUPDWLRQ FDQ VWLOO EH H[WUDFWHG W

6WHYH

W W

-LP 6WHYH

W W W

-LP 6WHYH -LP

W W

6WHYH -LP

, ZRQGHU LI \RX¶UH ZLOOLQJ WR GR D OLWWOH H[SHULPHQW ZLWK PH" :KDW¶V WKDW" ,¶G OLNH WR JLYH \RX DQRWKHU DFKLHYHPHQW WDVN WKDW ZRXOG QRUPDOO\ SXOO IRU WKH ORVHU OHQV DQG VHH LI ZH FDQ NHHS LW IURP KDSSHQLQJ 2. +RZ ZRXOG ZH GR WKDW" 'R \RX KDYH DQ\ LGHDV EDVHG RQ ZKDW ZH WDONHG DERXW" :HOO , JXHVV ILUVW , VKRXOG MXVW NHHS JRLQJ QR PDWWHU KRZ EDGO\ , WKLQN ,¶P JRLQJ *RRG LGHD $QG ZKDW PLJKW WKDW EH OLNH" , JXHVV ,¶OO IHHO DQ[LRXV

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λilloc LV SURYLGHG 2I FRXUVH LW LV DOZD\V SRVVLEOH WR JHW WKH SUDJPDWLF DGWUHHV²EXLOW XSRQ WKH PRUSKRV\QWDFWLF DGWUHHV DV ZHOO²H[SOLFLW XQGHU UHTXHVW EXW WKH IHHG EDFN UHFHLYHG E\ WKH ILUVW DSSOLFDWLRQV RI &R&$/ ZH KDG ZLWK SV\FKRWKHUDSLVWV LV WKDW WKH WUDQVFULSW D WDEOH DQG D FRPPHQW ZULWWHQ LQ QDWXUDO ODQJXDJH LV DGHTXDWH IRU D JRRG UHSRUW 0DLQO\ WKH IUDJPHQW LV EDVHG RQ DVVHUWLYHV±ZLWK 6WHYH H[SODLQLQJ WKH OLWWOH H[SHULPHQW LH WKH WDVN SURSRVHG WR -LP²DQG GLUHFWLYHV²ZLOO -LP DFFHSW WR GR WKH WDVN DV UHTXHVWHG E\ 6WHYH" ,Q WXUQ  WKH WKHUDSLVW PDNHV D UHTXHVW ↑ D XQGHU D EHOLHI ↓ A  EXW WKH DQVZHU LQ WXUQ  LV QRW D FRPPLVVLYH EXW UDWKHU D UHTXHVW IRU FODULILFDWLRQ ↑ D  6R LQ WXUQ D WKH WKHUDSLVW VRIWHQV WKH UHTXHVW ↑ D  H[SODLQLQJ

'LVFRXUVH DQG EH\RQG



7DEOH  7KH &RQVWUXFWLYH &RQYHUVDWLRQDO $QDO\VLV RI )LQQ   WXUQ W W WD WE WF WD WE W W WD WE WD WE

VSHDNHU 6WHYH -LP 6WHYH 6WHYH 6WHYH -LP -LP 6WHYH -LP 6WHYH 6WHYH -LP -LP

YHUEDQW ZRQGHU LV OLNH JLYH ZRXOG SXOO VHH LI 2. ZRXOG GR KDYH JXHVV JRRG LGHD PLJKW OLNH JXHVV IHHO

 st DFW 6WHYH WDVN 6WHYH WDVN ZH -LP ZH -LP -LP 6WHYH WDVN -LP -LP

 st DFW WDVN

 st DFW

λloc

λilloc



 

WDVN

-LP



         

↓A ↑D ↓A ↓A ↓A ↓A ↑D ↓A ↑C =E ↓A ↓A =E

↑D ↑D ↑D ↓A ↓A ↑C ↑D ↑D ↓A ↓A ↑D ↓A =E

WDVN WDVN WDVN LGHDV WDVN

   DQ[LRXV

ZK\ KH EHOLHYHV ↓ A  WXUQ EF WKDW WKH UHTXHVW ↑ D LV XVHIXO DQG DSSURSULDWH IRU WKH FOLHQW 7KH WXUQLQJ SRLQW LV LQ WXUQ D ZKHQ -LP VD\V 2. DFFHSWLQJ WR WDNH LQ FKDUJH WKH UHTXHVW DV D FRPPLWPHQW ↑ C  LQ IDFW KH XVHV WKH SURQRXQ ZH LH -LP DQG 6WHYH WRJHWKHU ,Q RWKHU ZRUGV WKH WDVN LV SHUIRUPHG E\ -LP EXW -LP LV QRW DORQH LQ GRLQJ LW 7KH UHTXHVW IRU FODULILFDWLRQ ↑ D LQ WXUQ E LV REYLRXV 7XUQ  VKRZV D GLIIHUHQW NLQG RI UHTXHVW ↑ D  6WHYH ZDQWV WR NQRZ -LP¶V EHOLHIV ↓ A EHIRUH WR VWDUW ZLWK WKH WDVN LWVHOI DQG -LP DQVZHUV LQ WKH IROORZLQJ WXUQ  ,Q WXUQ  WKH WKHUDSLVW DSSURYHV FRQILUPV ERWK DW D OHYHO RI EHOLHIV DQG RI HPRWLRQV = E  ZKDW H[SHFWHG E\ -LP EXW KH LV VWLOO XQVDWLVILHG DV KH UHTXHVWV ↑ D -LP¶V IHHOLQJV DERXW WKH WDVN DQG LQ IDFW -LP WHOOV KH IHHOV DQ[LRXV = E LQ WXUQ  ,W LV TXLWH FOHDU WKDW WKH FRQYHUVDWLRQDO VWUDWHJ\ E\ WKH WKHUDSLVW LV WR JHW -LP FRPIRUWDEOH RQ RQH KDQG DQG WR PDNH KLP VD\ KLV DQ[LHW\ RQ WKH RWKHU KDQG LQ D GHOLFDWH HTXLOLEULXP

Chapter Seven Conclusion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²HJ FRUSRUD RE WDLQHG IURP WUDQVFULSWV RI WKHUDSHXWLF VHWWLQJV WHOHYLVLRQ RU UDGLR GLDORJXHV RU HYHQ OLWHUDU\ FULWLFLVP SURVH SRHWU\ DQG WKHDWUH²&RQVWUXFWLYH $GSRVLWLRQDO *UDPPDU DQDO\VLV FDQ EH SHUIRUPHG /LWHUDU\ FULWLFV VFKRODUV EHORQJLQJ WR KX PDQLWLHV LQ JHQHUDO²DV ZHOO DV SKLORVRSKHUV RI ODQJXDJH²FDQ DSSO\ WKH PRGHO WR VKRZ WKH UHVXOWV RI WKHLU HIIRUWV LQ D QHZ DQG XQXVXDO ZD\ ZKLFK KDV WKH DG YDQWDJH RI EHLQJ IRUPDOO\ VRXQG ,Q IDFW &RQVWUXFWLYH &RQYHUVDWLRQDO $QDO\VLV &R&$/ VKRZHG WKDW WKH DG SRVLWLRQDO SDUDGLJP DQG LQ SDUWLFXODU WKH OLQJXLVWLF DQG IRUPDO PRGHO SUHVHQWHG LQ WKLV ERRN FDQ EH WXQHG IRU VSHFLILF QHHGV DQG FRQFUHWH DSSOLFDWLRQV VRPH GH WDLOV FDQ EH OHIW KLGGHQ²EHFDXVH QRW LPSRUWDQW IRU WKH VSHFLILF SXUSRVH²EXW DW WKH VDPH WLPH WKH\ FDQ EH UHFRYHUHG XQGHU UHTXHVW %\ WKH PRPHQW H[SHULPHQWDO HYLGHQFH RI &R&$/ LV VWLOO ODFNLQJ EXW ZH DUH FRQILGHQW WKDW UHVXOWV ZLOO EH DYDLODEOH ZKHQ WKH IUXLWIXO FROODERUDWLRQ ZLWK D UHVHDUFK WHDP LQ SV\FKRWKHUDS\ ZLOO EH FRQWLQXLQJ ,Q JHQHUDO ZKHQHYHU D OLQJXLVWLF FRUSXV RI ZULWWHQ WH[W LV SURGXFHG LQ SULQFL SOH &RQVWUXFWLYH $GSRVLWLRQDO *UDPPDUV FDQ EH XVHG 7KH PRUSKRV\QWDFWLF ED VLV JLYHV DOVR DQ DFFRXQW RI VHPDQWLFV ZKLOH SUDJPDWLFV FDQ EH UHQGHUHG WKURXJK 6HDUOH¶V SUDJPDWLF FKDUDFWHUV RU RWKHU SHUVSHFWLYHV  $ IXUWKHU DSSOLFDWLRQ SURSRVDO LV FRQVWUXFWLYH FULWLFLVP ZKHQ D IL[HG VHW RI WH[WXDO UROHV WR DFWDQWV LV JLYHQ WR DQDO\VH WH[WV )RU LQVWDQFH *UHLPDV¶ $FWDQWLDO 0RGHO FRXOG EH DQRWKHU SRVVLEOH GHFRUDWLRQ RI DGSRVLWLRQDO WUHHV IRU WKH SXUSRVHV RI OLWHUDU\ DQDO\VLV DQG FULWLFLVP *UHLPDV  



&KDSWHU 6HYHQ

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²ZKDW )UHJH FDOOHG 6LQQ VHQVH DQG %HGHXWXQJ UHI HUHQFH  (DFK SUDJPDWLF DFW SURGXFHV D PHDQLQJ FORXG WKDW JHQHUDWHV²DQG UH JHQHUDWHV²WKDW FXOWXUDO FRQYHQWLRQ XVXDOO\ FDOOHG µQDWXUDO ODQJXDJH¶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¶V WRSRL :H VWXGLHG WKH FDWHJRU\ RI DGWUHHV WKURXJKRXW WKH ZKROH ERRN :KDW LI WKH DGWUHHV DUH FRQVLGHUHG DV GHQRWLQJ REMHFWV RI D FDWHJRU\ ZKLFK LV D VSHFLDO PRGHO RI WKH ZRUOGVFHQH ZH DUH VSHDNLQJ RI" ,I ZH FRQVLGHU WKDW DOO WKH JRYHUQRUV RI D VHW DGWUHHV IRUP D VLHYH DQG DOO WKH DGPLWWHG FRQVWUXFWLRQV VWDUWLQJ IURP D JLYHQ DGWUHH IRUP WKH FRVLHYH ZH VHH WKDW PDWKHPDWLFDOO\ WKH ZRUOG ZH DUH VSHDNLQJ RI EHFRPHV D JHQHUDOLVHG WRSRORJLFDO VSDFH²D VLWH²ZKRVH VSDWLDO VWUXFWXUH LV GHVFULEH E\ WKH VLHYHV RU GXDOO\ E\ WKH FRVLHYHV WKDW LV E\ WKH LQQHU VWUXFWXUH RI WKH ODQJXDJH ZH DUH XVLQJ WR GHVFULEH WKH ZRUOG LWVHOI 7KLV PHDQV WKDW WKH PHDQLQJ DQG WKH VWUXFWXUH RI WKH ODQJXDJH SURMHFWV LWVHOI RQWR WKH ZRUOG JLYLQJ LW WKH VKDSH RI D µVSDFH¶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²XQOLNH WKH FODVVLF &KRPVN\DQ SHUVSHFWLYH² WKLV JHQHUDWLRQ FDQQRW EH UHGXFHG WR D FRPSXWDWLRQDO RU DOJRULWKPLF PRGHO 7KH

&RQFOXVLRQ



UHYHUVH LV WUXH D FRPSXWDWLRQDO DOJRULWKPLF PRGHO FDQ EH H[WUDFWHG IURP WKH PDWKHPDWLFDO JHQHUDWLRQ ZLWKLQ RXU WRSRVWKHRUHWLFDO PRGHO EXW ZKDW LV OLQJXLV WLFDOO\ UHSUHVHQWHG LV ERXQG WR EH D SDUWLDO VQDSVKRW RI D QDWXUDO ODQJXDJH LQ D JLYHQ PRGHO ,Q RWKHU ZRUGV ZH FDQ JHQHUDWH JUDPPDU DQG PHDQLQJ EXW ZH FDQQRW JHW WKLV JHQHUDWLRQ FRPSOHWHO\ H[SOLFLW²QRW DOO PHDQLQJ FDQ EH ZULWWHQ GRZQ DV WKH WRSRV ZH GHDO ZLWK LV UHDOO\ D ELJ HQWLW\ XVXDOO\ D SURSHU FODVV DQG QRW PHUHO\ D VHW &RQVWUXFWLYH OLQJXLVWLFV JLYH D FDQRQLFDO DQG V\VWHPLF PHWKRGRORJ\ WR SXW WZR QDWXUDO ODQJXDJHV LQ FRPSDULVRQ D FRQVWUXFWLYH OLQJXLVW ZRXOG WDNH WKH WZR FODVVHV RI EDVLF VHPHPHV²PRVW SUREDEO\ WKH YHUEDQWV²DQG WKH SDWWHUQV RI WUDQVIRUPDWLRQV RI FRQVWUXFWLRQV VWDUWLQJ IURP WKHP ,Q IDFW WRSRL DQG LQ SDUWLFXODU *URWKHQGLHFN¶V WRSRL FDQ EH VHHQ DV D FRRUGLQDWHG FROOHFWLRQ RI LQIRU PDWLRQ )RU WKLV UHDVRQ ZH DUH GHHSO\ FRQYLQFHG WKDW *URWKHQGLHFN¶V WRSRL DUH WKH ULJKW PDWKHPDWLFDO LQVWUXPHQW WR IRUPDOLVH ODQJXDJHV DQG WKHLU UHJXODULWLHV $IWHU DOO V\PPHWU\ KDV DOZD\V D GHHS UHDVRQ ,I QRW WKLV ERRN FRXOG QRW KDYH EHHQ ZULWWHQ

Appendix A Examples $OO H[DPSOHV RI DGSRVLWLRQDO WUHHV JLYHQ WKURXJKRXW WKH ERRN DUH SUHVHQWHG KHUH DV OLQHDULVHG DGWUHHV (SVLORQUHGXFWLRQV DUH PDGH ZKHUH DSSURSULDWH

$ ,QWURGXFWLRQ  ² SDJH  /D YHFFKLD SRUWD OD VEDUUD ǫ→ (OD)O2  ǫ ← (/D YHFFKLD SRUWD)O1  (VEDUUD)I2 I22 I21

(OD VEDUUD)O2  ǫ → (/D YHFFKLD)O1  (SRUWD)I2 ǫ← I22 I21  ² SDJH  7LPH IOLHV OLNH DQ DUURZ DQG IUXLW IOLHV OLNH D EDQDQD → → (DQ)  (DUURZ)  DQG↔ 0 OLNH 0 ǫ A O I

ǫ← (WLPH)O  (IOLHV)I1  I O I11 → ← → ← ǫ 2 ǫ (D)A  (EDQDQD)O  ǫ 2 ǫ (IUXLW)A  (IOLHV)O  (OLNH) 2 I I2 O I1

 ² SDJH  Ê OD URVVD GL 0DUDQHOOR ǫ← GL← 0DUDQHOORO  ǫ → OD  ǫ → (URVVD)A  O1  ǫ →   Ë 2 O A O I22 O I21 O1 I

$ 6\QWD[ D ² SDJH  ,¶YH QRW VHHQ /L]D 6KH ZDV QRW ZLWK 3DXO ǫ ↔ (6KH ZDV QRW«)I  (,·YH QRW«)I I

E ² SDJH  ,¶YH QRW VHHQ /L]D VKH ZDV QRW ZLWK 3DXO ǫ ← (6KH ZDV QRW«)I  (,·YH QRW«)I I



$SSHQGL[ $

F ² SDJH  ,¶YH QRW VHHQ /L]D VKH ZDV QRW ZLWK 3DXO ǫ → (6KH ZDV QRW«)I  (,·YH QRW«)I I

D ² SDJH  7KH ELF\FOH EHORQJV WR .LP WR→ .LPO2  I2 2

ǫ← (7KH ELF\FOH)O1  (EHORQJV)I2 I21

E ² SDJH  .LP RZQV WKH ELF\FOH ǫ← (WKH ELF\FOH)O2  ǫ → .LPO1  (RZQV)I2 I22 I21

D ² SDJH  7KH MDQLWRU ZLOO RSHQ WKH GRRU ZLWK WKH NH\ ZLWK→ 3 (WKH NH\)Z 

I3

(WKH MDQLWRU)X  (ZLOO RSHQ)I3 (WKH GRRU)Y  ǫ → ǫ← I31 I32

E ² SDJH  7KH MDQLWRU ZLOO RSHQ WKH GRRU ǫ← (WKH GRRU)Y  ǫ → (WKH MDQLWRU)X  (ZLOO RSHQ)I2 I22 I21

F ² SDJH  7KH NH\ ZLOO RSHQ WKH GRRU ǫ← (WKH GRRU)Y  ǫ → (WKH NH\)X  (ZLOO RSHQ)I2 I22 I21

G ² SDJH  7KH GRRU ZLOO RSHQ ZLWK WKH NH\ ZLWK→ 3 (WKH NH\)Y 

I3

(WKH GRRU)X  (ZLOO RSHQ)I3 ǫ← I31

H ² SDJH  7KH GRRU ZLOO EH RSHQHG ZLWK WKH NH\ ZLWK→ 3 (WKH NH\)Y 

I3

(WKH GRRU)X  (ZLOO EH RSHQHG)I3 ǫ← I31

I ² SDJH  7KH GRRU ZLOO EH RSHQHG E\ WKH MDQLWRU E\→ 2 (WKH MDQLWRU)Y 

I2

(WKH GRRU)X  (ZLOO EH RSHQHG)I2 ǫ← I31

J ² SDJH  7KH MDQLWRU ZLOO RSHQ WKH GRRU ZLWK WKLV NH\ IRU WKH /DG\ IRU→ (WKH ODG\)O  ZLWK→ (WKLV NH\)Z  I0 I3 3

ǫ← (WKH GRRU)Y  ǫ → (WKH MDQLWRU)X  (ZLOO RSHQ)I3 I32 I31

([DPSOHV

D ² SDJH  $QQ JDYH .LP WKH FDU QRW WKH ELF\FOH $QQX  JDYHI3 .LPY  ǫ → (WKH FDU)Z  ǫ ← ǫ→ I31 I32 I33 E ² SDJH  $QQ JDYH WKH FDU WR .LP QRW WR %UXFH WR→ 3 .LPZ 

I3

$QQX  JDYHI3 (WKH FDU)Y  ǫ → ǫ← I31 I32

F ² SDJH  $QQ JDYH KLP WKH FDU ǫ→ (WKH FDU)Z  ǫ ← KLPY  ǫ → $QQX  JDYHI3 I33 I32 I31

D ² SDJH  0DULD GHX R OLYUR SDUDDǫ 3HGUR DSDUDǫ → 3 3HGURZ 

I3

0DULDX  (GHX)I3 (R OLYUR)Y  ǫ → ǫ← I31 I32

E ² SDJH  0DULD GLHGH LO OLEUR D 3LHWUR D→ 3 3LHWURZ 

I3

ǫ← (LO OLEUR)Y  ǫ → 0DULDX  GLHGHI3 I32 I31

F ² SDJH  0DULD JOL GLHGH LO OLEUR JOLZ  GLHGHI3 0DULDX  ǫ ← (LO OLEUR)Y  ǫ → ǫ→ I31 I32 I33 G ² SDJH  0DULD JOL GLHGH LO OLEUR ǫ← (LO OLEUR)Y  ǫ → 0DULDX  GLHGHI2 I22 I21

D ² SDJH  'HU 0DQQ JDE GHU )UDX GDV $XWR ǫ← (GDV $XWR)Y  ǫ → (GHU )UDX)Z  I32 [Acc] I33 [Dat] → (GHU 0DQQ)X  JDEI3 ǫ3 I1 [Nom]

E ² SDJH  'HU 0DQQ JDE HV GHU )UDX ǫ→ (GHU )UDX)Z  ǫ ← HV  ǫ → (GHU 0DQQ)X  JDEI3 I33 [Dat] I32 [Acc] Y I31 [Nom]

D ² SDJH  :DNRQJH ZDSHOH PE\LD ZDQDFH (:DNRQJH)X  ZDSHOHI3 (PE\LD)Y  ǫ ↔ (ZDQDFH)Z  ǫ ↔ ǫ↔ I31 I32 I33





$SSHQGL[ $

E ² SDJH  :DNRQJH ZDSHOH ZDQDFH PE\LD (:DNRQJH)X  ZDSHOHI3 (ZDQDFH)Z  ǫ ↔ (PE\LD)Y  ǫ ↔ ǫ↔ I31 I33 I32

$ &RQVWUXFWLRQV  ² SDJH  $K $KI

 ² SDJH  'HDU PH  GHDU)  PH  ǫ ← \RX    ((( 2 DP ← ǫ → ( FRQVLGHU ZKR A O2 I2  O1  ( I I2 O2 2

1

← ǫ → GHDUA  PHO2  I2 O2 2

(ǫ)I2 1

D ² SDJH  3DXO DSRORJLVHV WR /L]D WR← 2 /L]DY 

I2

ǫ→ 3DXOX  (DSRORJLVHV)I2 I21

E ² SDJH  3DXO DSRORJLVHV

  ǫ → 3DXO  (DSRORJLVHV) 2 WR←  /L]D  Y I2 X I I2 2

1

D ² SDJH  3DXO EURNH WKH YDVH 3DXOX  (EURNH)I2 (WKH YDVH)Y  ǫ → ǫ← I21 I22 E ² SDJH  7KH YDVH EURNH

  (EURNH) 2 3DXO ǫ← (WKH YDVH)Y  ǫ →  X I I22 I21 F ² SDJH  3DXO ERXJKW D QHZ YDVH ǫ← (D QHZ YDVH)Y  ǫ → 3DXOX  (ERXJKW)I2 I22 I21

D ² SDJH  1JDUUNXQWX DUL NDQ\LUU ǫ→ NDQ\LUUY  WX→ 1JDUUNXQX  DULI2 I22 I21

([DPSOHV



E ² SDJH  1JDUUNXQ DULOL NDQ\LUUNX NX→ 2

I2 > E

NDQ\LUUO  ǫ ← 1 1JDUUNXQX  (DULOL)I2−1 I1

F ² SDJH  ,Q~ JD KDVtWWH LPiVX JD← 1 ,Q~X 

I1

ǫ→ LPiVXE  KDVtWWHI1 I1

G ² SDJH  ,Q~ ZD KDVtWWH LPiVX ZD→ 1 ,Q~X 

I1

LPiVXE  KDVtWWHI1 ǫ→ I1

H ² SDJH  <XNt ZD VLUyL GHVX GHVXE  ZD→ <XNtX  VLUyLA ǫ← I11 I11 I ² SDJH  6RQy EjUD ZD DNiL GHVX ǫ← GHVXE  ZD→ ǫ ← 6RQyA  EDUjX  DNiLA I11 I11 X

D ² SDJH  , VZHDW ǫ→ ,  (VZHDW)I1 I11 X

E ² SDJH  6DODNVKD ǫ← 6DX  ODNVKDI1 I11

F ² SDJH  LR KR VXGDWR ǫ→ LR X  (KR VXGDWR)I2 I21

D ² SDJH  3DROR KD FRUVR SHU XQ¶RUD   FRUV→ RA  ǫ ←  ǫ→ ǫ ← XQA  D←   RUO  ǫ ← A O O I22 Y I22 A > Yaux E > I22 O →    2   ǫ 2 ( 3DROR)X   FRUU Yaux  Imean I1 → ← ǫ 2 R X  3DROX  KD 2 I I1 X

SHU←



$SSHQGL[ $

E ² SDJH  3DROR q FRUVR D FDVD D←

E > I22

D←   FDVO  ǫ →  ǫ→ FRUV→ RA  O O A I22 A > Yaux → ←   )   ǫ 2 Y  ǫ 2 ( 3DROR X FRUUI2  Yaux  mean

I2 I1 ← ǫ← 2 RX X  3DROX  qI2 I1

mean

F ² SDJH  3DROR FRUVH ǫ→ R←   3DROX  FRUVHI2 I11 X X

D ² SDJH  EDOO WDEOH ǫ← WDEOHE  EDOOI2 I22 1

E ² SDJH  WKH EDOO LV RQ WKH WDEOH → → RQ→ )  ǫ ← (   WDEOH)O  (  EDOO)X   WKH D EDOO LV 2 E > A D  (
ǫ I2 
ǫ Y  Y I2 WKH I 2

D ² SDJH  PRUH PLON ǫ← PRUHA  PLONY I22

E ² SDJH  , ZDQW PRUH PLON

 2 ǫ← ǫ ← PRUHA  PLONY 
ǫ → ,   ZDQW I I21 X I22 Y D ² SDJH  PRUH JUDSHV ǫ← PRUHA  JUDSHVY I22

E ² SDJH  , ZDQW PRUH JUDSHV

 2 ,   ǫ ← PRUHA  JUDSHVY 
ǫ → ǫ← ZDQW I I21 X I22 Y D ² SDJH  DQFRUD PHOD ǫ← DQFRUDA  PHODY I22

1

([DPSOHV

E ² SDJH  LR YRJOLR DQFRUD PHOD  2 ǫ← ǫ ← DQFRUDA  PHODY 
ǫ → LR  YRJOLR I I21 X  I22 Y D ² SDJH  DQFRUD SDVWD ǫ← DQFRUDA  SDVWDY I22

E ² SDJH  LR YRJOLR DQFRUD SDVWD  2 LR  YRJOLR ǫ← ǫ ← DQFRUDA  SDVWDY 
ǫ → I I21 X  I22 Y D ² SDJH  MXLFH JRQH ǫ← ǫ → JRQHA  MXLFHX  govI1 I1 X

E ² SDJH  WKH MXLFH LV JRQH

  MXLFHX   WKH ǫ← ǫ → (JRQH)I > A  ǫ ← LV 1 X  A I I11 X D ² SDJH  R QRIR SHSH ǫ← SHSHX  R QRIRI1 I11

E ² SDJH  R QRIR LD SHSH LD→ 1 SHSHX  R QRIRI1

I1

D ² SDJH  IRUWHV YHQWRV ǫ ← (IRUWHV)A  (YHQWRV)O O

E ² SDJH  YHQWRV IRUWHV ǫ → (IRUWHV)A  (YHQWRV)O O

D ² SDJH  QRVWUD PHPRULD D← (QRVWU)A  (PHPRULD)O

O

E ² SDJH  PHPRULD QRVWUL L→ (QRVWU)A  (PHPRULD)O

O





$SSHQGL[ $

D ² SDJH  DPRU SDWULV LV↔ SDWUA  DPRUO

O

E ² SDJH  DPRU SDWULV LV↔ SDWUA  DPRUO

O

D ² SDJH  WKH HOHSKDQW ǫ ← WKHA  HOHSKDQWO O

E ² SDJH  WKDW HOHSKDQW ǫ → WKDWA  HOHSKDQWO O

F ² SDJH  ,¶YH VHHQ WKH RQH ǫ ← WKHA  RQHO O

H ² SDJH  ,¶YH VHHQ WKDW RQH ǫ → WKDWA  RQHO O

I ² SDJH  ,¶YH VHHQ WKDW ǫ → WKDWA  O O

D ² SDJH  'RPDQL YHQJR ǫ ← GRPDQLE  ǫ → LR X  YHQJRI1 I I11

E ² SDJH  9HQJR GRPDQL LR X  YHQJRI1 ǫ ← GRPDQLE  ǫ → I I11 F ² SDJH  4XDQGR YHUUDL" ǫ→ (TXDQGR)E  ǫ → WX X  YHUUDLI1 I11 I11

 ² SDJH  WKDW KLJKO\ VHQVLWLYH WRSLF ǫ → WKDWA  ǫ ← ǫ → O\→ D  KLJKA  (VHQVLWLYH). . . > A  O O A E WRSLFO

([DPSOHV



 ² SDJH  XQ YUDLPHQW EHDX SD\VDJH ǫ ← XQA  ǫ ← ǫ ← PHQW→ D  YUDLA  EHDXA  O O A E

(SD\VDJH). . . > O

$ 7UDQVIRUPDWLRQV D ² SDJH  /L]D ZDON /L]DX  ZDONI1 ǫ→ I11 E ² SDJH  /L]D ZDONV ǫ→ /L]DX  (ZDONV)I1 I11

F ² SDJH  /L]D >noun: proper, singular@ ZDONV >verb: [tense: simple present: [3rd person, singular]]@ ǫ→ /L]DX >noun@ >singular@  ǫ ← V  ZDONI1 rd I11 I1 I >3 person@ >singular@

D ² SDJH  /L]D ZDONV DQG 3DXO ZDONV DQG↔ 

X

V  ZDONI1 V  ZDONI1  ǫ → /L]DX  ǫ ← ǫ→ 3DXOX  ǫ ← I11 I1 I I11 I1 I

E ² SDJH  /L]D DQG 3DXO ZDON ǫ→ DQG↔ 3DXOO  /L]DO  ZDONI1 X I11

D ² SDJH  /L]D LV D TXLHW JLUO /L]DX  LVI2 ǫ→  ǫ ← D  ǫ → TXLHWA  JLUOY  ǫ ← I21 I22 Y A Y E ² SDJH  /L]D LV TXLHW ǫ→  ǫ → TXLHWA  Y  ǫ ← /L]DX  LVI2 I22 Y I21

F ² SDJH  %H D TXLHW JLUO → 2 

I2

ǫ ← DA  ǫ → TXLHWA  JLUOY  ǫ ←   EHI2 Y Y I21 X



$SSHQGL[ $

G ² SDJH  %H TXLHW → 2 

ǫ → TXLHWA  Y  ǫ ←   EHI2 Y I21 X

I2

D ² SDJH  3DXO LV VWXG\LQJ PDWKV

   ǫ ← PDWKVYmean  ǫ →  3DXO ǫ→  LQJ→ Xmean  VWXG\I2  Yaux D I22 I21 I22 ǫ← 3DXOXaux  LVI2 I21 aux E ² SDJH  3DXO LV JRLQJ WR VWXG\ PDWKV

  VWXG\ 2  3DXO  LQJ→   WR← ǫ ←   ǫ ← PDWKVY  ǫ → ǫ→ X Yaux D I22 Yaux+ D I22 I I21 I22 → ←   ǫ 2 3DXOX  JRI2  ǫ 2 3DXOXaux  LVI2 aux+ I1 I1 aux+ aux F ² SDJH  0DWKV LV SUHSDUHG E\ 3DXO E\→

E>I

→ 3DXOXact  ǫ → 2  ǫA > Y I2

aux

G→ 2

I2 > A

  PDWKV Yact 

 ǫ→ 3DXO  Xact  SUHSDUHI2  I22 ←  PDWKV  Yact  ǫ I2 PDWKVYact { Xpass  LVI2aux 1

G ² SDJH  0DWKV LV SUHSDUHG →   ǫ→  ǫ→ G→  PDWKV PDWKV Yact  ǫ I2 Xact  SUHSDUHI2   Yact  I22 A > Yaux I22 > A 2 ǫ← 2 PDWKVYact { Xpass  LVI2 I1

aux

H ² SDJH  3DXO LV SUHSDUHG

 3DXO ǫ→  ǫ→ G→   ǫ →  Xact  SUHSDUHI2  Yact  I22 A > Yaux I22 > A Yact I22 ǫ← 3DXOXact  LVI2 I21 aux I ² SDJH  %H SUHSDUHG

  SUHSDUHI2  Yact  ǫ→  ǫ→ G→   ǫ → \RX I22 A > Yaux I22 > A Yact I22  Xact ← X  EH 2 \RX ǫ 2  act Iaux I1

([DPSOHV

D ² SDJH  7KH VKDK VOHSW LQ WKH EHGV LQ→ 2 (WKH EHGV)Y 

I2

ǫ→ (WKH VKDK)X  VOHSWI2 I21

E ² SDJH  7KH EHGV ZHUH VOHSW LQ E\ WKH VKDK

(() WKH(EHGV VOHSW LQ→ (( (WKH VKDK)Xact  ǫ →  ǫ→ Yact  I22 > A I22 A > Yaux (()  2    WKH(VKDK VOHHS ǫ→ (( Xact   Yaux  Imean I21 ← ǫ 2 (WKH EHGV)Y  ZHUH 2 act I

E\→

E>I

I1

aux

F ² SDJH  6KDK¶V VOHHSLQJ ·V→

A>O

6KDKO  LQJ→   VOHHSI O D

D ² SDJH  $ FDPHO VWHSSHG RQ WKH SDFNDJH ((()Y  ǫ → ($ FDPHO)X  VWHSI2 SHG RQ→ (WKH(SDFNDJH I2 I2 ( 1

2

E ² SDJH  7KH SDFNDJH ZDV VWHSSHG RQ E\ D FDPHO

((()Y  SHG RQ→ (WKH(SDFNDJH (D FDPHO)Xact  ǫ →  ǫ→ act I22 > A ( I22 A > Yaux (() WKH(FDPHO  VWHS    ǫ→ 2 2 (( Xact Yaux Imean I1 ǫ←  ( WKH SDFNDJH )  ZDV 2 2 Yact I

E\→

E>I

I1

aux

F ² SDJH  7KH FDPHO¶V VWHSSLQJ ·V→ (7KH FDPHO)O  SLQJ→ D  VWHSI

O

O

ǫ ← 7KH ·V→ FDPHOO  SLQJ→ D  VWHSI O O O

D ² SDJH  7KH LFH FXEH PHOWHG LQ WKH RYHQ → WKH  RYHQ  LQ← 2 ǫ A O I2

O

(PHOWHG)I2

ǫ← ǫ → 7KHA  ǫ → LFHO > A  FXEHO  O I21 O

F ² SDJH  7KH PHOWLQJ RI WKH LFH FXEH RI← ǫ → WKHA 

O

O

  PHOWI WKHA  LQJ→ ǫ→ LFHO  FXEHO  ǫ ← O D O A>O





$SSHQGL[ $

D ² SDJH  7KH WRRWKSDVWH RR]HG LQWR WKH VLQN ← WKH  VLQN  LQ← 2 ǫ A O I2

O

ǫ← ǫ ← 7KHA  (WRRWKSDVWH)O  (RR]HG)I2 I21 O

F ² SDJH  7KH RR]H RI WKH WRRWKSDVWH RI→ ǫ → WKHA  (WRRWKSDVWH)O 

O

O

ǫ ← 7KHA  ǫ → D  RR]HI O O

D ² SDJH  /LWWOH 5HG 5LGLQJ +RRG YDQLVKHG LQ WKH ZRRGV LQ← ǫ ← WKHA  (ZRRGV)O 

I

O

ǫ→ (/LWWOH 5HG 5LGLQJ +RRG)O  (YDQLVKHG)I1 I11

F ² SDJH  7KH YDQLVKLQJ RI /LWWOH 5HG 5LGLQJ +RRG RI← (/LWWOH 5HG 5LGLQJ +RRG)O 

O

ǫ ← WKHA  LQJ← D  YDQLVKI O O

D ² SDJH  ,W¶V D FDU ǫ ← D  FDUO  ·→ ,W  LV 2 ǫ← I21 O I I22 O A E ² SDJH  7KDW¶V WKH HOHSKDQW WKDWO  LVI2 ǫ ← WKHA  HOHSKDQWO  ·→ ǫ← I21 I22 O D ² SDJH  7KDW¶V P\ PXP WKDWO  LVI2 ǫ→ ǫ → P\A  PXPO  ·← I21 I22 O E ² SDJH  ,W¶V 3DXO¶V EURWKHU ǫ→ ·V→ 3DXOO  EURWKHUO  ·← ,W  LV 2 I22 O I21 O I

F ² SDJH  7KHUH DUH P\ VKRHV ǫ→ (P\ VKRHV)Y  ǫ ←   WK← 2 HUHE  DUHI I22 I21 X E>I

G ² SDJH  7KHUH LV /L]D (/L]D)Y  ǫ ←   WK← 2 HUHE  LVI ǫ→ I22 I21 X E>I

([DPSOHV

H ² SDJH  +HUH¶V D JLIW ǫ→ (D JLIW)Y  ǫ ←   K← HUHE  LVI I22 I21 X E > I2

D ² SDJH  0\ VKRHV DUH WKHUH WK→

E > I22

← HUHE  ǫ → 2 Y  ǫ 2 (0\ VKRHV)X  DUHI2 I2

I1

E ² SDJH  /L]D LV WKHUH WK→

E > I22

← HUHE  ǫ → 2 Y  ǫ 2 (/L]D)X  LVI2 I2

I1

F ² SDJH  3DXO LV KHUH K→

E > I22

← HUHE  ǫ → 2 Y  ǫ 2 3DXOX  LVI2 I2

I1

 ² SDJH  NHGLP YDU PY  ǫ ← NHGLX  YDUI2 ǫ→ I22 I21 D ² SDJH  3DXO KDV D %HQWOH\ ǫ← (D %HQWOH\)O  ǫ → 3DXOO  KDVI2 I22 I21

E ² SDJH  3DXO KDV JRW D %HQWOH\ ǫ←  ǫ → ǫ → (D %HQWOH\)Ymean  I22 Yaux I22 > A →  ǫ 2  3DXOX  JRWI2  Yaux  mean I1 mean ǫ→ 2 3DXOXaux  KDVI2 I1 aux

F ² SDJH  3DXO KDV JRW D )RUG (D )RUG)Ymean   ǫ → ǫ → ǫ← I22 Yaux I22 > A →  ǫ 2  3DXO Xmean  JRWI2mean  Yaux  I1 ǫ→ 3DXOXaux  KDVI2 I21 aux





$SSHQGL[ $

G ² SDJH  3DXO KDV ZDVKHG KLV FDU ǫ←  ǫ → HG→ (KLV FDU)Ymean  I22 Yaux I22 > A →  3DXO ǫ 2  Xmean  ZDVKI2mean  Yaux  I1 ǫ→ 3DXOXaux  KDVI2 I21 aux

H ² SDJH  3DXO JRW D )RUG ǫ← (D )RUG)O  ǫ → 3DXOO  JRWI2 I22 I21

I ² SDJH  3DXO ZDVKHG KLV FDU ǫ← (KLV FDU)O  ǫ → 3DXOO  (ZDVKHG)I2 I22 I21

D ² SDJH  3DROD KD FRUVR OD PDUDWRQD HQWUR TXDWWUR RUH   RUO  ǫ ← TXDWWURA  H← O O E > I22 O ǫ←  ǫ → FRUV→ RA  ǫ ← (OD PDUDWRQD)Y  A I22 Yaux I22 )  FRU   2  Yaux  ǫ→ ( 3DROD UH X Imean I21 → ← ǫ 2 D X  3DROX  KD 2 I I1 X

HQWUR←

E ² SDJH  3DROD q FRUVD D FDVD D←

D←   FDVO  ǫ →  ǫ → V→ D  O O I22 Yaux A A )  FRU   2  Yaux  ǫ→   ǫ ← ( 3DROD UH X Imean I22 Ymean I21 ← ← ǫ 2 D X  3DROX  q 2 X I

E > I22

I1

D ² SDJH  0DULR KD ODYDWR OD FDPLFLD (3DROR)X  KDI2  ǫ ← (ODYDWR OD FDPLFLD)I2 > A  Yaux  ǫ → ǫ← I21 I22 Yaux E ² SDJH  0DULR KD OD FDPLFLD ODYDWD ǫ←  ǫ → (ODYDWD)I2 > A  (OD FDPLFLD)Yaux  ǫ → (3DROR)X  KDI2 I22 Yaux I21

([DPSOHV



 ² SDJH  0HHWLQJ SHRSOH LV HDV\ (  ǫ ← LQJ→   ǫ ← SHRSOH ((( VRPHWKLQJ ǫ→ ǫ → HDV\A  ( Ybe Ymeet  Xbe D I22 I21 I22 Yaux → ǫ 2 X  PHHWI2  LVI2 meet I1

meet

be

D ² SDJH  7KH PDFKLQH QHHGV IL[LQJ () → VRPHERG\ ((() ((( WKH(PDFKLQH ǫ← LQJ→ (( Xfix  IL[I2  Yfix  ǫ I2 (( I22 I22 > Yneed fix 1 → ǫ 2 (WKH PDFKLQH)X  (QHHGV)I2 need I1

need

E ² SDJH  0\ KRXVH UHTXLUHV SDLQWLQJ () → VRPHERG\ ) ((( ǫ← LQJ→ (P\KRXVH Xpaint  SDLQWI2 Ypaint  ǫ I2 (( I2 I2 > Yreq  2

2



paint

1

ǫ→ (0\ KRXVH)Xreq  (UHTXLUHV)I2 I21 req

 ² SDJH  3DXO LV D ZRUNLQJ FODVV KHUR

) ǫ→ 3DXOO1  ǫ ← ǫ ← D  ǫ ← ǫ ← LQJ→ ( D ZRUN Ywork  I22 I21 Ybe A A > Ybe O I22 > O  →  ) ǫ 2 ( ZRUNHU Xwork  ZRUNI2  FODVVO  KHURYbe  (LV)I2 I1 work D ² SDJH  3DXO LV D GHDG PDQ ZDONLQJ

→  LQJ→  ZK ǫ→ 3DXOO1  ǫ ← ǫ ← D   RX  ZDONI1  A O walk I22 I21 Ybe A walk → GHDGI > A  PDQYbe  (LV)I2 ǫ Ybe  ² SDJH  :LWKRXW WHOOLQJ KLP /L]D FDQQRW EH KDSS\ (  ǫ ←   ((( VRPHWKLQJ ( KLPZ  ǫ ← ZLWKRXW← LQJ→ Y I3 /L]DX  WHOOI3  («)I E>I I3 I3 > O 3

2

1

D ² SDJH  $YHQGR WHOHIRQDWR /LVD 3DROR SLDQVH     3DROR H←  ǫ → D{DWR→ QGR→ Y I22 > A I22 > E > I I22 Yaux
→ ǫ 2 /LVDX  WHOHIRQI2  Yaux  mean I1 mean   /LVD  ǫ→  K D { DY   2  Xaux Iaux (3DROR SLDQVH)I I21

3



$SSHQGL[ $

F ² SDJH  (VVHQGR SDUWLWD /LVD 3DROR SLDQVH QGR→ 2

H→  ǫ → LW→ D  ǫ → /LVDXmean  SDUWI1  Yaux  I2 > E > I I22 Yaux I11 > A A I11 mean  ǫ← 2 /LVDXaux  HVVI2  (3DROR SLDQVH)I I1 aux

G ² SDJH  3DUWLWD /LVD 3DROR SLDQVH

→  QGR 2

D  ǫ → /LVDXmean  SDUWI1  Yaux  H→  ǫ → LW→ I11 > A A I11 I2 > E > I I22 Yaux mean  2  (3DROR SLDQVH)I  HVV ǫ← 2 /LVDXaux   I I1 aux

D ² SDJH  $ /LVD SLDFH EDOODUH D→ 2 /LVDY 

I2

  EDOO 2  SLDFH 2 /LVD   ǫ →  ǫ← DUH→ X Xpiace Y I21 I I I21

 ² SDJH  3DROR YXROH SURYDUH DG DQGDUH D IDUH XQD YDFDQ]D ǫ←  DUH→  DG DUH→  D DUH→ (XQD YDFDQ]D)Y  I22 I22 > Y I22 > Y I22 > Y   DQG 2  ǫ →    SURY 2    ǫ→ 3DRORX  II2  ǫ → 3DROR  3DROR X X I I I21 I21 I21 → ǫ 2 3DRORX  YXROH 2 I I1

 ² SDJH  /DPHQWR HOHV WHUHP SHUGLGR R FRPERLR ǫ → LGR→ (R FRPERLR)Yperd  ǫ→ HP→ I22 > A I22 I2 > Ylam. Yter →  ǫ→  HOHV Xperd  SHUGI2  Yter  ǫ I2 HOHVXter  WHUI2ter  (ODPHQWR)I21 I21 perd 1 D ² SDJH  0DULR KD XQD FDPLFLD ODYDELOH D VHFFR

((()  (FDPLFLD ǫ←  ǫ → D→ (VHFFR)I > A  ELO→ H  ǫ → DI  ǫ → XQD (( Y A A I22 I22 Y A I22 → → ǫ 2 0DULRX  ODY 2  (XQD FDPLFLD)Y  ǫ 2 0DULRX  KD 2 I I I1 I1  ² SDJH  /H OLYUH GH 3LHUUH ǫ → GH→ D  3LHUUHO  (OH OLYUH)O O A

 ² SDJH  8QH WDVVH GH WKp ǫ → GH→ D  WKpO  (XQH WDVVH)O O A

([DPSOHV

 ² SDJH  8QH VDOOH GH FODVVH ǫ → GH→ D  FODVVHO  (XQH VDOOH)O O A

 ² SDJH  -H pFULUH GH OD PDLQ JDXFKH GH← (OD PDLQ JDXFKH)O  (MH pFULUH)I

E

 ² SDJH  -H UpSqWH GH PpPRLUH GH← (PpPRLUH)O  (MH UpSqWH)I

E

 ² SDJH  /H WUDLQ SDUWL GH 3DULV«

) ǫ → GH← 3DULVO  ( SDUWL I > A  (OH WUDLQ)O E O  ² SDJH  /L]D ZLSHG WKH WDEOH FOHDQ

  ǫ→   FOHDQ 2  (WKH WDEOH)  →  → D  ǫ → ǫ←  ZK HG  LFK VKH Y I2  X Y Y A I I22 I22 1 → ǫ 2 /L]DX  (ZLSHG) 2 I I1 D ² SDJH  3DXO KDV JRW KLV FDU ZDVKHG

 → HG→ D   ǫ→ ǫ →  3DXO ZK ǫ← ǫ →  Xgot  JRWI2got   Ygot A I22 Yaux Yaux I22 > A I21 → →  ǫ 2  LFKY  ǫ 2 KHX  ZDVK 2  (KLV FDU)Y  got I I2 I1 → ǫ 2 3DXOX  KDV 2 aux Iaux I1 E ² SDJH  +H GURYH KHU PDG

→ KHUY  ZK ǫ← ǫ → +HXmean  GURYHI2   Ymean mean I22 I21 mean → ← ←   D  ǫ 2 PDGA > Y  ǫ 2  HG VKHX   LV 2  A I I2 I1 D ² SDJH  $OIUHG FDQ SD\ EHFDXVH KH LV ULFK EHFDXVH← 

ǫ→ ǫ → ULFKA  Y  ǫ → KHX  LVI2  I I22 Y I21 dep → $OIUHG  FDQ  SD\  ǫ ǫ← 2 X I > O I2 Igov I22 1





$SSHQGL[ $

D ² SDJH  $OIUHG SHXW SD\HU SDUFH TXH LO HVW ULFKH SDUFH TXH← 

ǫ→ ǫ → ULFKHA  Y  ǫ → LO  HVWI2  I22 Y I21 X dep → ǫ← 2 SD\HUI > O  ǫ 2 $OIUHGX  SXHWI2 I2 I1 gov I

D ² SDJH  $OIUHG SXz SDJDUH SHUFKp q ULFFR

  q 2  ǫ→ ǫ → ULFFRA  Y  ǫ → HJOL I I22 Y I21  X Idep ǫ← SDJDUHI > O  ǫ → $OIUHGX  SXzI2 I22 I21 gov

SHUFKp← 

E ² SDJH  $OIUHG FDQ SD\ KHQFH KH LV ULFK KHQFH→ 

ǫ→ ǫ → ULFKA  Y  ǫ → KHX  LVI2  I I22 Y I21 dep → ǫ← 2 SD\I > O  ǫ 2 $OIUHGX  FDQI2 I2 I1 gov

E ² SDJH  $OIUHG SHXW SD\HU GRQF LO HVW ULFKH GRQF→ 

ǫ→ ǫ → ULFKHA  Y  ǫ → LO  HVWI2  I I22 Y I21 X dep → $OIUHG  SXHW ǫ←  SD\HU  ǫ 2 I > O I2 X Igov I22 1

E ² SDJH  $OIUHG SXz SDJDUH GXQTXH q ULFFR

  q 2  ǫ→ ǫ → ULFFRA  Y  ǫ → HJOL I I22 Y I21  X Idep ǫ← SDJDUHI > O  ǫ → $OIUHGX  SXzI2 I22 I21 gov

GXQTXH→ 

D ² SDJH  $OIUHG ZKR LV ULFK FDQ SD\ ǫ← SD\I > Y  ǫ → ZK← ǫ → ULFKA > Ydep  I > A > X I22 I22 I21 ǫ→ RXdep  LVI2  $OIUHGX  FDQI2 I21 dep

E ² SDJH  $OIUHG ZKR FDQ SD\ LV ULFK ǫ← ULFKA > Y  ǫ → ZK← ǫ → SD\I > Ydep  I > A > X I22 I22 I21 ǫ→ RXdep  FDQI2  $OIUHGX  LVI2 I21 dep

([DPSOHV



D ² SDJH  WKH PDQ ZKR ERXJKW WKH ERRN IRU WKH JLUO ZK→

IRU→ (WKH JLUO)O  ǫ ← (WKH ERRN)Y  I>A>O E>I I42 → ǫ 4 RX  (ERXJKW) 4  (WKH PDQ)O Idep I1

E ² SDJH  WKH ERRN ZKLFK WKH PDQ ERXJKW IRU WKH JLUO ZK→

IRU→ (WKH JLUO)O  ǫ ← (LFK)Y  I>A>O E>I I42 ǫ→ (WKH PDQ)X  (ERXJKW)I4  (WKH ERRN)O I41 dep

F ² SDJH  WKH JLUO IRU ZKRP WKH PDQ ERXJKW WKH ERRN ZK→

IRU→ (RP)O  ǫ ← (WKH ERRN)Y  E>I I>A>O I42 ǫ→ WKH PDQX  (ERXJKW)I4  (WKH JLUO)O I41 dep

G ² SDJH  WKH ER\ ZKRVH ERRN WKH PDQ ERXJKW IRU WKH JLUO ǫ → RVHA  ERRNY  (WKH JLUO)O  ǫ ← IRU→ I>A>O E>I I42 Y (WKH PDQ)X  (ERXJKW)I4  (WKH ER\)O ǫ→ I41 dep

ZK→

I ² SDJH  :KR ERXJKW WKH ERRN IRU WKH JLUO" 7KH PDQ "→ (WKH PDQ)O  ZK→

I>A>O

I

IRU→4 (WKH JLUO)O  ǫ ← 4 (WKH ERRN)Y 

ǫ→ RX  (ERXJKW)I4  O I41

E2

I2

D ² SDJH  :KHQ 3DXO ZLOO FRPH EDFN /L]D ZLOO VPLOH ZK→

EDFNE  (ZLOO FRPH)I1   ǫ ← HQE  ǫ → 3DXOX  ǫ → E > I11 I11 I11 I1 ǫ→ /L]DX  (ZLOO VPLOH)I1 I11

E ² SDJH  /L]D ZLOO VPLOH ǫ→ /L]DX  (ZLOO VPLOH)I1 I11



$SSHQGL[ $

F ² SDJH  :KHQ ZLOO /L]D VPLOH" :KHQ 3DXO ZLOO FRPH EDFN "→ ZK→

ǫ ← HQE  ǫ → 3DXOX  ǫ → 1 EDFNE  (ZLOO VPLOH)I1  G  I > E I11 I11 E>I ← /L]D  (ZLOO VPLOH)   ZK→ ǫ ←  HQ  ǫ E I1 X G I > E I11 I1

I

D ² SDJH  , ZRQGHU KRZ PDQ\ HUURUV , GLG K→ 2 

I2

ǫ→  ǫ → ǫ → RZE  PDQ\A  (HUURUV)Y  ǫ ← ,  GLGI2  I22 > O Y A I21 X dep → ǫ 2 ,X  ZRQGHU 2 I I1 gov

E ² SDJH  :KDW WLPH LV LW" ZK→ 2 

I2

ǫ ← DWA  WLPHY  ǫ ← LW  LV 2 Y I21 X I

F ² SDJH  +RZ PDQ\ HUURUV , GLG" , ZRQGHU → ← → → "→ ǫ → 1 ,X  ZRQGHUI1  KI > A > O ǫ 2 ǫ Y ǫ A RZE  PDQ\A  I I1

I2

(HUURUV)Y  ǫ → 2 ,X  GLGI2  O I1

D ² SDJH  .DUO JLHVW GLH %OXPHQ ǫ← (GLH %OXPHQ)Y  ǫ → .DUOX  JLHVWI2 I22 I21

E ² SDJH  ,FK ODVVH .DUO GLH %OXPHQ JLH‰HQ JLH‰HQ→ 2+1 (GLH %OXPHQ)Y 

I3

ǫ→ .DUOX  ǫ ← ,FKQ  (ODVVH)I2+1 I2+1 I2+1 cause 2 1

F ² SDJH  ,FK ODVVH GLH %OXPHQ JLH‰HQ JLH‰HQ→ 2+1−1 (GLH %OXPHQ)Y 

I3

  ǫ ← ,FK  (ODVVH) 2+1  .DUO ǫ→ Q X I2+1 Icause I2+1 1 2

 ² SDJH  3DXO PDNHV /L]D EX\ D FDU E\ 5RQ¶V IRU  SRXQGV → ← IRU← 4+1 ( SRXQGV)W  E\ 4+1 (5RQ·V)Z  EX\ 4+1 (D FDU)Y  I5

I4 I3 → (3DXO)  (PDNHV) ǫ→  /L]D  ǫ 4+1 X I4+1 Q Icause I4+1 2 1

D ² SDJH  +LP EH D GRFWRU EH→ 2+1 (D GRFWRU)Y 

I3

Q   \RX  ǫ→ KLPX  ǫ ← O HW 2 Icause I2+1 I2+1 2 1

([DPSOHV



E ² SDJH  0\ PRWKHU ULGH D WUDLQ ULGH← 2+1 (D WUDLQ)Y 

I3

Q   \RX O HW 2 ǫ→ (0\ PRWKHU)X  ǫ ←  Icause I2+1 I2+1 2 1

F ² SDJH  +HU ZDVK WKH GLVKHV ZDVK← 2+1 (WKH GLVKHV)Y 

I3

Q   ǫ→ KHUX  ǫ ← O HW 2 \RX  Icause I2+1 I2+1 2 1

D ² SDJH  /HW KHU GR LW GR← 2+1 LWY 

I3

Q   \RX O HW 2 ǫ→ KHUX  ǫ ←  Icause I2+1 I2+1 2 1

E ² SDJH  +HOS KLP SXW KLV VKRHV SXW← 2+1 (KLV VKRHV)Y 

I3

 2 Q   ǫ→ KLPX  ǫ ← KHOS \RX  Icause I2+1 I2+1 2 1

F ² SDJH  0DNH WKLV VWD\ RSHQ VWD\← 2+1 (RSHQ)Y 

I3

 2  Q   \RX PDNH ǫ→ (WKLV)X  ǫ ←  Icause I2+1 I2+1 2 1

$ &RQVWUXFWLYH GLFWLRQDULHV 7KH H[DPSOHV LQ &KDSWHU  DUH QRW UHSRUWHG VLQFH WKH\ DUH QRW µUHIHUHQFH¶ H[DP SOHV ZKLFK FDQ EH H[WUDFWHG IURP WKH FRQWH[W WKH\ KDYH EHHQ SUHVHQWHG DQG XVHG WR LQVWDQFH RWKHU FDVHV RQ WKH VDPH JXLGHOLQHV

$ 'LVFRXUVH DQG EH\RQG D ² SDJH  ,¶YH VHHQ 0DU\ ZLWK 3DXO QR HPSKDVLV ǫ→ ZLWK↔ 3DXOO  0DU\Y  (,·YH VHHQ)I2 A>Y I22 1

E ² SDJH  ,¶YH VHHQ 0DU\ ZLWK 3DXO HJ QRW /L]D ǫ→ ZLWK← 3DXOO  0DU\Y  (,·YH VHHQ)I2 A>Y I22 1



$SSHQGL[ $

F ² SDJH  ,¶YH VHHQ 0DU\ ZLWK 3DXO HJ QRW ZLWK -RKQ ǫ→ ZLWK→ 3DXOO  0DU\Y  (,·YH VHHQ)I2 A>Y I22 1

D ² SDJH  , ZRQ WKH UDFH , DP WHOOLQJ WKDW , ZRQ WKH UDFH ǫ ← ǫ ← (WKH UDFH)(Y, S)  ǫ → ,  ZRQ↓ A  (DVVHUW)(↓ A, S) ↓ A I22 I21 S

E ² SDJH  :LQ WKH UDFH , RUGHU \RX WR ZLQ WKH UDFH (WKH UDFH)(Z, R)  ǫ ← \RX R  ZLQ↑ D  (GLUHFW)(↑ D, S) ǫ ← ǫ ← ↑ D I22 I21 F ² SDJH  ,¶OO ZLQ WKH UDFH , SURPLVH P\VHOI WR ZLQ WKH UDFH ǫ ← ǫ ← (WKH UDFH)(Z, S)  ǫ ← ,  (·OO ZLQ)↑ C  (FRPPLW)(↑ C , S) ↑ C I22 I21 S

G ² SDJH  , WKDQN P\ WHDP IRU WKHLU KHOS ← ← ǫ← = E IRUE (WKHLU KHOS)(Y, S)  ǫ I22 (P\ WHDP)R  (, WKDQN)(Y, S) 

(H[SUHVV)(= E, S)

H ² SDJH  DQG WKH ZLQQHU RI WKH UDFH LV DQG← (WKH ZLQQHU RI WKH UDFH LV)l

λ

D  (Declare)l D

 ² SDJH  6SHDNHU DVVHUWV WKDW VSHDNHU¶V EHOLHI H[LVWV ǫ → ·V→ (VSHDNHU)X = S > A  (EHOLHI)Y  (H[LVWV)Ix  ↓A Y Y → (VSHDNHU)X = S  (DVVHUWV)↓ A ↓A

WKDW←

 ² SDJH  , WHOO \RX ZKDW , IRXQG LQ WKH OLEUDU\ ←

↓A

(\RX ZKDW , IRXQG LQ WKH OLEUDU\)↑ D  (I Btell)↓ A

 ² SDJH  6SHDNHU GLUHFWV UHFHLYHU WR GR UHTXHVW ǫ ← ǫ → (UHTXHVW)Z  ǫ ↔ (UHFHLYHU)Y = R  (WRBGR)Ix  Ix ↑ D Ix → (VSHDNHU)X = S  (GLUHFWV)↑ D  ↑D

([DPSOHV



 ² SDJH  /L]D RUGHUHG 3DXO WR OHDYH ǫ ← (3DXO WR OHDYH)(Z, R)  (/L]D RUGHUHG)(↑ D, S) ↑D

 ² SDJH  6SHDNHU SURPLVHV WKDW VSHDNHU ZLOO GR WKH SURPLVH ǫ ← ǫ → (SURPLVH)Z  ǫ ↔ (VSHDNHU)Y = S  (ZLOOBGR)Ix  Ix ↑ C Ix →  (VSHDNHU)X = S  (SURPLVHV)↑ C ↑C

 ² SDJH  6SHDNHU H[SUHVVHV VSHDNHU¶V HPRWLRQ RQ UHFHLYHU (VSHDNHU)S  (HPRWLRQ)Ix (UHFHLYHU)R  ·V→ RQ← Ix Ix ǫ→ = E (VSHDNHU)X = S  (H[SUHVVHV)= E

= Y

 ² SDJH  6SHDNHU 'HFODUHV µWKH 5HFHLYHU KDV WKH 'HFODUHG 6WDWXV¶ UHFHLYHUY = R  KDVIx  ǫ ← VWDWXVS  ǫ → Ix l D Ix → VSHDNHUX = S  'HFODUHVl D ǫ lD

←

 ² SDJH  )DWKHU
 ² SDJH  'LG \RX VHH WKH QHZV" "←

('LG \RX VHH WKH QHZV)↓ A  (DVVHUW)↓ A

↓A

 ² SDJH  :K\ KDYH \RX VWLOO WR ILQLVK \RXU KRPHZRUN" "←

↑D

(:K\ KDYH \RX VWLOO WR ILQLVK \RXU KRPHZRUN)↑ D  (GLUHFW)↑ D

 ² SDJH  2Q ZKDW , KDYH P\ PLQG IL[HG WRGD\" "←

↑C

(:K\ KDYH \RX VWLOO WR ILQLVK \RXU KRPHZRUN)↑ C  (FRPPLW)↑ C

 ² SDJH  +RZ VKRXOG , IHHO DERXW WKDW" "←

= E (+RZ VKRXOG , IHHO DERXW WKDW)= E  (H[SUHVV)= E



$SSHQGL[ $

 ² SDJH  , SURPLVH \RX¶OO GR LW ǫ → (\RX·OO GR LW)(↑ D, S)  (, SURPLVH)(↑ C , S) ↑D

 ² SDJH  , UHTXHVW P\VHOI WR EH EUDYH ǫ → (WR EH EUDYH)(↑ C , S)  (, UHTXHVW)(↑ D, S) ↑C

 ² SDJH  :K\ VKRXOG , EH DQJU\ ZLWK KLP" "←

↑D

(VKRXOG , EH DQJU\ ZLWK KLP)(= E, S)  (tellBme ZK\)(↑ D, S)

 ² SDJH  , ZRQGHU LI , DP DVKDPHG WR IROORZ KHU LI←

↓A

(, DP DVKDPHG WR IROORZ KHU)(= E, S)  (, ZRQGHU)(↓ A, S)

Appendix B The Formal Model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



$SSHQGL[ %

% *UDPPDU FDWHJRULHV ,Q WKH IROORZLQJ ZH GHDO ZLWK JHQHUDO FDWHJRULHV $V DQ LQWXLWLYH JXLGHOLQH WKH UHDGHU PD\ WKLQN WR REMHFWV LQ D FDWHJRU\ DV DGWUHHV DQG WR DUURZV DV FRQVWUXF WLRQV 7KLV YLHZ DOWKRXJK LQVSLULQJ QHHGV VRPH ZRUN WR EH FRQVLVWHQW VR ZH ZLOO LQWURGXFH D VHULHV RI GHILQLWLRQV WR IL[ WKH IXQGDPHQWDO SURSHUWLHV OHDGLQJ WR WKH LQWHQGHG LQWHUSUHWDWLRQ 7KH IXQGDPHQWDO SURSHUW\ RI JUDPPDU FKDUDFWHUV LV WKDW HYHU\ REMHFW KDV H[ DFWO\ RQH JUDPPDU FKDUDFWHU $OVR ZH UHTXLUH WKDW WKH VHW RI JUDPPDU FKDUDFWHUV LV PHDQLQJIXO LH HYHU\ JUDPPDU FKDUDFWHU FRQWDLQV DW OHDVW RQH REMHFW 'HILQLWLRQ % *UDPPDU FKDUDFWHU *LYHQ D VPDOO FDWHJRU\ C ZH VD\ WKDW G LV D VHW RI JUDPPDU FKDUDFWHUV RQ C LI G LV D SDUWLWLRQ RQ Obj C WKH VHW RI REMHFWV LQ C VXFK WKDW QR FODVV LV HPSW\ S )RUPDOO\ G = {Gi }i∈GC VXFK WKDW i∈GC Gi = Obj C DQG IRU DQ\ i, j ∈ GC  LI i , j WKHQ Gi ∩ G j = ∅ DQG Gi , ∅ RWKHUZLVH

,Q RUGHU WR H[DFWO\ GHILQH ZKDW ZH LQWHQG IRU FRQVWUXFWLRQV ZH QHHG WKH WHFK QLFDO FRQFHSW RI JUDPPDU SURGXFW 'HILQLWLRQ % *UDPPDU SURGXFW )L[HG D VPDOO FDWHJRU\ C D VHW G = {Gi }i∈GC RI JUDPPDU FKDUDFWHUV ZLWK W ∈ G ZH FDOO JUDPPDU SURGXFW RQ C G W DQ\ SDLU hY1 × · · · × Yn , (z1 , . . . , zn )i ZKHUH n LV D QDWXUDO QXPEHU FDOOHG WKH GHJUHH RI WKH SURGXFW × LV WKH &DUWHVLDQ SURGXFW RI VHWV DQG IRU HYHU\ i LQ 1 . . . n Yi ∈ G \ {W} DQG zi ∈ W 

7KH UHDGHU LV LQYLWHG WR QRWLFH WKDW JUDPPDU SURGXFWV DUH QRW SURGXFWV LQ WKH FDWHJRU\ C²ZH GR QRW HYHQ UHTXLUH WKDW C KDV SURGXFWV ,QVWHDG WKH\ VKRXOG EH WKRXJKW RI DV ILQLWH SURGXFWV RI JUDPPDU FKDUDFWHUV ZKHUH WKH iWK SURMHFWRU LV QDPHG E\ DQ HOHPHQW RI W  ZKLFK GHQRWHV WKH FODVV RI DGSRVLWLRQV &RQVWUXFWLRQV DUH IDPLOLHV RI DUURZV ZLWK WKH VDPH GRPDLQ DQG ZKRVH FR GRPDLQ OLHV LQ D VLQJOH JUDPPDU FKDUDFWHU ZKLFK LV QRW WKH RQH RI DGSRVLWLRQV 7KHVH DUURZV DUH LQGH[HG E\ D JUDPPDU SURGXFW 'HILQLWLRQ % *UDPPDU FRQVWUXFWLRQ *LYHQ D VPDOO FDWHJRU\ C D VHW G = {Gi }i∈GC RI JUDPPDU FKDUDFWHUV ZLWK n oW ∈ G D JUDPPDU FRQVWUXFWLRQ ηP,x RYHU P IURP x LV DQ LQGH[HG FROOHFWLRQ f j ZKHUH ′ j∈P

7KH )RUPDO 0RGHO



‡ P = hP′ , ai LV D JUDPPDU SURGXFW RQ C G W  ‡ x LV DQ REMHFW RI C ‡ WKHUH LV V ∈ G \ {W} VXFK WKDW IRU HYHU\ j ∈ P′  f j ∈ HomC (x, y) ZKHUH y ∈ V :H GHQRWH WKH VHW V E\ cod ηP,x  WKH FRGRPDLQ RI WKH JUDPPDU FRQVWUXFWLRQ 6LPLODUO\ dom ηP,x = x DQG ZH FDOO P WKH SURGXFW RI ηP,x  6RPHWLPHV ZH ZLOO ZULWH η j,x IRU f j   $ IDPLO\ ηP,x x∈U RI JUDPPDU FRQVWUXFWLRQV RYHU P IURP x YDU\LQJ LQ WKH U JUDPPDU FKDUDFWHU IRUPV D JUDPPDU FRQVWUXFWLRQ ηP,U RYHU P IURP U ZKHQ DOO LWV HOHPHQWV VKDUH WKH VDPH FRGRPDLQ :H GHQRWH WKH FRPPRQ FRGRPDLQ ZLWK cod ηP,U  $OVR dom ηP,U = U DQG P LV WKH SURGXFW RI WKH FRQVWUXFWLRQ $JDLQ ZH ZLOO ZULWH η j,x WR LQGLFDWH WKH jWK FRPSRQHQW RI WKH xWK FRPSRQHQW RI ηP,U  :H VD\ WKDW WKH FRQVWUXFWLRQ η RYHU P = hY1 × · · · × Yn , (z1 , . . . , zn )i RQ WKH REMHFW x KDV x DV JRYHUQRU DQG LWV GHSHQGHQWV DUH WKH HOHPHQWV RI Y1 , . . . , Yn  LWV DGSRVLWLRQV DUH z1 , . . . , zn  6R LWV SURGXFW P GHVFULEHV WKH DGSRVLWLRQDO VWUXFWXUH WKDW η LPSRVHV RYHU WKH JRYHUQRU )RU V\PPHWU\ JLYHQ D FRQVWUXFWLRQ η DV DERYH LW LV XVHIXO WR FRQVLGHU WKH FRQVWUXFWLRQV ZKLFK GLIIHU IURP η E\ H[FKDQJLQJ D GHSHQGHQW ZLWK WKH JRYHUQRU 'HILQLWLRQ % &RQMXJDWH FRQVWUXFWLRQ )L[HG D VPDOO FDWHJRU\ C D VHW G = {Gi }i∈GC RI JUDPPDU FKDUDFWHUV ZLWK W ∈ G DQG D JUDPPDU FRQVWUXFWLRQ n o  η = f j : x → c(x, j) ′ j∈P

x∈V

′

RYHU WKH SURGXFW P = hP = P1 × · · · × Pn , (a1 , . . . , an )i IURP WKH V JUDPPDU FKDUDFWHU D JUDPPDU FRQVWUXFWLRQ θ RYHU WKH SURGXFW Q IURP WKH JUDPPDU FKDUDFWHU U LV VDLG WR EH FRQMXJDWH WR η LI IRU VRPH k LQ 1 . . . n U = Pk DQG

Q = hP1 × · · · × Pk−1 × V × Pk+1 × · · · Pn , (ak , a2 . . . , ak−1 , a1 , ak+1 . . . , an )i DQG IRU DOO (x, j1 , . . . , jn ) ∈ C × P′  cod η( j1 ,..., jn ),x = cod θ( j1 ,..., jk−1 ,x, jk+1 ,..., jn ), jk  :H QRWLFH WKDW LQ JHQHUDO D FRQVWUXFWLRQ PD\ KDYH DQ\ QXPEHU RI FRQMXJDWHV IRU HDFK HOHPHQWV LQ LWV SURGXFW HYHQ ]HUR &RQVWUXFWLRQV IURP JUDPPDU FDWHJRULHV FDQ EH FRPSRVHG WR REWDLQ PRUH FRPSOH[ FRQVWUXFWLRQV



$SSHQGL[ %

'HILQLWLRQ % &RPSRVLWLRQ RI FRQVWUXFWLRQV *LYHQ D VPDOO FDWHJRU\ C D VHW G = {Gi }i∈GC RI JUDPPDU FKDUDFWHUV ZLWK W ∈ G DQG JUDPPDU FRQVWUXF WLRQV  

η=

n

f(y1 ,...,yn ) : x → c(x, y1 , . . . , yn )

o

y1 ∈P1 ,...,yn ∈Pn x∈V

RYHU WKH SURGXFW P = hP1 × · · · × Pn , (a1 , . . . , an )i IURP WKH V JUDPPDU FKDU DFWHU DQG n o θ = g(z1 ,...zm ) : x → d(x, z1 , . . . , zm ) z1 ∈Q1 ,...,zm ∈Qm x∈U

RYHU WKH SURGXFW Q = hQ1 × · · · × Qm , (b1 , . . . , bm )i IURP WKH U JUDPPDU FKDU DFWHU WKH FRPSRVLWLRQ θ ◦ η LV GHILQHG ZKHQ dom θ = U = cod η ,Q WKLV FDVH n  o θ ◦ η = g(z1 ,...zm ) ◦ f(y1 ,...yn ) y1 ∈P1 ,...,yn ∈Pn ,z1 ∈Q1 ,...,zm ∈Qm x∈V

DQG dom θ ◦ η = dom η = V  cod θ ◦ η = cod θ DQG WKH SURGXFW RI θ ◦ η LV

hP1 × · · · Pn × Q1 × · · · × Qm , (a1 , . . . , an , b1 , . . . , bm )i . $V WKH UHDGHU PD\ FKHFN WKH JUDPPDU FKDUDFWHUV DORQJ ZLWK DOO WKH SRVVLEOH FRQVWUXFWLRQV DQG ZLWK WKH FRPSRVLWLRQ MXVW GHILQHG IRUPV D FDWHJRU\ $OWKRXJK WKLV FDWHJRU\ LV RI LQWHUHVW DV ZH ZLOO EULHIO\ GLVFXVV LQ WKH IROORZ LQJ WKH NHUQHO RI WKH IRUPDO PRGHO FRQFHQWUDWHV XSRQ DQRWKHU FDWHJRU\ 'HILQLWLRQ % *UDPPDU FDWHJRU\ &RQVLGHU D VPDOO FDWHJRU\ C D VHW RI JUDPPDU FKDUDFWHUV RQ LW G = {Gi }i∈GC ZLWK W ∈ G DQG D VHW C RI JUDP PDU FRQVWUXFWLRQV RYHU VRPH SURGXFW RQ C G W IURP D JUDPPDU FKDUDFWHU LQ G 7KHQ WKH VWUXFWXUH hC, G, W, Ci LV VDLG WR EH D JUDPPDU FDWHJRU\ ZKHQ LW VDWLVILHV WKH IROORZLQJ SURSHUWLHV

 7KHUH LV D FROOHFWLRQ M RI REMHFWV LQ C FDOOHG WKH DWRPV RI WKH FDWHJRU\ VXFK WKDW IRU HDFK x ∈ Obj C WKHUH LV DQ DUURZ f LQ C ZLWK dom f ∈ M DQG cod f = x PRUHRYHU LI x ∈ M  WKHQ f = id x   )RU HDFK DUURZ f : a → b LQ C WKHUH LV ηP,V ∈ C VXFK WKDW a ∈ V DQG f ∈ ηP,a  ZKHUH ηP,a LV WKH aFRPSRQHQW RI ηP,V   (YHU\ FRQVWUXFWLRQ η ∈ C LV WKH FRPSRVLWLRQ RI D VHTXHQFH θ1 , . . . , θn RI FRQVWUXFWLRQV LQ C HDFK RQH KDYLQJ GHJUHH 1

7KH )RUPDO 0RGHO



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hC, G, U, Ci DQG G LV LQGH[HG E\

n o GC = {A, E, O, U} ∪ I p : p LV D JUDPPDU SURGXFW RQ C, G, U .

:H UHTXLUH WKDW WKH FROOHFWLRQ RI I p V LV ZLGH HQRXJK WR DOORZ WKH GHILQLWLRQ RI DOO WKH UHODWHG FRQVWUXFWLRQV PDLQO\ YDOHQF\

% $GWUHHV /HW hC, G = {Gi }i∈GC , W, Ci EH D JUDPPDU FDWHJRU\ DQG OHW η EH D JUDPPDU FRQ VWUXFWLRQ RYHU hY1 × · · · × Yn , (a1 , . . . , an )i IURP WKH REMHFW x n o η = f(y1 ,...,yn ) : x → c(x,y1 ,...,yn ) . y1 ∈Y1 ,...,yn ∈Yn

:H FDQ HTXLYDOHQWO\ ZULWH HDFK DUURZ LQ η DVD

x

f(y1 ,...,yn )

/ an (yn , an−1 (. . . , a1 (y1 , x) . . .)) = c(x, y1 , . . . , yn ) ∈ cod η .

7KH DERYH UHSUHVHQWDWLRQ LV HYLGHQWO\ XQLTXH DV IDU DV x LV WKH JRYHUQRU DQG (y1 , . . . , yn ) DUH WKH GHSHQGHQWV WDNHQ LQ WKH JLYHQ RUGHU VR ZH KDYH VKRZQ WKDW HYHU\ REMHFW LQ D JUDPPDU FDWHJRU\ FDQ EH UHSUHVHQWHG DV DQ DGWUHH ZKRVH OHDYHV DUH DWRPV 2I FRXUVH LI ZH WDNH D FRQMXJDWH FRQVWUXFWLRQ  η∗  WKH JRYHUQRU ZRXOG EH yk DQG WKH GHSHQGHQWV ZRXOG EH (y1 , . . . , yk−1 , x, yk+1 , . . . , yn ) FRUUH VSRQGLQJ WR WKH UHSUHVHQWDWLRQ

an (yn , an−1 (. . . , ak1 (yk−1 , a1 (x, ak+1 (. . . (ak (y1 , yk )) . . .)) . . .)) D

:H XVH OLQHDULVHG WUHHV IRU FRPSDFWQHVV



$SSHQGL[ %

RI WKH VDPH REMHFW c(x, y1 , . . . , yn ) 7R VRPH H[WHQW WKH FRQYHUVH DOVR KROGV LI ZH WDNH DV REMHFWV WKH DGWUHHV DV DUURZV WKH FRQVWUXFWLRQV GHVFULEHG LQ WKH ERRN DORQJ ZLWK WKHLU FRQMXJDWHV ZH REWDLQ DQ DGSRVLWLRQDO FDWHJRU\ ,Q WKLV FDVH ZH KDYH WKDW D OLQJXLVWLF FRQ VWUXFWLRQ η JHQHUDWHV D VHW RI JUDPPDU FRQVWUXFWLRQV LWVHOI SOXV WKH FRQVWUXFWLRQV ZKLFK DUH FRQMXJDWHV WR η ,W LV LQWHUHVWLQJ WR QRWLFH WKDW JUDPPDU FDWHJRULHV ZKHQ WKRXJKW RI DV FDWH JRULHV RI DGWUHHV JLYH UDLVH WR D FDWHJRU\ RI JUDPPDU FKDUDFWHUV 7KHRUHP % )L[HG D JUDPPDU FDWHJRU\ hC, G = {Gi }i∈GC , W, Ci LI

η=

n

f(x,y1 ,...,yn ) : x → c(x,y1 ,...,yn )

o



y1 ∈Y1 ,...,yn ∈Yn x∈V

LV D FRQVWUXFWLRQ RYHU hY1 × · · · × Yn , (a1 , . . . , an )i IURP WKH JUDPPDU FKDUDFWHU V  WKHQ IRU HYHU\ (y1 , . . . , yn ) ∈ Y1 × · · · × Yn  FRQVLGHU n o θ(y1 ,...,yn ) = f(x,y1 ,...,yn ) . x∈V

7KH VWUXFWXUH KDYLQJ GC DV REMHFWV DQG WKH θ¶V DERYH DV DUURZV LV D FDWHJRU\ 3URRI ,PPHGLDWH IURP WKH GHILQLWLRQV QRWLFLQJ WKDW HDFK θ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

7KH )RUPDO 0RGHO



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³ORFDO´ WKDW LV WKH\ DSSO\ RQ VSHFLILF DQG VPDOO LQ SUDFWLFH VXEWUHHV RI D JLYHQ DGWUHH $OVR VXFK UXOHV FDQ EH H[SUHVVHG DV D WUHHSDWWHUQ ZKLFK LQGXFHV D VXEVWLWXWLRQ RQ WKH PDWFK )RU H[DPSOH D UXOH IRU DUWLFOHV YV QRXQV LQ ,WDOLDQ LV LI WKH QRXQ LV IHPLQLQH WKH DUWLFOH PXVW EH IHPLQLQH DV ZHOO LI QRW FKDQJH LW WR D IHPLQLQH DUWLFOH :H FDQ IRUPDOLVH WKLV UXOH DV LI ǫ(L, N) LV \RXU DGWUHH DQG LW LV FRQVWUXFWHG YLD WKH ³GHWHUPLQHUV´ FRQVWUXFWLRQ VHH &KDSWHU   DQG N KDV WKH ³IHPLQLQH´ DWWULEXWH ZKLFK LV DQ DWWULEXWH LQ WKH JUDPPDU FDWHJRU\ RI PRUSKHPHV DQG L KDV QRW WKH ³IHPLQLQH´ DWWULEXWH WKHQ VXEVWLWXWH ³OD´ IRU L 2I FRXUVH LQ D FRPSOH[ DGWUHH ZH VKRXOG DSSO\ UHFXUVLYHO\ WKLV UXOH WR HYHU\ VXEWUHH ,Q WKLV UHVSHFW WKH FRPSXWDWLRQDO DQDO\VLV RI DOJRULWKPV RQ DGWUHHV FDQ EH VRPHZKDW VLPSOLILHG E\ WKH IROORZLQJ UHVXOW :H VD\ WKDW DQ DGWUHH LV OLQHDU ZKHQ LWV JRYHUQRU DQG DOO LWV GHSHQGHQWV DUH DWRPV 0RUHRYHU LI WKH DGWUHH a(x, T 0 ) LV REWDLQHG E\ PHDQV RI WKH η FRQVWUXFWLRQ WKHQ a(T 0 , x) LV REWDLQHG E\ PHDQV RI WKH η∗ FRQMXJDWH FRQVWUXFWLRQ :H VD\ WKDW T 1 ∼ T 2 ZKHQ T 1 = T [a(x, T 0 )] DQG T 2 = T [a(T 0 , x)] LH ZKHQ T 1 DQG T 2 GLIIHU E\ D VLQJOH VXEWUHH ZKLFK DSSHDUV LQ WKH UHJXODU IRUP LQ T 1 DQG LQ WKH FRQMXJDWH IRUP LQ T 2  DQG HYLGHQWO\ LW KROGV WKDW WKH REMHFW GHQRWHG E\ T 1 HTXDOV WKH REMHFW GHQRWHG E\ T 2  :H GHQRWH E\ ≈ WKH UHIOH[LYH V\PPHWULF DQG WUDQVLWLYH FORVXUH RI WKH ∼ UHODWLRQ (YLGHQWO\ ≈ LV DQ HTXLYDOHQFH UHODWLRQ RYHU DGWUHHV :H FDOO LW HTXLYDOHQFH PRGXOR FRQMXJDWHV RU FHTXLYDOHQFH IRU VKRUW 7KHRUHP % /HW A EH D JUDPPDU FDWHJRU\ 7KHQ HYHU\ REMHFW RI A LV GH QRWHG E\ DQ DGWUHH x DQG WKHUH LV DQ DGWUHH y GHQRWLQJ WKH VDPH REMHFW VXFK WKDW x ≈ y DQG y LV OLQHDU

3URRI :H SURYH WKDW HYHU\ DGWUHH T LV FHTXLYDOHQW WR VRPH OLQHDU DGWUHH L GHQRWLQJ WKH VDPH REMHFW DV T  :H SURFHHG E\ LQGXFWLRQ RQ WKH VWUXFWXUH RI T 



$SSHQGL[ %

‡ %DVLV ,I T LV DQ DWRP L = T LV OLQHDU DQG FHTXLYDOHQW WR T E\ UHIOH[LYLW\ DQG L DQG T GHQRWH WKH VDPH REMHFW ‡ ,QGXFWLRQ VWHS ,I T = a(T 2 , T 1 ) WKHQ E\ LQGXFWLRQ K\SRWKHVLV WKHUH DUH

L1 = bk (tk , bk−1 (. . . , b1 (t1 , t0 ) . . .)) DQG L2  ERWK OLQHDU VXFK WKDW T 1 ≈ L1  T 2 ≈ L2  T 1 DQG L1 GHQRWH WKH VDPH REMHFW DQG T 2 DQG L2 GHQRWH WKH VDPH REMHFW 7KXV T ≈ a(L2 , L1 ) DQG WKH\ GHQRWH WKH VDPH REMHFW GHULYLQJ IURP DQ DSSOLFDWLRQ RI WKH VDPH FRQVWUXFWLRQ WR LGHQWLFDO REMHFWV 6R FRQVLGHULQJ WKH FRQMXJDWH RI WKH FRP SRVHG FRQVWUXFWLRQ

T ≈ a(L2 , bk (tk , bk−1 (. . . , b1 (t1 , t0 ) . . .)) ≈ ≈ b1 (t0 , bk (tk , bk−1 (. . . , a(t1 , L2 ) . . .)) = L , DQG L LV OLQHDU DQG GHQRWHV WKH VDPH REMHFW DV T  &RUROODU\ % ,Q D JUDPPDU FDWHJRU\ HYHU\ DGWUHH T [T 1 ] LH DQ DGWUHH KDYLQJ T 1 DV D VXEWUHH LV FHTXLYDOHQW WR DQ DGWUHH KDYLQJ T 1 DV JRYHUQRU

3URRI 7KH VDPH LQGXFWLRQ DUJXPHQW SURYHV WKH VWDWHPHQW &RUROODU\ % *LYHQ D JUDPPDU FDWHJRU\ WKH FRQVWUXFWLRQV FDQ EH SDUWL WLRQHG LQWR WKH EDVLF RQHV DQG WKHLU FRQMXJDWHV 7KHQ HYHU\ DGWUHH FRQVWUXFWHG YLD EDVLF FRQVWUXFWLRQV LV FHTXLYDOHQW WR D OLQHDU DGWUHH DQG YLFH YHUVD

3URRI $ WHGLRXV DQDO\VLV RI WKH SURRI RI WKH WKHRUHP ZKHUH ZH NHHS WUDFN RI FRQMXJDWHV DOORZV WR SURYH WKH UHVXOW &RUROODU\ % ,Q D SXUH JUDPPDU FDWHJRU\ HYHU\ REMHFW LV XQLTXHO\ LGHQWLILHG ZLWK WKH TXRWLHQW RI WKH VHW RI LWV DGWUHHV YLD WKH ≈ UHODWLRQ

$V D VLGH HIIHFW RI FRUROODU\ % ZH JHW DQ DEVWUDFW SDUVLQJ DOJRULWKP IRU DQ\ JUDPPDU FDWHJRU\ ,Q IDFW D OLQHDU DGWUHH LV WKH VDPH WKLQJ DV D VHTXHQFH RI PRUSKHPHV ZKHUH DGSRVLWLRQV ZKLFK FDQ EH PHFKDQLFDOO\ H[WUDFWHG DUH SXW LQ WKH ³ULJKW´ SODFHV 6R WKH PHDQLQJ RI FRUROODU\ % LV WKDW LW LV SRVVLEOH WR UHFRQVWUXFW IURP VXFK D OLQHDU DGWUHH DQRWKHU DGWUHH ZKLFK LV EXLOW E\ EDVLF FRQ VWUXFWLRQV RQO\ LH DQ DGWUHH LQ WKH IRUPDW ZH XVHG DORQJ DOO WKH ERRN 2I FRXUVH

7KH )RUPDO 0RGHO



VXFK DQ DOJRULWKP LV ³XQLYHUVDO´ VLQFH LW DSSOLHV WR DQ\ JUDPPDU FDWHJRU\ EXW GHVSHUDWHO\ LQHIILFLHQW VLQFH LW LV KLJKO\ QRQGHWHUPLQLVWLF 6XFK D SDUVLQJ DOJRULWKP LV XQDEOH WR GLVWLQJXLVK GLIIHUHQW UHSUHVHQWDWLRQV RI WKH VDPH REMHFWV XQOHVV WKH\ DUH FHTXLYDOHQW 6R LW VKRXOG EH XVHG RQO\ RQ SXUH JUDPPDU FDWHJRULHV %\ WKH ZD\ DOO WKH JUDPPDU FDWHJRULHV ZH GHDOW ZLWK LQ WKLV PRQRJUDSK DUH SXUH

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× {←, →, ↔} DV WKH VHW RI DGSRVLWLRQV LQ WKH JUDPPDU FDWHJRU\ WR HQVXUH WKDW HDFK DGSRVLWLRQ LV GHFRUDWHG E\ DQ LQGLFDWRU 2WKHU DWWULEXWHV DUH WUHDWHG VLPLODUO\ 0RUHRYHU ZH XVXDOO\ UHTXLUH WKDW WKHUH LV D VSHFLDO PRUSKHPH ǫ  LQ WKH VHW RI DGSRVLWLRQV UHSUHVHQWLQJ WKH HPSW\ DGSRVLWLRQ :H DOVR UHTXLUH WKDW  LV DQ HOHPHQW RI HDFK JUDPPDU FKDUDFWHU UHSUHVHQWLQJ WKH HPSW\ HOHPHQW RI WKDW FODVV WR EH SUHFLVH ZH VKRXOG VSHDN RI A  E  O  «ZKLFK DUH GLVWLQFW REMHFWV LQ WKH JUDPPDU FDWHJRU\ EXW WKH DPELJXRXV  V\PERO GRHV QRW FDXVH DQ\ KDUP LQ WKH XVXDO SUDFWLFH DV LW LV DOZD\V LQ D FRQWH[W FODULI\LQJ LWV FRUUHFW PHDQLQJ )XUWKHUPRUH ZH IUHTXHQWO\ XVHG FDQFHOOHG DWRPV WR GHQRWH REMHFWV ZKLFK DUH SUHVHQW LQ D OLQJXLVWLF VWUXFWXUH EXW WKH\ DUH DEVHQW IURP LWV WH[WXDO UHSUH VHQWDWLRQ²ZH VDLG WKH\ DUH ³KLGGHQ´ $JDLQ WKHVH HOHPHQWV UHTXLUH QR VSHFLDO WUHDWPHQW LQ WKH GHILQLWLRQ RI JUDPPDU FDWHJRULHV LI M LV WKH VHW RI DWRPV LQ WKH ODQJXDJH LW VXIILFHV WR WDNH M = M ⊔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



$SSHQGL[ %

,QIRUPDOO\ D WUDQVIRUPDWLRQ LV D PDS IURP DGWUHHV WR DGWUHHV LQ D JLYHQ JUDP PDU FDWHJRU\ $V ZH KDYH VHHQ LQ VHFWLRQ % IL[HG D JUDPPDU FDWHJRU\ C DQ DGWUHH LV D UHSUHVHQWDWLRQ RI DQ LQVWDQFH RI D FRQVWUXFWLRQ ZKLFK PDNHV H[SOLFLW LWV SURGXFW LWV GHSHQGHQWV DQG LWV JRYHUQRU RUJDQLVLQJ WKHP LQ D ELQDU\ WUHH VWUXFWXUH $OVR HYHU\ REMHFW LQ C H[FHSW IRU DGSRVLWLRQV FDQ EH UHSUHVHQWHG E\ DQ DGWUHH DQG XVXDOO\ E\ PRUH WKDQ RQH :H ZLOO FDOO Ad(C) WKH FROOHFWLRQ RI DOO DGWUHHV LQ C SOXV WKH HPSW\ DGWUHH GHQRWHG E\ ⊥ LQ IDFW Ad(C) LV D FDWHJRU\ ZKRVH DUURZV DUH WKH DUURZV RI C LH WKH LQVWDQFHV RI WKH FRQVWUXFWLRQV RI C WKRXJKW RI DV DSSOLHG WR DGWUHHV LQVWHDG RI EHLQJ DSSOLHG WR REMHFWV 0RUHRYHU ZH DVVXPH WKDW WKHUH LV D XQLTXH DUURZ IURP ⊥ WR DQ\ RWKHU DGWUHH RQ C VR ⊥ LV DQ LQLWLDO REMHFW LQ Ad(C) 'HILQLWLRQ % 7UDQVIRUPDWLRQ *LYHQ D JUDPPDU FDWHJRU\ C D WUDQVIRU PDWLRQ RQ Ad(C) LV DQ HQGRIXQFWRU LQ Ad(C)

7KH SUHYLRXVO\ GHVFULEHG UHGXQGDQF\ WUDQVIRUPDWLRQV VDWLVI\ WKH DERYH GHIL QLWLRQ ,Q JHQHUDO DOO WKH ³WUDQVIRUPDWLRQV´ ZH FRQVLGHUHG LQ WKLV ERRN DUH WUDQV IRUPDWLRQV LQ WKH GHILQHG IRUPDO VHQVH H[FHSW IRU ³ǫ WUDQVIRUPDWLRQV´ ZKLFK DV LW KDV EHHQ UHPDUNHG DUH MXVW D FRQYHQLHQW ZD\ WR FRQGHQVH DGWUHHV WKDW LV D PDWWHU RI KXPDQ UHDGDELOLW\ ,W LV ZRUWK GHVFULELQJ LQ VRPH GHWDLO KRZ UHGXQGDQF\ WUDQVIRUPDWLRQV RSHU DWH ERWK WR FODULI\ KRZ WKH\ VKRXOG EH FRQFHLYHG DQG XQGHUVWRRG DQG WR LQWUR GXFH LQ D IRUPDO ZD\ WKH QRWLRQ RI FRUUHFW DGWUHHV ZLWK UHVSHFW WR UHGXQGDQFLHV $V DQ H[DPSOH FRQVLGHU WKH UHGXQGDQF\ UXOH ZKLFK VD\V ³LI WKH QRXQ LV IHP LQLQH PRGLI\ WKH DUWLFOH WR IHPLQLQH´ ,Q WKH JUDPPDU FDWHJRU\ IRU WKH ,WDOLDQ ODQJXDJH WKLV UXOH EHFRPHV D IXQFWRU F RQ DGWUHHV DV IROORZV DQ DGWUHH T EH FRPHV WKH F(T ) DGWUHH ZKHUH HYHU\ RFFXUUHQFH RI D VXEWUHH ǫ(a, n) ZLWK a DUWLFOH DQG n IHPLQLQH QRXQ LV VXEVWLWXWHG ZLWK ǫ(a′ , n) ZLWK a′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f DGWUHH LV ILQDO IRU F RQ WKH DGWUHH t LI f LV D IL[HG SRLQW RI F DQG f = F ◦ · · · ◦ F t LH LI f LV WKH UHVXOW RI D ILQLWH

7KH )RUPDO 0RGHO



FRPSRVLWLRQ RI F ZLWK LWVHOI DSSOLHG WR t 7KH PHDQLQJ RI WKLV GHILQLWLRQ LV WKDW D WUDQVIRUPDWLRQ F LV DSSOLHG WR DQ DGWUHH t WR ³FRUUHFW´ LWV ³ZURQJ´ UHGXQGDQFLHV WKH WUDQVIRUPDWLRQ LV LWHUDWLYHO\ DSSOLHG XQWLO DOO WKH ³PLVWDNHV´ DUH UHPRYHG DQG WKH UHVXOWLQJ DGWUHH GRHV QRW FKDQJH DQ\PRUH 7KH VHW RI ILQDO DGWUHHV IRU D UHGXQGDQF\ WUDQVIRUPDWLRQ R GHSULYHG RI ⊥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hM, G M , W M , C M i FDOOHG WKH FDWHJRU\ RI PRUSKHPHV DQG DQRWKHU JUDPPDU FDWHJRU\ L = hL, G L , WL , C L i FDOOHG WKH OLQJXLVWLF FDWHJRU\ DQG D PDS φ : Obj M → Obj L ZKRVH LPDJH OLHV LQ WKH DWRPV RI L 'HILQH C = hC, G, W, Ci ZKHUH ‡ WKH FDWHJRU\ C KDV DV REMHFWV  M SOXV Obj L ⊔ Obj M ZKHUH M = { M }



$SSHQGL[ %

DQG  M LV QRW DQ REMHFW RI L DQG M WKH DUURZV RI C DUH WKH DUURZV RI L DQG WKRVH RI M SOXV WKH LQVWDQFHV RI φ ‡ WKH DWRPV RI C DUH FOHDUO\ WKH DWRPV RI M SOXV  M  ‡ WKH JUDPPDU FKDUDFWHUV RI M DUH G = G L ⊔ G M ⊔ M  ‡ WKH DGSRVLWLRQV RI C DUH W = WL ⊔ W M ⊔ {ǫ M } ‡ WKH FRQVWUXFWLRQV RI C DUH n o C = C L ⊔ C M ⊔ θ j : x → φ(x)



j∈M x∈α

: α ∈ GM



.

(YLGHQWO\ C LV D JUDPPDU FDWHJRU\ ,QIRUPDOO\ C FRUUHVSRQGV WR WKH GLVMRLQW XQLRQ RI M DQG L ZKHUH WKH DWRPV RI L DUH VXEVWLWXWHG PRGXOR DQ ǫ WUDQVIRUPDWLRQ ZKLFK KLGHV WKH θ FRQVWUXFWLRQ E\ WKH PRUSKHPHV LH WKH REMHFWV RI M YLD WKH φ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

7KH )RUPDO 0RGHO



:H ZLOO QRW GHYHORS KHUH WKH ZKROH PDWKHPDWLFDO PDFKLQHU\ ZKLFK LV UDWKHU FRPSOH[ EXW ZH ZDQW WR JLYH WKH UHDGHU DQ LQWXLWLRQ RI ZKDW WR H[SHFW DQG ZK\ ZH EHOLHYH WKLV DSSURDFK FRXOG EH RI LQWHUHVW :H UHFDOO WKDW D VLHYH RQ DQ REMHFW c LQ D FDWHJRU\ C LV D VHW S RI DUURZV RI C ZLWK FRGRPDLQ c VXFK WKDW LI f ∈ S DQG f ◦ h LV GHILQHG WKHQ f ◦ h ∈ S  6SHFLDOLVLQJ WKLV QRWLRQ WR SXUH JUDPPDU FDWHJRULHV ZH JHW WKDW D VLHYH S RQ c LV D VHW RI LQVWDQFHV RI FRQVWUXFWLRQV LQ ELMHFWLYH FRUUHVSRQGHQFH ZLWK D VHW S ′ RI DGWUHHV GHILQHG DV IROORZV LI f : b → c ∈ S  WKHQ b ∈ S ′ DQG IRU HYHU\ d VXFK WKDW WKHUH LV g : d → b d ∈ S ′  ,QWXLWLYHO\ D VLHYH S RQ c IL[HV D VHW B RI LQVWDQFHV RI FRQVWUXFWLRQV RI c ZKRVH JRYHUQRUV DUH LQ S ′  DQG WKH VLHYH FRQWDLQV DOO WKH LQVWDQFHV RI FRQVWUXFWLRQV RI c ZKRVH ODVW VWHS LV LQ B 'XDOLVLQJ D FRVLHYH S RQ c LQ D SXUH JUDPPDU FDWHJRU\ LV D VHW RI LQVWDQFHV RI FRQVWUXFWLRQV RI c LQ ELMHFWLYH FRUUHVSRQGHQFH ZLWK D VHW S ′ RI DGWUHHV GHILQHG DV IROORZV LI f : c → b ∈ S  WKHQ b ∈ S ′ DQG IRU HYHU\ DGWUHH d ZKRVH JRYHUQRU LV b WKH DGWUHH d′ ∈ S ′  ZKHUH d′ LV REWDLQHG E\ d H[SDQGLQJ WKH FRQVWUXFWLRQ RI b VR WR PDNH c LWV JRYHUQRU ,Q RWKHU ZRUGV FRVLHYHV DUH EXLOW IL[LQJ D VHW B RI FRQVWUXFWLRQV KDYLQJ c DV JRYHUQRU DQG WDNLQJ DOO WKH FRQVWUXFWLRQV ZKLFK DUH H[WHQVLRQV RI WKRVH LQ B ([DPSOHV RI VLHYHV DUH DV IROORZV VXSSRVH c LV WKH UHVXOW RI D YDOHQF\ FRQ VWUXFWLRQ RYHU WKH SURGXFW hO, (ǫ)i IURP v LQ VRPH DGSRVLWLRQDO FDWHJRU\ WKHQ WKH VLHYH S JHQHUDWHG E\ WKLV DUURZ FRQWDLQV DOO WKH FRQVWUXFWLRQV RI c KDYLQJ v DV JRYHUQRU HYHQWXDOO\ VXEVWLWXWHG E\ LWV FRQVWUXFWLRQV 6LPLODUO\ WKH FRVLHYH RQ WKH REMHFW v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



$SSHQGL[ %

VWUXFWLRQV LW LV ZRUWK FRQVLGHULQJ WKH PHDQLQJ RI *URWKHQGLHFN WRSRORJLHV LQ WKH FRQWH[W RI SXUH JUDPPDU FDWHJRULHV  :H UHFDOO WKDW D *URWKHQGLHFN WRSRORJ\ RQ D FDWHJRU\ C LV D IXQFWLRQ J PDSSLQJ HYHU\ REMHFW c RI C LQWR D FROOHFWLRQ J(c) RI VLHYHV RQ c VXFK WKDW  tc = { f : cod f = c} ∈ J(c) LH WKH PD[LPDO VLHYH RQ c LV DOZD\V LQ J(c)  LI S ∈ J(c) WKHQ IRU HYHU\ h : d → c LQ C

h∗ (S ) = {g : cod g = d DQG h ◦ g ∈ S } ∈ J(d) ;  LI S ∈ J(c) DQG R LV DQ\ VLHYH RQ c VXFK WKDW h∗ (R) ∈ J(d) IRU DOO h : d → c LQ S  WKHQ R ∈ J(c) $ VLWH LV D SDLU hC, Ji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∈ J(c) DV D VHW RI DGPLVVLEOH LQVWDQFHV RI FRQVWUXFWLRQV ZLWK UHVSHFW WR J  6R h∗ (S ) EHFRPHV WKH VHW RI LQVWDQFHV RI FRQ VWUXFWLRQV WKDW FRPSRVHG ZLWK h JLYH DQ DGPLVVLEOH FRQVWUXFWLRQ RI WKH REMHFW c +HQFH WKH VWDELOLW\ D[LRP LH WKH VHFRQG UHTXLUHPHQW LQ WKH GHILQLWLRQ RI D WRSRORJ\ LV QRWKLQJ PRUH WKDQ UHTXLULQJ WKDW h∗ (S ) LV DGPLVVLEOH ZKLFK LV D YHU\ QDWXUDO FRQGLWLRQ 7KH WKLUG UHTXLUHPHQW DPRXQWV WR D JHQHUDOLVHG WUDQVLWLYLW\ 7KXV FRPSRVLQJ DGPLVVLEOH FRQVWUXFWLRQV ZLWK WKHPVHOYHV SURGXFHV DGPLVVLEOH FRQVWUXFWLRQV ZKLFK LV WKH PHDQLQJ RI WUDQVLWLYLW\ $V D FRQVHTXHQFH D *URWKHQGLHFN WRSRORJ\ J RQ D SXUH JUDPPDU FDWHJRU\ C LV D ZD\ WR FRKHUHQWO\ LGHQWLI\ DGPLVVLEOH LQVWDQFHV RI FRQVWUXFWLRQV %XW WKH VKHDYHV RQ D VLWH hC, Ji IRUP D WRSRV Sh(C, J) WKDW FRQWDLQV WKH ZKROH DPRXQW RI LQIRUPDWLRQ RQ WKH VLWH :H UHPLQG WKDW D SUHVKHDI RQ C LV VLPSO\ D IXQFWRU Cop → Set DQG D VKHDI RQ hC, Ji LV D SUHVKHDI P RQ C VXFK WKDW IRU HYHU\ REMHFW c LQ C DQG HYHU\ VLHYH S ∈ J(c) WKH LQFOXVLRQ S ֌ Hom(−, c) LQGXFHV DQ LVRPRUSKLVP Hom(S , P)  Hom(Hom(−, c), P) :H GR QRW ZDQW WR H[SODLQ KHUH WKH GHWDLOV RI ZKDW D VKHDI LV LQ D SXUH JUDP PDU FDWHJRU\ DQG WKH SUHFLVH FRQVHTXHQFHV RI Sh(C, J) EHLQJ D WRSRV DV WKHVH

7KH )RUPDO 0RGHO



H[SODQDWLRQV DUH IDU EH\RQG WKH VFRSH RI WKH SUHVHQW WH[W ,W VXIILFHV WR VD\ WKDW LI ZH WKLQN RI DGPLVVLEOH FRQVWUXFWLRQV DV D VRUW RI DEVWUDFW V\QWD[ IRU WKH ODQJXDJH PRGHOOHG E\ WKH FDWHJRU\ C WKHQ WKH WRSRV Sh(C, J) LV DEOH WR SURYLGH D ORJLFDO GHVFULSWLRQ IRU WKDW V\QWD[ ZKLFK EHFRPHV DQ DEVWUDFW JUDPPDU IRU WKH ODQJXDJH DV ZHOO DV D JHRPHWULFDO LQWHUSUHWDWLRQ RI WKH ODQJXDJH DV D PDWKHPDWLFDO VSDFH ZKLFK LV D QRYHO DQG GLIIHUHQW ZD\ WR ORRN DW OLQJXLVWLF SKHQRPHQD :H EHOLHYH WKDW WKH DQDO\VLV RI Sh(C, J) ZKHQ C LV D SXUH JUDPPDU FDWHJRU\ ZLOO EH D GLIILFXOW EXW GHHSO\ UHZDUGLQJ IXWXUH GHYHORSPHQW IRU WKH IRUPDO PRGHO WKDW PD\ XQGHUFRYHU DQG H[SODLQ PDQ\ VXEWOHWLHV RI QDWXUDO ODQJXDJHV DQG WKDW PD\ OHDG WR D GHHSHU XQGHUVWDQGLQJ DQG XQLILFDWLRQ RI OLQJXLVWLF SKHQRPHQD RQ D FRPSOHWHO\ DEVWUDFW EDVLV IRXQGHG RQ WKH SXUH WRSRVWKHRUHWLF IUDPHZRUN

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hV, Σ, S , Pi ZKHUH V DQG Σ DUH GLVMRLQW ILQLWH VHWV S ∈ V DQG P LV D ILQLWH VHW RI H[SUHVVLRQV RI WKH IRUP A → α ZKHUH A ∈ V DQG α ∈ (V ∪ Σ)∗  7KH HOHPHQWV RI V DUH FDOOHG WKH QRQWHUPLQDO V\PEROV WKRVH RI Σ DUH FDOOHG WKH WHUPLQDOV S LV FDOOHG WKH VWDUW V\PERO DQG WKH HOHPHQWV RI P DUH FDOOHG WKH SURGXFWLRQV RU GHULYDWLRQ UXOHV 'HILQLWLRQ % /HW G = hV, Σ, S , Pi EH D FRQWH[WIUHH JUDPPDU 7KH ODQJXDJH JHQHUDWHG E\ G LV   G

L(G) = x ∈ Σ∗ : S −→ x

,



$SSHQGL[ % G

ZKHUH −→ LV WKH UHIOH[LYH DQG WUDQVLWLYH FORVXUH RI WKH ◮ UHODWLRQ ZKLFK JLYHQ α, β ∈ (V ∪ Σ)∗  LV GHILQHG DV α ◮ β LI WKHUH LV v ∈ V VXFK WKDW α = α′ · v · α′′ DQG β = α′ · β′ · α′′ ZKHUH (v → β′ ) ∈ P $ ODQJXDJH L LV VDLG WR EH FRQWH[WIUHH LI WKHUH LV D FRQWH[WIUHH JUDPPDU G VXFK WKDW L = L(G) G

/HW G = hV, Σ, S , Pi EH D FRQWH[WIUHH JUDPPDU &RQVLGHU WKH UHODWLRQ −→⊆ V × (V ∪ Σ)∗  E\ GHILQLWLRQ LW LV UHIOH[LYH DQG WUDQVLWLYH VR LW QDWXUDOO\ LQGXFHV D FRPSRVLWLRQ RSHUDWLRQ 'HILQH C′ DV WKH FDWHJRU\ ZKRVH REMHFWV DUH WKH VWULQJV G

σ RQ WKH V ∪ Σ DOSKDEHW VXFK WKDW S −→ σ DQG ZKRVH DUURZV DUH H[DFWO\ WKH G

LQVWDQFHV RI WKH −→ UHODWLRQ 1RZ GHILQH C DV WKH FDWHJRU\ C′ ⊔ 1 ZKHUH ⊔ LV WKH FRSURGXFW RI FDWHJRULHV DQG 1 KDV RQO\ RQH REMHFW ǫ  ZLWK LWV LGHQWLW\ DV WKH XQLTXH DUURZ /H G EH WKH GLVFUHWH SDUWLWLRQ RI Obj C ZKRVH FODVVHV DUH {c} IRU HYHU\ RE MHFW c 2EYLRXVO\ G LV LQGH[HG E\ Obj C )L[LQJ DV C DOO WKH LQVWDQFHV RI WKH G

−→ UHODWLRQ RQH REWDLQV LQ D WULYLDO ZD\ WKDW G = hC, G, {ǫ}, Ci LV D JUDPPDU FDWHJRU\  ZKRVH DWRPV DUH {S , ǫ}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¶V KLHUDUFK\  0RUHRYHU WKH UHDGHU LV LQYLWHG WR QRWLFH KRZ WKLV FKDUDFWHULVDWLRQ UHODWHV WR WKH GLVFXVVLRQ RQ ³FRUUHFW´ DGWUHHV DQG UHGXQGDQF\ WUDQVIRUPDWLRQV LQ IDFW ZH FDQ HTXLYDOHQWO\ VD\ WKDW L(G) LV LVRPRUSKLF WR WKH VHW RI QRQHPSW\ DGWUHHV LQ G ZKLFK DUH IL[HG SRLQWV ZLWK UHVSHFW WKH WUDQVIRUPDWLRQ PDSSLQJ HDFK DGWUHH GHQRWLQJ c ∈ Σ∗ ZKRVH JRYHUQRU LV S LQWR LWVHOI DQG HDFK RWKHU DGWUHH LQWR WKH HPSW\ DGWUHH 8QDPELJXRXV FRQWH[WIUHH ODQJXDJHV FDQ EH FKDUDFWHULVHG LQ D GLIIHUHQW DQG PRUH VSHFLILF ZD\ DV VSHFLDO HOHPHQWV LQ D JUDPPDU FDWHJRU\ )LUVWO\ VXSSRVH Λ WKH HPSW\ VWULQJ RI WHUPLQDO V\PEROV LV QRW LQ L(G) ZKHUH G = hV, Σ, S , Pi LV VRPH XQDPELJXRXV FRQWH[WIUHH JUDPPDU

7KH )RUPDO 0RGHO



$ VWDQGDUG UHVXOW VWDWHV WKDW LI G = hV, Σ, S , Pi LV D FRQWH[WIUHH JUDPPDU WKHQ WKHUH LV DQRWKHU FRQWH[WIUHH JUDPPDU G′ = hV ′ , Σ, S , P′ i VXFK WKDW L(G) = L(G′ ) DQG G′ LV LQ &KRPVN\ QRUPDO IRUP LH HYHU\ SURGXFWLRQ LQ p′ LV HLWKHU RI WKH IRUP A → B · C ZLWK B, C ∈ V ′  RU RI WKH IRUP A → a ZLWK a ∈ Σ 'HILQH C∗ DV WKH FDWHJRU\ KDYLQJ DV REMHFWV WKH VWULQJV RQ Σ∗ DQG DV DUURZV WKH GHULYDWLRQ UXOHV GHILQHG DV IROORZV DORQJ ZLWK FRQVWUXFWLRQV DQG JUDPPDU FKDUDFWHUV ‡ LI (A → a) ∈ P′ WKHQ a ∈ G A  ‡ LI (A → B · D) ∈ P′ DQG b ∈ G B  d ∈ G D  WKHQ b · d ∈ G A  PRUHRYHU WKH DUURZV b → b · d DQG d → b · d DUH LQ C∗  )LQDOO\ WKHVH DUURZV DUH LQVWDQFHV RI WKH REYLRXV FRQVWUXFWLRQV RYHU WKH SURGXFWV hG D , (ǫ)i IURP G B  DQG RYHU hG B , (ǫ)i IURP G D  UHVSHFWLYHO\ 7KHVH FRQVWUXFWLRQ DUH LQ WKH VHW C RI FRQVWUXFWLRQV :H REVHUYH WKDW WKH ODWWHU FRQVWUXFWLRQ LV WKH FRQMXJDWH RI WKH IRUPHU RQH 1RZ FDOO C WKH IXOO VXEFDWHJRU\ RI C∗ ZKRVH REMHFWV DUH LQ (YLGHQWO\ * + [ C, {ǫ} ∪ Gv , {ǫ}, C

S

v∈V ′


Gv ∪ {ǫ}

v∈V ′

LV D JUDPPDU FDWHJRU\ DQG L(G) = L(G′ ) = GS  ,Q D WULYLDO ZD\ WKH FRUUHFW DGWUHHV DUH GHILQHG DV WKH QRQHPSW\ IL[HG SRLQWV RI WKH WUDQVIRUPDWLRQ ZKLFK PDSV HYHU\ DGWUHH GHQRWLQJ DQ REMHFW LQ GS LQWR LWVHOI DQG DQ\ RWKHU DGWUHH LQWR WKH HPSW\ RQH ,W LV LQWHUHVWLQJ WR QRWLFH WKDW WKH DGWUHHV LQ WKLV JUDPPDU FDWHJRU\ ZKHQ RQO\ FRQMXJDWH FRQVWUXFWLRQV DUH DOORZHG DUH H[DFWO\ WKH XVXDO GHULYDWLRQ WUHHV LQ WKH &KRPVN\ WUDGLWLRQ

Notes

&KDSWHU  

$V WKH UHDGHU ZLOO VHH WKURXJKRXW WKH ERRN RXU PRUSKRV\QWDFWLF IUDPHZRUN KDV LPSRUWDQW FRQVHTXHQFHV LQ VHPDQWLFV DQG HYHQ PRUH DW D SUDJPDWLF OHYHO 3KRQRORJ\ LV QRW FRQVLGHUHG KHUH GLVWLQFWLYHO\ H[FHSW ZKHQ LW LV D YHKLFOH RI SUDJPDWLF SXUSRVHV 

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µV\QWDFWLFL]DWLRQ¶ UDWKHU WKDQ JUDPPDWLFDOL]DWLRQ :H EHOLHYH WKDW V\QWDFWLFL]DWLRQ LV QRW D JRRG WHUP DV PRUSKRORJ\ LV DOVR LQYROYHG²QRW WR PHQWLRQ SKRQRWDFWLF SKHQRPHQD 

$Q DQDO\VLV RI VLPLODULWLHV DQG GLIIHUHQFHV RI WKH SLRQHHUV RI WKH &RJQLWLYH 5HYROXWLRQ FDQ EH IRXQG LQ $OOHQ +DUULV  LQ .LEEHH   ZKR TXRWHG 7KDJDUG  LQ 'HUU\ HW DO    (YHQ )LOOPRUH¶V )UDPH 6HPDQWLFV²ZKLFK LV WKH PRVW GHYHORSHG JUDPPDU IRUPDOL VDWLRQ ZLWKLQ WKH FRJQLWLYH OLQJXLVWLFV DSSURDFK²ODUJHO\ QHJOHFWV PRUSKRV\QWDFWLF IDFWV )RU DQ DFFRXQW VHH DW OHDVW )LOOPRUH  LQ *HHUDHUWV HW DO   

$ QRWDEOH H[FHSWLRQ LV /DQJDFNHU  LQ 'RQGHOLQJHU HW DO   ZKLFK HQOLJKW HQV KRZ PXFK 7qVQLHUH¶V 6WUXFWXUDO 6\QWD[ LV FRPSDWLEOH ZLWKLQ WKH FRJQLWLYH JUDPPDU WHQHW 

:H DUH LQ GHEW ZLWK WKDW ZRUN DQG WKH SHUVRQ WKDW H[SODLQHG 7qVQLHUH¶V LGHDV WR XV WKDW LV )DEUL]LR $ 3HQQDFFKLHWWL ZKR EDVHG KLV V\QWDFWLF DQDO\VLV RI SUHSRVLWLRQDO V\V WHPV RQ &HFFDWR  DQG %U¡QGDO   EHVLGHV 7HVQLqUH  FODVVLF ZRUN 3HQ QDFFKLHWWL KDV ZRUNHG RQ SUHSRVLWLRQV LQ D XQLTXH DQG RULJLQDO ZD\ IRU PRUH WKDQ WKUHH GHFDGHV²DQG VWLOO FRQWLQXHV 7KH PRVW FRPSOHWH DWWHPSW WR IRUPDOLVH KLV SUHSRVLWLRQDO V\VWHPV LV SUHVHQW LQ *REER   KRZHYHU KLV WD[RQRP\ DW ODVW UHOLHV LQ KLV OLQJXLVWLF LQWXLWLRQ DQG KHQFH LW FDQQRW EH IXOO\ IRUPDOLVHG 0RVW RI WKH ZRUNV SXEOLVKHG E\ 3HQ QDFFKLHWWL DUH LQ ODQJXDJHV RWKHU WKDQ (QJOLVK $Q H[FHSWLRQ LV 3HQQDFFKLHWWL  LQ 6KDPXHO   DQ DSSOLFDWLRQ RI KLV PRGHO WR &ODVVLF 6\ULDF DQG 6XUHWK ZKHUH UHDGHUV



1RWHV

FDQ EH LQWURGXFHG WR WKH JHQHUDO PRGHO DV ZHOO $Q XSWRGDWH YHUVLRQ IXOO\ DSSOLHG WR ,WDO LDQ SUHSRVLWLRQV FDQ EH IRXQG LQ 3HQQDFFKLHWWL   ZKLOH WKH HDUO\ V\VWHP²TXLWH GLI IHUHQW EXW E\ QR PHDQV ZLWKRXW LQWHUHVW²ZDV DSSOLHG WR (VSHUDQWR EDFN LQ 3HQQDFFKLHWWL   7KHUH DUH IHZ DFWXDO DSSOLFDWLRQV RI 3HQQDFFKLHWWL¶V SHUVSHFWLYH RQ SUHSRVLWLRQV 7RVFR  LQ %RUERQH HW DO  DSSOLHG LW²ZLWK VRPH DGDSWDWLRQ²WR *DZZDGD )RU D SUHVHQWDWLRQ RI WKH PDLQ UHVXOWV LQ WHUPV RI IRUPDOLVDWLRQ LQ (QJOLVK ,WDOLDQ DQG (VSHUDQWR VHH *REER   

3KRQHWLFV DQG SKRQRORJ\ DUH FORVHO\ UHODWHG WR WKH QDWXUDO ODQJXDJH WKH\ EHORQJ WR VR WKHLU WUHDWPHQW LV OHIW DV D IXUWKHU ZRUN  7KH XQDFFXVDWLYH K\SRWKHVLV ZDV IXOO\ GHYHORSHG E\ 3HUOPXWWHU DQG 3RVWDO  LQ 3HUOPXWWHU DQG 5RVHQ   :KLOH WKH GLVWLQFWLRQ EHWZHHQ XQDFFXVDWLYH DQG XQHUJD WLYH YHUEV ZDV HQOLJKWHQLQJ IRU XV WKH 8QLYHUVDO $OLJQPHQW +\SRWKHVLV ZDV FRQWURYHU VLDO VLQFH DW OHDVW ²VHH HJ *ROGEHUJ   7KH UHILQHPHQW RI WKH 8QLYHUVDO $OLJQPHQW +\SRWKHVLV LQ D &KRPVN\DQ SHUVSHFWLYH LH WKH 8QLYHUVDO 7KHWD $VVLJQPHQW +\SRWKHVLV 87$+  ZDV SXW LQ GLVFXVVLRQ HYHQ DPRQJ &KRPVN\DQ OLQJXLVWV ZKR GR QRW DJUHH DERXW LWV IRUPXODWLRQ DQG FRQVHTXHQFHV²VHH DW OHDVW %DNHU  LQ +DHJH PDQ  ±  2Q WKH RWKHU KDQG WKH JUDSKV SURSRVHG LQ WKH 5HODWLRQDO *UDPPDU VHHP WR EH XQILW WR EH SURSHUO\ IRUPDOLVHG 0RUHRYHU WKH WKHRU\ HYHQWXDOO\ EULQJV WR $UF 3DLU *UDPPDU ZKLFK LV ³H[WUHPHO\ KHDY\ JRLQJ ODUJHO\ EHFDXVH RI LWV GLIILFXOWWRUHDG UHODWLRQDO QHWZRUNV DQG EL]DUUH WHUPLQRORJ\´ %ODNH    

,Q WKLV UHVSHFW LW LV ZRUWK PHQWLRQLQJ WKH QRWLRQ RI JUDPPDU SURGXFW DV GHYHORSHG LQ $SSHQGL[ % ZKLFK LV WKH IRUPDO FRXQWHUSDUW RI VHPDQWLF UROHV LQ RXU IRUPDO PRGHO 

6HH &URIW  IRU DQ H[WHQVLYH WUHDWPHQW RI WKLV SDUWLFXODU FDVH DQG &KDSWHU  IRU WKH QRWLRQ RI VHPHPH 

)RU D VXUYH\ RI WKH OLWHUDWXUH LQ 7\SH /RJLF *UDPPDU VHH 0RUULOO  

 :KHQ D VSHFLILF ODQJXDJH LV IL[HG WKHQ RXU PRGHO SURYLGHV D ZD\ WR HQFRGH LW LQ ORJLFDO WHUPV DV GRQH IRU (VSHUDQWR LQ *REER   ZKLFK ZDV FKRVHQ DV D VSHFLDO FDVH EHLQJ ERWK D OLYLQJ DQG D SODQQHG ODQJXDJH VKRZLQJ KLJK GHJUHH RI UHJXODULW\ DQG D ORZ GHJUHH RI JUDPPDWLFDOL]DWLRQ DQG KHQFH RI LGLRPDWLF H[SUHVVLRQV²ZKLFK GR H[LVW LQGHHG DV VKRZQ LQ WKH ERRNV DERXW SKUDVHRORJ\ E\ )LHGOHU     7HFKQLFDOO\ WKH DGWUHH RQ WKH OHIW RI )LJXUH  LV REWDLQHG E\ DSSO\LQJ D FRQMX JDWH FRQVWUXFWLRQ VHH $SSHQGL[ % :H FKRVH WKLV UHSUHVHQWDWLRQ LQVWHDG RI WKH FDQRQLFDO FRQVWUXFWLRQ WR HPSKDVLVH WKH V\PPHWU\ EHWZHHQ WKH WZR SRVVLEOH FRQVWUXFWLRQV 

&RUUHFWQHVV LQ WKH FDVH RI DGSRVLWLRQDO WUHHV LV VOLJKWO\ PRUH FRPSOH[ WR FKHFN LQ IDFW LW LV SRVVLEOH DQG FRQYHQLHQW WR DOORZ WKH IRUPDWLRQ RI LQFRUUHFW DGWUHHV DV IDU DV ZH FDQ GLVFULPLQDWH WKH FRUUHFW RQHV LQ D IRUPDO ZD\ :H ZLOO WUHDW WKLV DVSHFW XVLQJ WKH VRFDOOHG UHGXQGDQF\ WUDQVIRUPDWLRQV

1RWHV





8QIRUWXQDWHO\ WKH ZRUG FDWHJRU\ KDV D GRXEOH WHFKQLFDO PHDQLQJ LQ 0DWKHPDWLFV LW LV DQ DOJHEUDLF VWUXFWXUH ZKHUHDV LQ FRPSXWDWLRQDO OLQJXLVWLFV LW UHIHUV WR D FODVV RI V\QWDFWLFDOO\ GHFRUDWHG H[SUHVVLRQV ,Q WKH ILUVW FDVH ZH ZLOO VSHDN RI PDWKHPDWLFDO FDW HJRULHV ZKLOH ZH XVH WKH WHUP OLQJXLVWLF FDWHJRULHV IRU WKH VHFRQG XVDJH :H ZLOO RPLW WKH VSHFLILFDWLRQ ZKHQ LW LV FOHDU IURP WKH FRQWH[W 

:H PDNH D VOLJKW GHYLDWLRQ IURP WKH VWDQGDUG SUDFWLFH RI &DWHJRU\ 7KHRU\ ZKHUH FRQ VWUXFWLRQV DUH LGHQWLILHG ZLWK DUURZV DQG DUURZV KDYH XQLTXH VWDUWLQJ DQG HQGLQJ SRLQWV ,QVWHDG ZH XVH WKH ZRUG µFRQVWUXFWLRQV¶ IRU GLVWLQJXLVKHG DQG XQLIRUP FODVVHV RI DUURZV IROORZLQJ WKH QDWXUDO XVDJH LQ OLQJXLVWLFV  ,Q $SSHQGL[ % ZH ZLOO VNHWFK DQ HYHQ GHHSHU DQG E\ IDU PRUH LQWHUHVWLQJ WRSRV WKHRUHWLF LQWHUSUHWDWLRQ RI RXU IRUPDO PRGHO 

,Q WKLV FRQWH[W WKH ZRUG µFDWHJRU\¶ LV XVXDOO\ XQGHUVWRRG DV OLQJXLVWLF FDWHJRU\ %XW LQ PRVW IRUPDOLVPV OLQJXLVWLF FDWHJRULHV DUH QRWKLQJ HOVH WKDW WKH REMHFW RI D PDWKHPDWLFDO FDWHJRU\ 7KLV IROORZV IURP WKH IDFW WKDW WKH PRGHOV RI λFDOFXOXV DUH &DUWHVLDQ FORVHG FDWHJRULHV VHH /DPEHN DQG 6FRWW   DQG WKDW PRVW IRUPDOLVPV FDQ EH LQWHUSUHWHG DV LQVWDQFHV RI VRPH W\SHG λFDOFXOXV 

,Q IDFW WKLV LV DQ LQVWDQFH RI RQH RI WKH PRVW FRPSHOOLQJ RSHQ SUREOHPV LQ 0DWKH PDWLFV DQG &RPSXWHU 6FLHQFH WKH 3 YV 13 TXHVWLRQ VHH *DUH\ DQG -RKQVRQ  

&KDSWHU  

:H ZLOO H[SODLQ LQ &KDSWHU  RXU WUHDWPHQW RI ZRUGV LQ WHUPV RI PRUSKRORJ\ %\ WKH PRPHQW ZH FRQVLGHU ZRUGV DV LQGLYLVLEOH XQLWV IRU WKH UHDGHU¶V VDNH  1RWH WKDW XQOLNH WKH FRPPRQ XVDJH ZH XVH PLQLPDO SDLUV DW DQ\ OLQJXLVWLF OHYHO QRW RQO\ SKRQRORJ\ 

7KH UHDGHU VKRXOG QRWLFH WKDW WKH VFHQH GRHV QRW FKDQJH DOWKRXJK D VLPSOLILHG H[ SUHVVLRQ LV XVHG WR GHVFULEH LW 6R DOWKRXJK µJRRG VROG KHUH¶ PD\ EH D YDOLG (QJOLVK H[SUHVVLRQ²DV µJRRG¶ LV DOVR D QRXQ²LW GRHV QRW GHVFULEH WKH VDPH VFHQH VR LW LV LQ YDOLG 

+HUH ZH DVVXPH WKH VLPSOLILHG YLHZ WKDW HYHU\ IRUPDO FRQVWUXFWLRQ LV XQLTXHO\ GHILQHG E\ LWV JUDPPDU SURGXFW VHH $SSHQGL[ % IRU WKH GHWDLOV ,Q JHQHUDO RQH VKRXOG VD\ WKDW WKH GHSHQGHQW VHOHFWV WKH VSHFLILF DUURZ DPRQJ WKH FRQVWUXFWLRQ RYHU VRPH SURGXFW IURP WKH JRYHUQRU 

,Q WKH IRUPDO WHUPV GHVFULEHG LQ &KDSWHU  RQH PD\ WKLQN WKDW WKHUH LV D µUXOH LQ WKH JUDPPDU¶ ZKLFK VHQGV WKH gov DGWUHH LQWR WKH DGWUHH KDYLQJ gov DV ULJKWEUDQFK dep DV OHIW EUDQFK DQG adp DV URRW $OVR WKH FRPSOHWH DGWUHH EHORQJV WR WKH JUDPPDWLFDO FODVV gc JUDPPDWLFDO FODVVHV DUH XVHG WR FRQWURO WKH FRQVWUXFWLRQ RI DGWUHHV



1RWHV



,W LV REYLRXV ZK\ WKH WULDQJOHV DUH XVHIXO ZLWKRXW WKHP D FRPSOHWHO\ H[SOLFLW DGWUHH RI D FRPSOH[ UHDOZRUOG FDVH FDQ HDVLO\ ILOO DOO WKH SDSHU EXW²HYHQ PRUH LPSRUWDQWO\²LW GRHV QRW KHOS WKH UHDGHU WR ILQG WKH DVSHFWV ZH DUH GHDOLQJ ZLWK LQ WKDW SDUWLFXODU PRPHQW  8VLQJ WKH WHUPLQRORJ\ LQWURGXFHG E\ /DQJDFNHU   WKH LQIRUPDWLRQ SURPLQHQFH LV ZKHUH WKH IRFXV RI DWWHQWLRQ LV SODFHG DQG LW LV FDOOHG WUDMHFWRU\ tr  ZKLOH WKH RWKHU HOHPHQW LV FDOOHG WKH ODQGPDUN lm  ,I VRPHWKLQJ HPHUJHV IURP WKH ODQGPDUN LW ZLOO EH D VHFRQGDU\ WUDMHFWRU\ VR WKDW WKLV DV\PPHWU\ FDQ EH DFWLYDWHG DJDLQ UHFXUVLYHO\ ,W LV ZRUWK QRWLFLQJ WKDW ZLWKLQ FRJQLWLYH OLQJXLVWLFV WKLV DV\PPHWU\ tr/lm LV XVHG WR GHILQH WKH VHPDQWLFV RI WKH FRQVWUXFWLRQ ZKLOH ZLWKLQ WKH DGSRVLWLRQDO SDUDGLJP WKLV DV\PPHWU\ LV XVHG WR FRQVWUXFW WKH DGWUHHV LH WKH V\QWD[ 7R DYRLG QDPH FODVKLQJ ZH FKRRVH WR DYRLG WKH XVH RI tr DQG lm KHUHE\ SUHIHUULQJ WR XVH LQVWHDG WKH H[SUHVVLRQV µLQIRUPDWLRQ SURPLQHQFH¶ µSURPLQHQFH¶ RU µSURPLQHQW¶ 

)RU D GLVFXVVLRQ RI KRZ WKH MRLQW DWWHQWLRQDO IUDPH ZRUNV DW D FRJQLWLYH OHYHO VHH LQ SDUWLFXODU 7RPDVHOOR    ,W LV ZRUWK QRWLFLQJ WKDW OLQJXLVWLF PHDQLQJ FDQQRW EH UHGXFHG WRXW FRXUW WR D IXOO\ FRPSRVLWLRQDO DQG FRPSXWDWLRQDO PRGHO 0HDQLQJ LQYROYHV QRW RQO\ WKH FRQVWUXDEOH LH WKH SURFHVV ZKHUHE\ FRQFHSWV DUH VWUXFWXUHG LQ D JLYHQ FRQVWUXFWLRQ EXW LW DOVR LQYROYHV WKH FRQWHQW HYRNHG ZKLFK LV HQF\FORS 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qUH   7KH WKHRUHWLFDO DVVXPSWLRQ EH KLQG DOO GHSHQGHQF\EDVHG PRGHOV LV WKDW ³WKH V\QWDFWLF VWUXFWXUH RI VHQWHQFHV UHVLGHV LQ ELQDU\ DV\PPHWULFDO UHODWLRQV KROGLQJ EHWZHHQ OH[LFDO HOHPHQWV´ 1LYUH    8QIRUWXQDWHO\ WKHUH LV QR DJUHHPHQW DPRQJ VFKRODUV DERXW WKH XVH RI WKH QRWLRQ RI GH SHQGHQF\ )RU H[DPSOH LQ 7RSRORJLFDO 'HSHQGHQF\ *UDPPDU 7'*  SURSRVHG E\ 'H EXVPDQQ   WKHUH DUH WZR GLIIHUHQW IRUPV RI GHSHQGHQFLHV FDOOHG µV\QWDFWLF GHSHQ GHQF\ WUHH ,' WUHH ¶ DQG µWRSRORJLFDO GHSHQGHQF\ WUHH /3 WUHH ¶ 0HO¶þXN DQG 3ROJXqUH  SRVWXODWHV WKUHH W\SHV RI V\QWDJPDWLF GHSHQGHQF\ UHODWLRQV QDPHO\ VHPDQWLF GH SHQGHQF\ V\QWDFWLF GHSHQGHQF\ DQG PRUSKRORJLFDO GHSHQGHQF\ 7KH RQO\ IHDWXUH WKDW

1RWHV



HYHU\ GHSHQGHQF\EDVHG PRGHO VKDUHV LV WKDW WKHUH LV QR DEVWUDFW LQWHUPHGLDWH QRGH VXFK DV V P 9HUEDO 3KUDVH  WR FRQVWLWXWH WKH ILQDO SKUDVH XQOLNH DOO &KRPVN\DQEDVHG JUDP PDUV ,Q WKLV VHQVH WKH DGSRVLWLRQDO SDUDGLJP LV VLPLODU WR GHSHQGHQF\ JUDPPDUV +RZ HYHU LQ DOO WKHVH PRGHOV SUHSRVLWLRQV DUH WUHDWHG DV PRGLILHUV RI QRXQV LH QRXQV DUH JRYHUQRUV SUHSRVLWLRQV DUH GHSHQGHQWV H[DFWO\ DV LI SUHSRVLWLRQV ZHUH DGMHFWLYHV²LQ RXU SHUVSHFWLYH D IDWDO HUURU 7KHUHIRUH ZH FRQVLGHU GHSHQGHQF\ LQ D GLIIHUHQW ZD\ LQVLGH FRQVWUXFWLYH DGSRVLWLRQDO JUDPPDUV ,W LV ZRUWK QRWLFLQJ WKDW 7HVQLqUH  QHYHU FRQ VLGHUHG KLV JUDPPDU EDVHG RQ WKH QRWLRQ RI GHSHQGHQF\ SUHIHUULQJ UDWKHU WKH PRUH JHQ HUDO WHUP FRQQH[LRQ µFRQQHFWLRQ¶ LQ )UHQFK  ,Q IDFW KH DOZD\V FDOOHG KLV RZQ PRGHO µVWUXFWXUDO V\QWD[¶ 

,Q WKH IRUPDO PRGHO GHSLFWHG LQ $SSHQGL[ % ZH ZLOO UHVHUYH WKH WHUP µYDOHQF\¶ IRU WKH YHUEDO FRQVWUXFWLRQV LQVWHDG ZH ZLOO XVH WKH PRUH JHQHUDO FRQFHSW RI JUDPPDU SURGXFW WR UHSUHVHQW WKH VWUXFWXUH RI DFWDQWV 

2QH FRXOG LQGHHG FRPSDUH WKH YHUE WR D NLQG RI FURVVHG DWRP ZKLFK FDQ DWWUDFW D QXPEHU PRUH RU OHVV KLJK RI DFWDQWV LQ SURSRUWLRQ WR WKH QXPEHU PRUH RU OHVV KLJK RI KRRNV QHHGHG WR PDLQWDLQ WKH UHVSHFWLYH GHSHQGHQFLHV RXU WUDQVODWLRQ   3OHDVH QRWH WKDW LQ FRJQLWLYH OLQJXLVWLFV WKH WHUP µYDOHQF\¶ LV XVHG LQ D GLIIHUHQW ZD\²VHH WKH JORVVDU\ LQ 7D\ORU  IRU WKDW 

3OHDVH QRWH WKDW ZH DUH QRW VSHDNLQJ DERXW µLQWUDQVLWLYH¶ RU µWUDQVLWLYH¶ YHUEV EXW LQVWHDG RI µPRQRYDOHQW¶ RU µELYDOHQW¶ YHUEV 8QIRUWXQDWHO\ WKH WUDGLWLRQDO DFFRXQW RI YDOHQF\ GLG QRW OHDUQ WKH PDLQ OHVVRQ IURP OLQJXLVWLF W\SRORJ\ LH WKDW WKH WUDGLWLRQDO GLFKRWRP\ µVXEMHFWREMHFW¶ LV WRR SRRU WR JLYH DQ DFFRXQW RI QRPLQDWLYHDFFXVDWLYH YV HUJDWLYHDEVROXWLYH YHUE FODVVHV 'L[RQ    7KH ZRUGLQJ µSDVVLYHO\¶ LV WHQWDWLYH D PRUH SUHFLVH DFFRXQW RI WKLV GLIIHUHQFH ZLOO EH FOHDU WKURXJKRXW WKH QH[W WZR FKDSWHUV 

7KH FRQVWUXFWLRQ Y VROG LV D GHULYHG RQH IURP X VHOO Y WR Z IRU W ZKHUH DOO DFWDQWV VDYH WKH Sold Objective Y DUH KLGGHQ  3OHDVH QRWH WKDW RXU WUHDWPHQW RI WKH H[DPSOH LV GLIIHUHQW LQ PDQ\ DVSHFWV )LOOPRUH E FROOHFWV KLV FODVVLF SDSHUV RQ VHPDQWLF UROHV ZULWWHQ EHWZHHQ  DQG  ,Q WKH VHTXHO ZH ZLOO UHIHU WR WKHVH SDSHUV LQ WKLV FROOHFWLRQ IRU WKH UHDGHU¶V VDNH  7KH UHDGHU VKRXOG QRWLFH WKDW H[DPSOHV KM FDQ EH ZHOOIRUPHG SKUDVHV EXW WKH SRLQW LV WKDW WKH\ FDUU\ D GLIIHUHQW PHDQLQJ WKDQ J  GHVFULELQJ D GLVWLQFW VFHQH 

)RU H[DPSOH &URIW  VKRZV KRZ WKH Eat IUDPH GLIIHUV LQ (QJOLVK DQG LQ *HUPDQ ZKHUH LQ WKH ODWWHU WKHUH LV D GLVWLQFWLRQ EHWZHHQ A-Eat IRU DQLPDOV IUHVVHQ DQG H-Eat IRU KXPDQV HVVHQ ZKLFK LQ (QJOLVK LV GHILQHG RWKHUZLVH 6HPDQWLF IUDPHV DQG WKH DQDO\VLV RI FRQVWUXFWLRQV FDQ EH IUXLWIXOO\ SXW LQWR UHODWLRQ LQ WKLV ERRN WKH IRFXV UHPDLQV WKH FRQVWUXFWLRQV ZKLOH WKH VHPDQWLF IUDPHV DUH SXW LQWR WKH EDFNJURXQG





1RWHV

:H ZLOO FRPH EDFN RQ WKLV FUXFLDO SRLQW LQ WKH QH[W FKDSWHUV



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

)RU DQ DQDO\VLV RI WKH FRQVWUXFWLRQ RI (QJOLVK GDWLYH DOWHUQDWLRQ VHH DW OHDVW *ROGEHUJ   'DWLYH DOWHUQDWLRQ LQ 'XWFK LV H[SODLQHG LQ FRPSDULVRQ DQG FRQWUDVW WR (QJOLVK LQ &KDSWHU  RI YDQ GHU %HHN   ZKLOH $EUHX *RPHV  H[SORUHV %UD]LOLDQ 3RU WXJXHVH ZLWK D UHIHUHQFH WR 7VXQJD IRU FRPSDULVRQ :H GR QRW SXUVXH D FRPSUHKHQVLYH WUHDWPHQW RI WKH SKHQRPHQRQ RI GDWLYH DOWHUQDWLRQ²WKDW ZRXOG RFFXS\ DW OHDVW D IXOO FKDS WHU GHGLFDWHG WR LW²EXW UDWKHU KRZ WUDQVIRUPDWLRQ ZRUNV LQ UHDOFDVH FRQVWUXFWLRQV 

,Q IDFW SURQRXQV EHLQJ RQO\ SODFHKROGHUV IRU QRXQV DUH XVXDOO\ QRW SURPLQHQW DV WKH VSHDNHU¶V QRQORFXWLRQDU\ DVVXPSWLRQ LV WKDW WKH OLVWHQHU NQRZV ZKR RU ZKDW WKH SURQRXQ LV UHIHUULQJ WR 

7HFKQLFDOO\ WKH DGWUHH RQ WKH ULJKW RI )LJXUH  LV D FRQMXJDWH FRQVWUXFWLRQ RI WKH RQH RQ WKH OHIW ZKHUH WKH VHFRQG DFWDQW LV H[FKDQJHG ZLWK WKH ILUVW RQH )RUPDOO\ WKH WZR WUHHV DUH HTXLYDOHQW H[FHSW IRU WKH GLIIHUHQW FRQWHQW RI WKH VHFRQG DFWDQW EXW WKH UHSUHVHQWDWLRQ SURYLGHV DQ DFFRXQW IRU HPSKDVLV DQG FROORFDWLRQ RQ WKH V\QWDJPDWLF D[LV VHH $SSHQGL[ % IRU WKH GHWDLOV 

1RWLFH KRZ D FRQMXJDWH FRQVWUXFWLRQ KDV EHHQ XVHG H[FKDQJLQJ WKH VHFRQG DQG WKH WKLUG DFWDQWV WR UHSUHVHQW WKH GLIIHUHQW FROORFDWLRQV RI PRUSKHPHV RQ WKH V\QWDJPDWLF D[LV 7KLV KROGV DOVR LQ ([DPSOH  

&KDSWHU  

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µFODVV¶ LQ D QDLYH VHQVH LH HTXLYDOHQW WR D ODEHOOHG VHW DOVR µVHW¶ LQ D QDLYH VHQVH  ZKLOH WKH WHUP µFDWHJRU\¶ ZLOO EH PRVWO\ XVHG LQ D PDWKHPDWLFDO VWURQJ VHQVH 6RPHWLPHV WKH WHUP µFDWHJRU\¶ ZLOO EH XVHG OLQJXLVWLFDOO\ LH HTXLYDOHQW WR

1RWHV



D GHILQLWH SUHGHWHUPLQHG FODVV 7KH FRQWH[W ZLOO FODULI\ ZKLFK VHQVH LV LQWHQGHG LI QRW WKH UHDGHU ZLOO EH KHOSHG ZLWK D SURSHU VSHFLILFDWLRQ LQ RUGHU WR GLVDPELJXDWH 

0RUHRYHU WKHUH LV DQ DGGLWLRQDO SUREOHP LQ XVLQJ WUDGLWLRQDO JUDPPDWLFDO FDWHJRULHV OLNH µQRXQ¶ µYHUE¶ µDGMHFWLYH¶ µDGYHUE¶ µSDVVLYH YRLFH¶ LH WKHVH FDWHJRULHV DUH XVXDOO\ FRQVLGHUHG µIL[HG LQWR WKH PRUSKHPH¶ EHFDXVH WKH\ GHULYHG IURP FODVVLFDO WUDGLWLRQ LH IURP DQFLHQW *UHHN DQG /DWLQ JUDPPDULDQV $V ZH ZLOO VHH LQ WKH VHTXHO ZH FRQVLGHU JUDPPDU FDWHJRULHV DV IXQFWLRQV RI JUDPPDU FKDUDFWHUV LQVWDQWLDWHG LQWR PRUSKHPHV 

$V IDU DV ZH NQRZ EHVLGHV *REER   RQO\ 0LQHU  XVHV :KRUI  



7KH WHUP µVWDWLYH¶ LV GHULYHG IURP µVWDWLYDWLRQ¶ DV XVHG E\ :KRUI   ZKLOH µYHU EDQW¶ LV D WHUP LQWURGXFHG LQ WKH VHQVH ZH XVH KHUH E\ +DJqJH    :H UHWDLQ WKH OLQJXLVWLF XVH RI WKH WHUP DV WKH GHIDXOW PHDQLQJ ZKLOH ZH ZLOO XVH WKH WHUP DGMXQFWLRQ LQ WKH WHFKQLFDO PDWKHPDWLFDO VHQVH 7KH FRQWH[W ZLOO KHOS WKH UHDGHU WR DYRLG DPELJXLW\ LI QRW ZH ZLOO H[SOLFLW LWV XVH 

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±  

%ODNH  VSHDNV RI µGHWUDQVLWLYLW\¶ DERXW WKH YDOHQF\ UHGXFWLRQ :H SUHIHU QRW WR XVH WKH WHUP µWUDQVLWLYLW\¶ DV LW FRYHUV WRR PDQ\ FDVHV RI LQIRUPDWLRQ SURPLQHQFH SUHIHU ULQJ WR XVH WKH H[SUHVVLRQV µYDOHQF\ GHFUHDVH¶ RU µYDOHQF\ LQFUHDVH¶  7KH WUDQVIRUPDWLRQ RI WKH JUDPPDU FKDUDFWHU I > A > Y LQ )LJXUH  UHIHUV WR WKH LQWHUQDO VWUXFWXUH RI WKH ZRUG µVXGDWR¶  2I FRXUVH KRORSKUDVHV  PRQWKV  ZKLFK KDYH RQO\ RQH HOHPHQW DUH UHDOO\ SUH PRUSKRV\QWDFWLF DV H[SODLQHG E\ 7RPDVHOOR   

(QJOLVK H[DPSOHV DUH UHSRUWHG LQ 7RPDVHOOR ZKLOH WKH ,WDOLDQ RQHV DUH WUDQVFULSWLRQV RI /HRQDUGR¶V VSHHFK  PRQWKV  )HGHULFR *REER¶V VRQ  ,Q FRQVWUXFWLYH OLQJXLVWLFV WKH PHDQLQJ RI WKH SDUWV LV WKH GRPDLQ RI VHPDQWLFV ZKLOH WKH PHDQLQJLQXVH LH WKH VLJQLILFDQFH RI WKH ZKROH LV WKH GRPDLQ RI SUDJPDWLFV :H ZLOO FRPH DJDLQ RQ WKLV FUXFLDO GLVWLQFWLRQ



1RWHV



8QIRUWXQDWHO\ WUDGLWLRQDO JUDPPDULDQV RI /DWLQ LQWURGXFHG D YHU\ FRQIXVLQJ WHUPL QRORJ\ QDPHO\ µVXEMHFWLYH JHQLWLYH¶ WKH IDWKHU EHLQJ WKH VXEMHFW RI ORYH LH ZLWK GHSHQ GHQF\ DQG µREMHFWLYH JHQLWLYH¶ WKH IDWKHU EHLQJ WKH REMHFW RI ORYH LH ZLWK JRYHUQPHQW  2XU SURSRVDO EHLQJ DEVWUDFW DQG RI JHQHUDO YDOLGLW\ KDV WKH JUHDWHU DGYDQWDJH QRW WR EH ERXQG WR D SDUWLFXODU JUDPPDU WUDGLWLRQ 2XU JXLGHOLQH LV VLPSOH ZH UHWDLQ WKH HVWDEOLVKHG WHUPLQRORJ\ LI DQG RQO\ LI LW LV QRW DPELJXRXV LQ FRQVWUXFWLYH OLQJXLVWLF WHUPV RWKHUZLVH ZH LQWURGXFH QRYHO QRQDPELJXRXV WHUPV 

:H XVH WKH ZRUG µFODVV¶ LQ D UHOD[HG VHQVH PHDQLQJ D QDPHG VHW ZKLOH D OLQJXLVWLF FDWHJRU\ LV D GHILQHG FODVV VXFK DV µ(QJOLVK SHUVRQDO SURQRXQV¶ 2I FRXUVH D OLQJXLVWLF FDWHJRU\ KDV VHQVH RQO\ ZLWKLQ D SDUWLFXODU ODQJXDJH )RU LQVWDQFH LI ZH VSHDN DERXW SHUVRQDO SURQRXQV ZLWKLQ WKH 6WDQGDUG $YHUDJH (XURSHDQ 6SUDFKEXQG WKH REMHFW ZH DUH UHIHUULQJ WR LV DOZD\V D FODVV QRW D OLQJXLVWLF FDWHJRU\  7KH ZRUG µTXDQWLILHU¶ LV XVHG LQ WKH OLQJXLVWLF VHQVH QRQ WKH ORJLFDO RQH XQOHVV RWKHUZLVH VSHFLILHG 

7KHUH LV RIWHQ D PLVXQGHUVWDQGLQJ DERXW GHWHUPLQHUV WKLV FODVV RI ZRUGV KDYH JUHDW FRQVHTXHQFHV DW D SUDJPDWLF OHYHO SDUWLFLSDQW¶V EHOLHIV EHLQJ D FRQVLGHUDEOH SDUW RI SUDJ PDWLF LQIRUPDWLRQ  QRQHWKHOHVV WKH\ DUH RIWHQ DQDO\VHG DW D VHPDQWLF OHYHO :H FRQVLGHU WKDW WKH DQDO\VHV RI GHWHUPLQHUV DV VHPDQWLF ZRUGV IROORZ D ZURQJ SHUVSHFWLYH 

,Q WKH JUDPPDU WUDGLWLRQ RI *HUPDQ WKHUH LV HYHQ D PQHPRQLF WR PHPRULVH WKH PDLQ FLUFXPVWDQFHV WKH ZRUG WHNDPROR PHDQV 7HPSRUDO WHPSRUDO  .DXVDO FDXVDO  0RGDO PRGDO DQG /RNDWLY ORFDWLYH  

)URP D GLDFKURQLFDOO\ SRLQW RI YLHZ WKH )UHQFK VWDWLYH SD\VDJH LV D JUDPPDWLFDO L]DWLRQ RI SD\V DQG DJH ,Q WKLV ERRN ZH ZRQ¶W GHOYH LQ WKLV NLQG RI JUDPPDWLFDOL]DWLRQ SKHQRPHQD ZKLFK DUH OHIW DV D IXUWKHU ZRUN 

$OWKRXJK WKH IRUPDO PRGHO DOORZV IRU D PRUH JHQHUDO QRWLRQ RI WUDQVIRUPDWLRQ ZKLFK LV XVHIXO DQG ODUJHO\ HPSOR\HG LQ WKH WH[W WKH V\QWKHVLV RI FRPSOH[ FRQVWUXFWLRQV LV WKH SULQFLSDO PRWLYDWLRQ EHKLQG WKH LQWURGXFWLRQ RI WUDQVIRUPDWLRQV

&KDSWHU  

2Q WKH RWKHU KDQG VRPHWLPHV YHU\ GLVWDQW W\SRORJLFDO ODQJXDJHV FDQ VKDUH YHU\ VLP LODU WUDQVIRUPDWLRQ SDWWHUQV 7KH UHODWLRQ EHWZHHQ W\SRORJLFDO SUR[LPLW\ LQ HYHU\ SDLU RI ODQJXDJHV DQG WKHLU UHVSHFWLYH WUDQVIRUPDWLRQ SDWWHUQV IRU WKH VDPH SKHQRPHQRQ LV EH \RQG WKH VFRSH RI WKH SUHVHQW ERRN 

,W LV LPSRVVLEOH WR JLYH DQ H[KDXVWLYH FRYHUDJH RI PRUSKRORJ\ HYHQ ZLWKLQ D VLQ JOH ODQJXDJH ZKDW ZH DLP WR GR LQ WKLV ERRN LV WR H[SODLQ KRZ WR UHSUHVHQW ZLWKLQ WKH DGSRVLWLRQDO SDUDGLJP VRPH UHOHYDQW DQG ZHOO NQRZQ PRUSKRORJLF SKHQRPHQD LQ SDU WLFXODU JUDPPDU FKDUDFWHU FKDQJH REWDLQHG E\ GHULYDWLRQ²IRU H[DPSOH KRZ WKH (QJOLVK

1RWHV



DGMHFWLYH ZHOO LV WUDQVIRUPHG LQWR WKH DEVWUDFW QRXQ ZHOOQHVV 7KLV OHYHO RI DQDO\VLV ZLOO EH H[SODLQHG LQ &KDSWHU  

:H PHDQ ILQDO JRYHUQRUV DQG GHSHQGHQWV LH WKH RQHV QRW IXUWKHU H[SDQGDEOH ,Q SUDFWLFH OHDYHV ZLWKRXW WKH WULDQJOHV △  )RU WKHVH UHDVRQV LW VHHPV IHDVLEOH WR XVH WZR GLIIHUHQW V\PEROV WR VLJQ HPSW\ DGSRVLWLRQV ǫ DQG YRLG JRYHUQRUV DQG GHSHQGHQWV   

7KLV LV QRW D UHDO WUDQVIRUPDWLRQ EXW LW KHOSV WKH UHDGHU WR XQGHUVWDQG HYHU\ FRPSDFW QRWDWLRQ ZH XVH WKURXJKRXW WKH ERRN WKHUHIRUH ZH GHFLGHG WR H[SODLQ WKLV SRLQW KHUH  ,W LV TXLWH REYLRXV WKDW ERWK JRYHUQRU DQG GHSHQGHQW FDQQRW EH YRLG DW WKH VDPH WLPH LI VR WKH DGSRVLWLRQ LV QRW DQ DGSRVLWLRQ EXW RQO\ D OHDI DQG WKHUHIRUH LW VKRXOG EH FRQVLGHUHG DV D JRYHUQRU 

)URP D IRUPDO SRLQW RI YLHZ LQIRUPDWLRQ SURPLQHQFH LV RQO\ DQ DGWUHH GHFRUD WLRQ²VHH $SSHQGL[ % IRU GHWDLOV 

:H DGRSW WKH ODZ RI SDUVLPRQ\ 2FFDP¶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

)RU WKLV UHDVRQ FRQVWUXFWLRQV VXFK DV ZLOO EH RU VKDOO EH VKRXOG EH OLVWHG DV FRQVWUXF WLRQV RI ZLOO DQG VKDOO UHVSHFWLYHO\ 7KH LPSHUDWLYH FRQVWUXFWLRQV LQ FG DUH DFWLYH IRUPV RI WR EH  3UDJPDWLFDOO\ LQ D WKH PDLQ SRLQW LV WKDW /L]D LV TXLHW QRW WKDW LV D JLUO ,I ZH RPLW WKH DGMHFWLYH REWDLQLQJ /L]D LV D JLUO WKH LPPHGLDWH UHDFWLRQ LV VR ZKDW" 7KHUH LV VRPHWKLQJ ODFNLQJ H[DFWO\ WKH LQIRUPDWLRQ ZKRVH YHKLFOH LV WKH DGMHFWLYH  :H KDYH DOUHDG\ VHHQ DQ H[DPSOH RI WKLV IDFW LQ  ²VHH DJDLQ )LJXUH  ,Q IDFW LQ Ê OD URVVD GL 0DUDQHOOR WKH VWDWLYH LV WKH VHFRQG DFWDQW ZKLFK LV SURPLQHQW QRW WKH ILUVW RQH  :LWK µFRPSOH[ FRQVWUXFWLRQV¶ ZH PHDQ LQIRUPDOO\ FRQVWUXFWLRQV ZLWK PRUH WKDQ RQH YHUEDQW LH KDYLQJ RQO\ RQH JRYHUQRU ZLWK WKH JUDPPDU FKDUDFWHU I LQ FRQWUDVW ZLWK µVLPSOH FRQVWUXFWLRQV¶ ZKHUH RQO\ D YHUEDQW LV IRXQG



1RWHV

 ,I ZH KDYH D WULYDOHQW YHUE OLNH LQ 3DXO LV JLYLQJ OHVVRQV WR 0DU\ WKH DGWUHH KDYLQJ JLYH DV WKH JRYHUQRU ZRXOG EH OHQJWKHQHG DSSURSULDWHO\ IRU WKH WKLUG DFWDQW Zmean  7KLV DGWUHH LV OHIW WR WKH UHDGHU 

7KLV H[DPSOH LV SUREDEO\ WKH PRVW FRPSOH[ LQ WKH ZKROH ERRN WKLV KDSSHQV EH FDXVH LW LQWHUOHDYHV FRQVWUXFWLRQV DW WKH PRUSKRORJLFDO OHYHO ZLWK FRQVWUXFWLRQV RQ WKH OLQJXLVWLF OHYHO PL[LQJ WKHP WRJHWKHU WR FRQYH\ WKH LQWHQGHG PHDQLQJ ,Q IDFW JRLQJ WR LV XVXDOO\ FRQVLGHUHG D FRPSOHWHO\ JUDPPDWLFDOL]HG FRQVWUXFWLRQ FDOOHG WKH µSUHVHQW SUR JUHVVLYH WHQVH¶ RXU DQDO\VLV VKRZV WKDW LW LV QRW VSHFLDO EXW UDWKHU D FRPSOH[ LQVWDQFH RI WKH LQILQLWLYH WKH JHUXQG DQG WKH HVVH FRQVWUXFWLRQV  7KLV FRQVWUXFWLRQ LV DOVR IRXQG LQ ,WDOLDQ DV ZHOO 3DROR q SUHSDUDWR FRUUHVSRQGV WR H ERWK V\QWDFWLFDOO\ DQG VHPDQWLFDOO\ :H JXHVV WKDW H[DFWO\ WKH VDPH FRQVWUXFWLRQ FDQ EH IRXQG LQ D FRQVLVWHQW QXPEHU RI ODQJXDJHV EHORQJLQJ WR WKH 6WDQGDUG $YHUDJH (XURSHDQ 6SUDFKEXQG  7KHVH H[DPSOHV E\ +RUQ  DUH TXRWHG E\ %ODNH LQ KLV YROXPH ZKLFK VXP PDULVHV WKH PDLQ UHVXOWV RI WKH UHVHDUFK PDGH ZLWKLQ WKH 5HODWLRQDO *UDPPDU SDUDGLJP %ODNH  VHFWLRQ   +HUH WKH\ KDYH EHHQ DGDSWHG WR WKH DGSRVLWLRQDO SDUDGLJP :H KDYH FKRVHQ QRW WR JLYH SUHFLVH QDPHV WR WKHVH FODVVHV RI ELYDOHQW (QJOLVK YHUEV EH FDXVH HYHU\ SRVVLEOH QDPH ZH IRXQG FODVKHG ZLWK VRPH WUDGLWLRQ LQ (QJOLVK OLQJXLVWLFV DQG WKLV ERRN LV QRW IRFXVHG RQ WKH (QJOLVK DGSRVLWLRQDO JUDPPDU  7KH LGLRPDWLF H[SUHVVLRQ WKHUH RQFH ZDV D WLPH DOWKRXJK LW VHHPV D WKHUHFRQ VWUXFWLRQ LV UHDOO\ JRYHUQHG E\ RQFH LQ IDFW RQFH ZDV D WLPH LV D V\QRQ\P ZKLOH WKHUH ZDV D WLPH LV QRW 

,W LV SRVVLEOH WKDW HVVHFRQVWUXFWLRQV FDQ EH UHFRQGXFWHG WR WKLV FODVV LQGHHG FRPSDUH DE WR KH EHFDPH VRPHRQH PDGH DQG KH LV VRPHRQH PDG +RZHYHU WKLV OLQH RI UHDVRQLQJ LV OHIW DV D IXUWKHU ZRUN DV LW LV RXW RI WKH IRXQGDWLRQDO VFRSH RI WKLV YROXPH 

7KHUH LV D ODVW DUJXPHQWDWLRQ TXHVWLRQ SRVHG E\ &LFHUR FDOOHG IDFXOWDV ZKLFK DQ VZHUV WKH TXHVWLRQ ³ZKLFK LQVWUXPHQWV DUH \RX XVLQJ LQ \RXU DUJXPHQWDWLRQ"´ 7KLV ZDV RPLWWHG IRU EUHYLW\ EXW WKLV RPLVVLRQ GRHV QRW FKDQJH RXU OLQH RI UHDVRQLQJ  4XDGULYDOHQW YHUEV DUH UDUH LQ IDFW EHIRUH WKH FRQFHSW RI PRQH\ ODQJXDJHV GLG H[SUHVV FRPPHUFLDO WUDQVDFWLRQ ZLWKRXW Price XVLQJ YHUEV OLNH GRQDWH  $FWXDOO\ WKH VDPH SKUDVH PD\ EH UHSUHVHQWHG E\ D GLIIHUHQW DGWUHH WKDW XVHV WKH LQILQLWLYH FRQVWUXFWLRQ WR EXLOG WKH LQYDOHQW DFWDQWV 7KLV UHSUHVHQWDWLRQ LV FRUUHFW EXW LW GLVUHJDUGV WKH FDXVDWLYH VHPHPH ZKLFK LV SUHVHQW LQ WKH YHUEDQW JRYHUQLQJ WKH SKUDVH 2XU SRLQW KHUH LV WKDW WKHUH LV D SURSHU FRQVWUXFWLRQ WKDW WDNHV SODFH EHFDXVH RI WKH SUHVHQFH RI WKH FDXVDWLYH VHPHPH 7KH DOWHUQDWLYH FRQVWUXFWLRQ KDV D VOLJKWO\ GLIIHUHQW PHDQLQJ LQ WKDW LW GRHV QRW FRQYH\ WKH µIRUFLQJ¶ RI WKH GHSHQGHQW DFWLRQV E\ WKH JRYHUQRU

1RWHV



&KDSWHU   3KRQRORJ\ LV WKH PRVW ODQJXDJHERXQG OHYHO RI DQDO\VLV DQG WKHUHIRUH LW LV QRW FHQWUDO IRU WKH SXUSRVHV RI WKLV ERRN ZKLOH SUDJPDWLFV ZLOO EH DGGUHVVHG LQ WKH QH[W FKDSWHU 

:LWKLQ WKH FRJQLWLYH JUDPPDU DSSURDFK RQO\ :LHU]ELFND  GRHV QRW IROORZ WKH SDQHQF\FORS GLF DSSURDFK 

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 GLF NQRZOHGJH VLPSO\ ZH DUH GHHSO\ FRQYLQFHG WKDW ODQJXDJH VKRXOG EH GHVFULEHG SULPDULO\ ZLWKLQ LWV FRKHUHQFH DV D V\VWHP LQVWHDG RI JLYLQJ DFFRXQW RI WKH V\PERO JURXQGLQJ DQG D SDUWLFXODU ZRUOG PRGHO ZKLFK LV DOZD\V TXHVWLRQDEOH ,Q UHVSHFW WR ZRUOG PRGHOV ZH DUH DJQRVWLF 

)URP WKH SRLQW RI YLHZ RI D OH[LFDO VHPDQWLFLVW ZH IROORZ WKH WUDGLWLRQ RI PRQRVHPLF DQDO\VLV EHJXQ DW OHDVW IURP 'H 6DXVVXUH   $GKHUHQWV RI WKH SRO\VHPLF DQDO\VLV OLNH .DW] DQG )RGRU   SUHIHU WR WUHDW FDVHV OLNH µEDFKHORU¶ DV D FRQWLQXXP ZKHUH WKHUH LV D SURWRW\SLFDO DEVWUDFW PHDQLQJ OLNH µXQIXOILOOHG LQ W\SLFDO PDOH UROH¶²VHH .RU QDL   IRU GHWDLOV ,Q RXU SHUVSHFWLYH ZKHQ SHUIRUPLQJ KXPDQ RU PDFKLQH WUDQVODWLRQ VXFK D SHUVSHFWLYH ZRXOG IXUWKHU LQFUHDVH WKH DOUHDG\ FRPSOH[ SUREOHP RI WUDQVIHUULQJ VHPDQWLFV IURP RQH ODQJXDJH WR DQRWKHU 2Q WKH FRQWUDU\ IURP D PRQRVHPLF SHUVSHFWLYH WKH IDFW WKDW WKHVH PRUSKHPHV DUH GLVMRLQW JUHDWO\ VLPSOLILHV WKH WDVN )RU H[DPSOH LQ ,WDOLDQ EDFKHORU1 LV UHQGHUHG ZLWK FHOLEH ZKLOH EDFKHORU3 ZLWK GLSORPDWR 

7KH SUREOHP RI WKH FRUUHVSRQGHQFH RI VHPHPHV DQG WKHLU FRQILJXUDWLRQ ZLWKLQ PRU SKHPHV DQG FRQVWUXFWLRQV EHORQJLQJ WR GLIIHUHQW ODQJXDJHV HYHQ LI DQ LPSRUWDQW DQG FKDO OHQJLQJ SUREOHP LV EH\RQG WKH VFRSH RI WKH SUHVHQW ERRN 

$V WKH UHDGHU DIWHU WKH SUHYLRXV FKDSWHUV PD\ JXHVV DGSRVLWLRQV DUH WKH IXQGDPHQWDO FRQVWLWXHQW RI WKH IXQFWLRQDO ZRUGV %XW DOWKRXJK IXQFWLRQDO ZRUGV DUH DOZD\V UHODWHG WR DGSRVLWLRQV WKHUH DUH HOHPHQWV RI WKLV FODVV QRW EHORQJLQJ WR WKH VHW RI DGSRVLWLRQV HJ SURQRXQV RU FRUUHODWLYHV 

+HUH DQG LQ WKH IROORZLQJ ZH XVH WKH ZRUG µFRQVWUXFWLYH¶ LQ D JHQHUDO VHQVH QRW LQ WKH VWULFWO\ PDWKHPDWLFDO RQH $OVR WKH QRWLRQ RI µRSHQ VHW¶ LV XVHG LQ D OLQJXLVWLF FRQWH[W DQG VKRXOG QRW EH FRQIXVHG ZLWK WKH WHFKQLFDO PHDQLQJ RI PDWKHPDWLFDO RSHQ VHW ZKLFK UHIHUV WR WRSRORJ\ +HUH RSHQ VHW PHDQV D VHW WKDW LV QRW IL[HG DQG WKDW FDQ YDU\ LQ WLPH



1RWHV

 ,Q GHYHORSLQJ KLV µVWUXFWXUDO V\QWD[¶²XQIRUWXQDWHO\ VWLOO QRW DYDLODEOH LQ (QJOLVK 7HVQLqUH  GHYRWHV 3DUW  DSSUR[LPDWHO\  SDJHV HQWLUHO\ WR WUDQVIHUHQFH $ SDU WLDO WUDQVODWLRQ RI 7HVQLqUH  LV DYDLODEOH LQ ,WDOLDQ E\ 3URYHUELR DQG 7URFLQL &HUULQD   EXW QRW WKH RQH GHYRWHG WR WUDQVIHUHQFH 1R RWKHU WUDQVODWLRQV DUH DYDLODEOH LQ WKH OLWHUDWXUH WR RXU NQRZOHGJH :H ZRXOG DSSUHFLDWH DQ\ GLIIHUHQW LQIRUPDWLRQ E\ UHDGHUV LQ VXFK UHVSHFW 

7HVQLqUH GLG GLVWLQJXLVK WKH WUDQVIpUHQGH µWUDQVIHUZRUWK¶  LH ZKHUH WUDQVIHU VWDUWV WKH WUDQVIpUp µWUDQVIHUUHG¶  WKH UHVXOW RI WKH WUDQVIHU DFW WKH WUDQVODWLI µWUDQVIHU UHU¶  WKH ³PRUSKRORJLFDO PDUNHU IRU WUDQVIHUHQFH´ 7HVQLqUH   RXU WUDQVODWLRQ  8QIRUWXQDWHO\ KH GLG QRW JHQHUDOLVH DFFRUGLQJO\ WKLV WULSOH OHWWLQJ WUDQVIHUUHUV LH RXU DGSRVLWLRQV H[LVW RQO\ LI PRUSKRORJLFDOO\ PDUNHG ,Q RXU YLHZ WKLV LV RQH RI WKH PDLQ OLPLW RI LWV PRGHO  ,W LV ZRUWK UHPDUNLQJ WKDW WKH FRQVWUXFWLRQV GHYRWHG WR EXLOG µZRUGV¶ DUH GLVWLQFW IURP FRQVWUXFWLRQV GHYRWHG WR WKH LQWHU RQ LQWUDSKUDVDO OHYHO $OWKRXJK WKH\ VKDUH WKH VDPH VWUXFWXUH DQG WKH VDPH SULQFLSOHV DQG WR VRPH H[WHQW WKH\ RSHUDWH E\ LQWHUOHDYLQJ²VHH HJ WKH FRUUHODWLYHV²PRUSKRORJLFDO FRQVWUXFWLRQV DUH GHYRWHG WR FRQVWUXFW WKH µDWRPV¶ IRU WKH OLQJXLVWLF OHYHO  :RUGV GHQRWLQJ QXPEHU DUH SX]]OLQJ LQ IDFW DV WZR LV D OH[HPH WZRKXQGUHG LV WKH UHVXOW RI D VSHFLDO FRQVWUXFWLRQ DOWKRXJK LW RSHUDWHV DV D OH[HPH ,Q WHFKQLFDO FRQWH[WV LW LV HYHQ DFFHSWHG WKH IROG IRUP HJ WRSRORJ\ 

7KH FDVH RI ODQJXDJH SROLF\ DQG SODQQLQJ RI SODQQHG ODQJXDJHV VXFK DV (VSHUDQWR LV GLIIHUHQW 7KH LQWHUHVWHG UHDGHU FDQ VHH DW OHDVW *REER   

%XW LW LV HDV\ WR GHVLJQ DQ DUWLILFLDO ODQJXDJH ZKLFK LV FRPSOHWHO\ VXSSOHWLYH ,Q WKLV UHVSHFW DUWLILFLDO ODQJXDJHV DUH RI LQWHUHVW VLQFH WKH\ SURYLGH SDWKRORJLFDO FRQWUDVWLYH H[DPSOHV 6LPLODUO\ LW LV HDV\ WR GHVLJQ DUWLILFLDO ODQJXDJHV ZKHUH VXSSOHWLRQ LV DEVHQW HJ PRVW FRPSXWHU SURJUDPPLQJ ODQJXDJHV DUH RI WKLV VRUW 3OHDVH QRWH WKDW SODQQHG ODQJXDJHV OLNH (VSHUDQWR DUH 4XDVL1DWXUDO /DQJXDJHV 41/  QRW DUWLILFLDO /\RQV  ±   6WULFWO\ VSHDNLQJ D WUDQVIHU LV D WUDQVIRUPDWLRQ ZLWK D ULJLG SDWWHUQ %XW IRU WKH PR PHQW EHLQJ ZH ZLOO LJQRUH WKLV GHWDLO DV WUDQVIHUV FDQ EH UHSUHVHQWHG DV WUDQVIRUPDWLRQV DV H[SODLQHG LQ WKH IROORZLQJ 

1RWLFH KRZ V\QRQ\PV FDQ EH UHWULHYHG E\ TXHU\LQJ IRU D VHW RI VHPHPHV 6R RXU GLFWLRQDU\ LV DOVR D WKHVDXUXV WKDQNV WR WKH LQIRUPDWLRQ FRQWHQW RI VHPHPHV  +HUH DQG LQ WKH IROORZLQJ UHSUHVHQWDWLRQ PHDQV WKH ZD\ D SLHFH RI GDWD DSSHDUV LQ WKH GDWDEDVH DV VHHQ E\ WKH XVHU DQG QRW LWV LQWHUQDO UHSUHVHQWDWLRQ ZKLFK UHOLHV RQ WKH WHFKQLFDOLWLHV RI GDWDEDVH WHFKQRORJ\

1RWHV





5HSUHVHQWLQJ DQ DEVWUDFW FRQVWUXFWLRQ DV D TXHU\ LV HTXLYDOHQW WR VD\ WKDW DQ DEVWUDFW FRQVWUXFWLRQ GHQRWHV WKH VHW RI DOO LWV SRVVLEOH LQVWDQFHV ZKLFK LQ WXUQ DUH WKH LQVWDQFHV RI WKH JHQHUDO FRQVWUXFWLRQV FRPSRVLQJ LW 

7KHUH DUH H[FHSWLRQV RI FRXUVH GXH WR WKH IDFW WKDW JUDPPDWLFDOL]DWLRQ LQ QRW XQL IRUP )RU H[DPSOH WKH SDVW WHQVH RI µJR¶ LV µZHQW¶ VHH 6HFWLRQ  XQGHU VXSSOHWLRQ DQG VR D WUDQVIRUPDWLRQ KDV WR SODQ IRU D FKDQJH RI PRUSKHPHV ZKHUH WKH QHZ PRUSK LV QRW VLPSO\ GHULYHG IURP WKH ROG RQH HJ DSSHQGLQJ D µHG¶ %XW WKLV HIIHFWV FDQ EH REWDLQHG YLD FRPSRVLWLRQ RI VLPSOHU WUDQVIRUPDWLRQV ZKHUH RQO\ WKH ODVW VWHS VXSSRUWV VXSSOHWLRQ %XW WKH FRPSXWDWLRQDO DQDO\VLV RI WKH DGSRVLWLRQDO SDUDGLJP LV IDU EH\RQG WKH VFRSH RI WKH SUHVHQW WH[W  2I FRXUVH DV XVXDO ZKHQ LQIHUULQJ JHQHUDO IDFWV IURP HPSLULFDO DQDO\VHV LQ WKH ODFN RI D VWURQJHU DUJXPHQW ZH ZDUQ WKH UHDGHU WKDW RXU FRQFOXVLRQV DOWKRXJK UHDVRQDEOH KDYH QRW EHHQ H[WHQVLYHO\ WHVWHG RQ ODUJH FRUSRUD RI H[DPSOHV IURP ODQJXDJHV RI DOO RYHU WKH ZRUOG

&KDSWHU   *UDPPDWLFDOL]DWLRQ LV QRW IUHH IURP WKH FRPPXQLW\ RI WKH ODQJXDJH VSHDNHUV LQ RWKHU ZRUGV WKH\ FDQ LQIOXHQFH WKH ODQJXDJH LWVHOI HLWKHU FRQVFLRXVO\ E\ ODQJXDJH SROLF\ DQG SODQQLQJ RU QRW E\ ODVVH] IDLUH 

,W PD\ EH WKDW D 8QLYHUVDO *UDPPDU²DV SXW E\ &KRPVN\ DQG JHQHUDWLYLVWV LQ JHQ HUDO²HYROYHG GXULQJ SK\ORJHQ\ RI WKH KXPDQ VSHFLHV XQIRUWXQDWHO\ ZH GR QRW NQRZ KRZ ODQJXDJH RULJLQDWHG LQ KXPDQ HYROXWLRQ 7RPDVHOOR   7KDW LV ZK\ ZH FRP SDUH JUDPPDWLFDOL]DWLRQ ZLWKLQ GLIIHUHQW ODQJXDJHV LQ RUGHU WR H[WUDFW FRPPRQ JHQHUDO SDWWHUQV RI XVH LH FRQVWUXFWLRQV  2QO\ KXPDQ EHLQJV DUH SRWHQWLDOO\ VLJQ SURGXFHUV DQG UHFHLYHUV DV IDU DV LW NQRZQ E\ QRZ DQG WKLV VZLWFKLQJ FDSDELOLW\ OHDG WR WKH SURSHUW\ FDOOHG µELGLUHFWLRQDOLW\ RI WKH VLJQ¶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¶V WKHVLV LV FXUUHQWO\ GHYRWHG WR WKLV UHVHDUFK SURJUDP ZULWWHQ LQ ,WDOLDQ E\ 5LFFDUGR 3UH]LRVL



1RWHV

 0RUH SUHFLVHO\ D LV H[WUDFWHG IURP 'DUYLOO(YDQV¶ LPDJLQDWLYH ERRN 'HFHLW   ZKLOH E LV SDUW RI WZR FRQYHUVDWLRQV UHFRUGHG E\ µ'RURWK\¶ 36 EHWZHHQ  DQG  0DUFK  ZLWK WZHQW\ILYH LQWHUORFXWRUV )LQDOO\ F LV SDUW RI  FRQ YHUVDWLRQV UHFRUGHG E\ µ$UWKXU¶ 367 EHWZHHQ  )HEUXDU\ DQG  0DUFK  ZLWK VHYHQ LQWHUORFXWRUV 

:H XVH WKH H[SUHVVLRQ µPHQWDO VWDWH¶ QDLYHO\ KHUH DV D GLVFRXUVH RQ WKH RQWRORJLFDO VWDWXV RI WKH PLQG DQG LWV VWDWHV LV RXW RI WKH VFRSH RI WKLV ERRN +RZHYHU DV LW ZLOO EH FOHDU WKH SKLORVRSKLFDO SHUVSHFWLYH RI UHDOLVP 6HDUOH¶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λFDOFXOXV VLQFH LWV FKDUDFWHULVLQJ RSHUDWLRQ LV DE VWUDFWLRQ 7KH LGHD LV WR DEVWUDFW WKH LOORFXWLRQDU\ LQIRUPDWLRQ IURP WKH OLQJXLVWLF ORFX WLRQDU\ SDUW ZKLFK LV WKH H[SUHVVHG RQH 

%URDGO\ ZH KDYH D WXUQ FKDQJH ZKHQ WKH UROHV RI VSHDNHU DQG OLVWHQHU DUH VZLWFKHG DPRQJ WKH DFWRUV RI WKH FRQYHUVDWLRQ )RU RXU SXUSRVHV ZH GR QRW QHHG DQ\ IXUWKHU UH ILQHPHQW RI WKH FRQFHSW RI WXUQ DQG WXUQ FKDQJH 

6HDUOH¶V ZRUN FDQ EH WUDFHG DW OHDVW IURP 6HDUOH   ZKHQ KH SURSRVHG DQ DOWHUQD WLYH WD[RQRP\ WR $XVWLQ¶V XQWLO 6HDUOH   PRUH IRFXVHG RQ WKH VRFLDO FRQVHTXHQFHV RI KLV SKLORVRSK\ RI ODQJXDJH  7KLV GHSLFW LV TXLWH QDWXUDO QRW RQO\ LQ :HVWHUQ SKLORVRSK\ EXW DOVR LQ RWKHU FXOWXUHV RI WKH ZRUOG VXFK DV &KLQHVH ZKHUH WKH KXPDQ EHLQJ LV FRQVLGHUHG WKH D[LV WKDW JOXHV WRJHWKHU WKH VN\ LH WKH PLQG DQG WKH HDUWK LH WKH ZRUOG   %HVLGHV ZKDW DOUHDG\ TXRWHG IURP 6HDUOH  DQG 6HDUOH   RWKHU UHOHYDQW VRXUFHV DUH UHIOHFWLRQV RQ WKH LQWHQWLRQDOLW\ RI VHHLQJ EHOLHYLQJ GHVLULQJ DQG UHPHPEHU LQJ LQ 6HDUOH   

7KLV LV RQH RI 6HDUOH¶V H[DPSOH 6HDUOH  

1RWHV





,W LV SRVVLEOH WKDW EHIRUH DJULFXOWXUH KXPDQ EHLQJV VKDUH FRPPRQO\ WKLV UROH DQ\KRZ LW LV LQGXELWDEOH WKDW WKH H[SUHVVLRQ RI IHHOLQJV E\ OLQJXLVWLF PHDQV LV D UHOHYDQW SDUW RI WKH KXPDQ VSHFLHV VSHFLILFLW\  ,Q RUGHU WR PDUN WKH VSHFLDO UROH RI 'HFODUDWLRQV WKH\ DUH LQGLFDWHG ZLWK D VSHFLDO FDSLWDO OHWWHU LQ V\PEROV DQG LQ WH[W 

7KHUH ZDV D VHFRQG H[DPSOH WDNHQ IURP WKH GHVFULSWLRQ PDGH E\ +DUU\ DQRWKHU FOLHQW GXULQJ D 5RUVFKDFK WHVW )LQQ    8QIRUWXQDWHO\ ZLWKRXW FRQYHUVDWLRQDO WXUQV ZLWK D FOHDU WDVN RI SLFWXUH GHVFULSWLRQ OLNH D 5RUVFKDFK PRVW WXUQV DUH VLPSO\ DVVHUWLYHV ZLWK VRPH SRZHUIXO H[SUHVVLYH OLNH , VHQVH D KHVLWDQFH LQ PH WR DFFHSW WKLV LGHD WKDW WKLV EDW PLJKW EH LQ WURXEOH +RZHYHU IURP D FRQVWUXFWLRQDO SRLQW RI YLHZ VXFK VDPSOH LV IDU OHVV LQIRUPDWLYH

&KDSWHU   $QRWKHU SHUVSHFWLYH FRXOG EH IRU LQVWDQFH WKH DQDO\VLV RI SROLWHQHVV LQ FRQVWUXF WLYH WHUPV %URZQ DQG /HYLQVRQ  RU GLDORJXH LQ WHUPV RI WKH 0L[HG *DPH 0RGHO :HLJDQG  

$SSHQGL[ %  1RWLFH WKDW ZH GHILQHG FRQMXJDWHV RQO\ IRU FRQVWUXFWLRQ IURP D JUDPPDU FKDUDFWHU +HUH ZH VXSSRVH η WR EH D FRPSRQHQW RI VXFK D FRQVWUXFWLRQ θ DQG WKH FRQMXJDWH η∗ LV WKH REYLRXVO\ FKRVHQ FRPSRQHQW RI VRPH FRQMXJDWH RI θ 

$OWKRXJK LW LV SRVVLEOH DQG QRW HVVHQWLDOO\ PRUH GLIILFXOW WR FRQVLGHU JHQHUDO JUDPPDU FDWHJRULHV XQGHUVWDQGLQJ WKH PHDQLQJ RI GHILQLWLRQV EHFRPHV PRUH FRPSOH[ DV DGWUHHV DUH QRW XQLTXH PRGXOR FRQMXJDWHV 

$FWXDOO\ WKH IRUPDO UHDGHU ZRXOG QRWLFH WKDW WKH VWDWHPHQW LV QRW SHUIHFWO\ FRUUHFW ZH GRQ¶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

:H DYRLGHG D WHFKQLFDO VWDWHPHQW EHFDXVH VRPH FDUH VKRXOG EH WDNHQ ZKHQ GHDOLQJ ZLWK HPSW\ VWULQJV DQG V\PERO 7KH VWDWHPHQW KROGV ZKHQ WKH HPSW\ V\PERO Λ LV H[SOLFLW LQ WKH VWULQJV 

$JDLQ ZH DUH DVVXPLQJ H[SOLFLW Λ V\PEROV :LWK LPSOLFLW HPSW\ V\PEROV D VOLJKWO\ PRUH FRPSOH[ GHILQLWLRQ PXVW EH JLYHQ

Bibliography &KULVWLQD $EUHX *RPHV  ³'DWLYH DOWHUQDWLRQ LQ %UD]LOLDQ 3RUWXJXHVH W\SRORJ\ DQG FRQVWUDLQWV´ /DQJXDJH 'HVLJQ  ± .D]LPLHU] $MGXNLHZLF]  ³'LH V\QWDNWLVFKH .RQQH[LWlW´ 6WXGLD 3KLORVRSKLFD  ± /RXLV * $OH[DQGHU  /RQJPDQ (QJOLVK *UDPPDU +DUORZ /RQJPDQ 5DQG\ $OOHQ +DUULV  ³&KRPVN\¶V RWKHU 5HYROXWLRQ´ ,Q .LEEHH   SS ± -RKQ /DQJVKDZ $XVWLQ  +RZ WR 'R 7KLQJV :LWK :RUGV &DPEULGJH 0$ DQG /RQGRQ +DUYDUG 8QLYHUVLW\ 3UHVV )UDQ] %DDGHU DQG -|UJ + 6LHNPDQQ  ³8QLILFDWLRQ WKHRU\´ ,Q 'RY 0 *DEED\ & - +RJJHU DQG - $ 5RELQVRQ HGLWRUV ³+DQGERRN RI /RJLF LQ $UWLILFLDO ,QWHOOLJHQFH DQG /RJLF 3URJUDPPLQJ´ SS ± 2[IRUG 2[IRUG 8QLYHUVLW\ 3UHVV 0DUN %DNHU  ³7KHPDWLF 5ROHV DQG 6\QWDFWLF 6WUXFWXUHV´ ,Q +DHJHPDQ   FKDSWHU  SS ±


%LEOLRJUDSK\

'RXJODV %ULGJHV DQG )UHG 5LFKPDQ  9DULHWLHV RI &RQVWUXFWLYH 0DWKHPDWLFV YRO XPH  RI /RQGRQ 0DWKHPDWLFDO 6RFLHW\ /HFWXUH 1RWHV 6HULHV &DPEULGJH &DP EULGJH 8QLYHUVLW\ 3UHVV 9LJJR %U¡QGDO  3U SRVLWLRQHUQHV 7KHRUL &RSHQKDJHQ (MQDU 0XQNVJDDUG 3HQHORSH %URZQ DQG 6WHSKHQ & /HYLQVRQ  3ROLWHQHVV 6RPH XQLYHUVDOV LQ ODQ JXDJH XVDJH &DPEULGJH &DPEULGJH 8QLYHUVLW\ 3UHVV 6LOYLR &HFFDWR HGLWRU  /LQJXLVWLF $QDO\VLV DQG 3URJUDPPLQJ IRU 0HFKDQLFDO 7UDQVODWLRQ 0LODQR  1HZ
&KLFDJR

7KLHUU\ &RTXDQG  ³$Q $OJRULWKP IRU 7\SHFKHFNLQJ 'HSHQGHQW 7\SHV´ 6FLHQFH RI &RPSXWHU 3URJUDPPLQJ  ±  ± *UHYLOOH * &RUEHWW  1XPEHU &DPEULGJH WH[WERRNV LQ OLQJXLVWLFV &DPEULGJH &DPEULGJH 8QLYHUVLW\ 3UHVV :LOOLDP &URIW  5DGLFDO &RQVWUXFWLRQV *UDPPDU 6\QWDFWLF 7KHRU\ LQ 7\SRORJLFDO 3HUVSHFWLYH 2[IRUG 2[IRUG 8QLYHUVLW\ 3UHVV :LOOLDP &URIW  ³&RQQHFWLQJ IUDPHV DQG FRQVWUXFWLRQV´ &RQVWUXFWLRQV DQG )UDPHV    ± )HUGLQDQG 'H 6DXVVXUH  ,QWURGX]LRQH DO VHFRQGR FRUVR GL OLQJXLVWLFD JHQHUDOH  ±   5RPD $VWURODELR (GLWRU 5REHUW *RGHO ,WDOLDQ HGLWLRQ 5DIIDHOH 6LPRQH

%LEOLRJUDSK\



5DOSK 'HEXVPDQQ  $ GHFODUDWLYH JUDPPDU IRUPDOLVP IRU GHSHQGHQF\ JUDPPDU 3K' WKHVLV 8QLYHUVLWlW GHV 6DDUODQGHV 6KDURQ - 'HUU\ 0RUWRQ $QQ *HUQVEDFKHU DQG &KULVWLDQ ' 6FKXQQ HGLWRUV  ,Q WHUGLVFLSOLQDU\ FROODERUDWLRQ DQ HPHUJLQJ FRJQLWLYH VFLHQFH /DZUHQFH (UOEDXP $V VRFLDWHV 0DKZDK 1- 5REHUW 0 : 'L[RQ  (UJDWLYLW\ &DPEULGJH &DPEULGJH 8QLYHUVLW\ 3UHVV *HUPDLQ 'RQGHOLQJHU )UDQFRLVH 0DGUD\/HVLJQH DQG -HDQQLQH 5LFKDUG=DSSHOOD HGL WRUV  /XFLHQ 7HVQLqUH DXMRXUG¶KXL 3HHWHUV 3XEOLVKHUV 6DELQH )LHGOHU  3ODQVSUDFKH XQG 3KUDVHRORJLH (PSLULVFKH 8QWHUVXFKXQJHQ ]X UHSURGX]LHUWHP 6SUDFKPDWHULDO LP (VSHUDQWR )UDQNIXUW DP 0DLQ 3HWHU /DQJ 6DELQH )LHGOHU  (VSHUDQWD IUD]HRORJLR 5RWWHUGDP 8QLYHUVDOD (VSHUDQWR$VRFLR &KDUOHV - )LOOPRUH  ³)UDPH 6HPDQWLFV´ ,Q *HHUDHUWV HW DO   FKDSWHU  SS ± 2ULJLQDOO\ SXEOLVKHG LQ  &KDUOHV - )LOOPRUH D 7KH &DVH IRU &DVH FKDSWHU  SS ± 9ROXPH  RI )LOOPRUH E &KDUOHV - )LOOPRUH HGLWRU E )RUP DQG 0HDQLQJ LQ /DQJXDJH 3DSHUV RQ 6HPDQWLF 5ROHV YROXPH  6WDQIRUG &$ &6/, 3XEOLFDWLRQV &KDUOHV - )LOOPRUH F 7RZDUG D 0RGHUQ 7KHRU\ RI &DVH FKDSWHU  SS ± 9RO XPH  RI )LOOPRUH E 6WHSKHQ ( )LQQ  ,Q 2XU &OLHQWV¶ 6KRHV 7KHRU\ DQG 7HFKQLTXHV RI 7KHUDSHXWLF $VVHVVPHQW /DZUHQFH (UOEDXP $VVRFLDWHV 0DKZDK 1- 'RY 0 *DEED\  /DEHOOHG 'HGXFWLYH 6\VWHPV YROXPH  YROXPH  RI 2[IRUG /RJLF *XLGHV 2[IRUG 2[IRUG 8QLYHUVLW\ 3UHVV 0LFKDHO 5 *DUH\ DQG 'DYLV 6 -RKQVRQ  &RPSXWHU DQG ,QWUDFWDELOLW\ $ *XLGH WR WKH 7KHRU\ RI 13&RPSOHWHQHVV 1HZ


%LEOLRJUDSK\

)HGHULFR *REER  ³)RQGDPHQWL GHOOH JUDPPDWLFKH DGSRVL]LRQDOL  )XQGDPHQWRM GH OD DGSR]LFLDM JUDPDWLNRM´ ,Q.RM ,QWHUOLQJYLVWLNDM .DMHURM    ± )HGHULFR *REER  1HL SDQQL GHOOH QRVWUH FRQYHUVD]LRQL WHUDSHXWLFKH DQDOLVL FRQ YHUVD]LRQDOH FRVWUXWWLYD 0LODQR 5DIIDHOOR &RUWLQD $GHOH ( *ROGEHUJ  &RQVWUXFWLRQV $ &RQVWUXFWLRQ *UDPPDU $SSURDFK WR $UJX PHQW 6WUXFWXUH &KLFDJR &KLFDJR 8QLYHUVLW\ 3UHVV $GHOH ( *ROGEHUJ  &RQVWUXFWLRQV DW ZRUN 2[IRUG 2[IRUG 8QLYHUVLW\ 3UHVV $OJLUGDV - *UHLPDV  6WUXFWXUDO 6HPDQWLFV $Q $WWHPSW DW D 0HWKRG 1HEUDVND 8QLYHUVLW\ RI 1HEUDVND 3UHVV 3DXO *ULFH  ³/RJLF DQG FRQYHUVDWLRQ´ ,Q 3HWHU &ROH DQG -HUU\ / 0RUJDQ HGLWRUV ³6\QWD[ DQG 6HPDQWLFV  6SHHFK $FWV´ SS ± 1HZ
%LEOLRJUDSK\



3HWHU -RKQVWRQH  6NHWFKHV RI DQ (OHSKDQW $ 7RSRV 7KHRU\ &RPSHQGLXP 9ROXPH  YROXPH  RI 2[IRUG /RJLF *XLGHV 2[IRUG 2[IRUG 8QLYHUVLW\ 3UHVV -HURPH .DJDQ  7KH 7KUHH &XOWXUHV 1DWXUDO 6FLHQFHV 6RFLDO 6FLHQFHV DQG WKH +XPDQLWLHV LQ WKH VW &HQWXU\ &DPEULGJH &DPEULGJH 8QLYHUVLW\ 3UHVV -HUUROG - .DW] DQG -HUU\ $ )RGRU  ³7KH VWUXFWXUH RI D VHPDQWLF WKHRU\´ /DQJXDJH  ± 5XWK .HPSVRQ :LOIULHG 0H\HU9LRO DQG 'RY *DEED\  '\QDPLF 6\QWD[ 7KH )ORZ RI /DQJXDJH 8QGHUVWDQGLQJ /RQGRQ %ODFNZHOO 'RXJODV $ .LEEHH HGLWRU  &KRPVN\DQ 5 HYROXWLRQV $PVWHUGDP -RKQ %HQ MDPLQV 3HNND .LOSHOlLQHQ  7UHH 0DWFKLQJ 3UREOHPV ZLWK $SSOLFDWLRQV WR 6WUXFWXUHG 7H[W 'DWDEDVHV 3K' WKHVLV 'HSDUWPHQW RI &RPSXWHU 6FLHQFH 8QLYHUVLW\ RI +HOVLQNL $YDLODEOH DV 5HSRUW $ +HOVLQNL )LQODQG 1RYHPEHU  $QGUiV .RUQDL  ³2Q WKH SURSHU GHILQLWLRQ RI LQIRUPDWLRQ´ ,Q 7HUUHOO :DUG %\QXP 0DULDFDUOD &DO]DURVVD ,YR GH /RWWR DQG 6LPRQ 5RJHUVRQ HGLWRUV ³/LYLQJ :RUNLQJ DQG /HDUQLQJ %H\RQG 7HFKQRORJ\´ SS ± 0DQWXD 8QLYHUVLW\ RI 3DYLD *HRUJH /DNRII  :RPHQ )LUH DQG 'DQJHURXV 7KLQJV :KDW &DWHJRULHV 5HYHDO DERXW WKH 0LQG &KLFDJR &KLFDJR 8QLYHUVLW\ 3UHVV 2ULJLQDO HGLWLRQ  -RDFKLP /DPEHN  ³7KH PDWKHPDWLFV RI VHQWHQFH VWUXFWXUH´ $PHULFDQ 0DWKHPDW LFDO 0RQWKO\  ± -RDFKLP /DPEHN DQG 3- 6FRWW  ,QWURGXFWLRQ WR +LJKHU 2UGHU &DWHJRULFDO /RJLF YROXPH  RI &DPEULGJH 6WXGLHV LQ $GYDQFHG 0DWKHPDWLFV &DPEULGJH &DPEULGJH 8QLYHUVLW\ 3UHVV 5RQDOG : /DQJDFNHU  )RXQGDWLRQV RI &RJQLWLYH *UDPPDU YROXPH  6WDQIRUG 8QLYHUVLW\ 3UHVV 7KHRUHWLFDO 3UHUHTXLVLWHV 5RQDOG : /DQJDFNHU  &RQFHSW ,PDJH DQG 6\PERO 7KH &RJQLWLYH %DVLV RI *UDP PDU %HUOLQ 1HZ


%LEOLRJUDSK\

6DXQGHUV 0DF /DQH  &DWHJRULHV IRU WKH :RUNLQJ 0DWKHPDWLFLDQ YROXPH  RI *UDGXDWH 7H[WV LQ 0DWKHPDWLFV )UDQNIXUW $P 0DLQ 6SULQJHU QG HGLWLRQ 6DXQGHUV 0DF /DQH DQG ,HNH 0RHUGLMN  6KHDYHV LQ *HRPHWU\ DQG /RJLF 8QLYHU VLWH[W )UDQNIXUW $P 0DLQ 6SULQJHU $QD 0DULD 0DGHLUD  ³2Q WKH 3RUWXJXHVH LQIOHFWHG LQILQLWLYH´ 8&/ :RUNLQJ 3DSHUV LQ /LQJXLVWLFV  &KULVWRSKHU ' 0DQQLQJ DQG +LQULFK 6FKW]H  )RXQGDWLRQV RI 6WDWLVWLFDO 1DWXUDO /DQJXDJH 3URFHVVLQJ &DPEULGJH 0$ 0,7 3UHVV -RKQ & 0DUWLQ  ,QWURGXFWLRQ WR /DQJXDJHV DQG WKH 7KHRU\ RI &RPSXWDWLRQ 3UR JUDPPLQJ /DQJXDJHV 6HULHV 0F*UDZ +LOO VHFRQG HGLWLRQ 3HU 0DUWLQ /|I  ,QWXLWLRQLVWLF 7\SH 7KHRU\ 1DSROL %LEOLRSROLV 3HWHU +XJRH 0DWWKHZV  *UDPPDWLFDO WKHRU\ LQ WKH 8QLWHG 6WDWHV IURP %ORRPILHOG WR &KRPVN\ &DPEULGJH &DPEULGJH 8QLYHUVLW\ 3UHVV ,JRU 0HO¶þXN DQG $ODLQ 3ROJXqUH  'HSHQGHQF\ LQ /LQJXLVWLF 'HVFULSWLRQ $PVWHU GDP -RKQ %HQMDPLQV .HQ 0LQHU  ³1RWR SUL HVSHUDQWDM UDGLNRM´ /LQJYD .ULWLNR 5LFKDUG 0RQWDJXH  ³7KH 3URSHU 7UHDWPHQW RI 4XDQWLILFDWLRQ LQ 2UGLQDU\ (QJOLVK´ ,Q +LQWLNND HW DO   SS ± $QGUHD 0RUR  %UHYH VWRULD GHO YHUER HVVHUH 0LODQR $GHOSKL *O\Q 0RUULOO  ³$ &KURQLFOH RI 7\SH /RJLFDO *UDPPDU ±´ 5HVHDUFK RQ /DQJXDJH &RPSXWDWLRQ  ± ,661  85/ KWWSG[GRL RUJV

-RDNLP 1LYUH  ³'HSHQGHQF\ JUDPPDU DQG GHSHQGHQF\ SDUVLQJ´ 7HFKQLFDO UHSRUW 9l[M| 8QLYHUVLW\ )DEUL]LR $ 3HQQDFFKLHWWL  ³/D SUHSR]LFLD VLVWHPR GH (VSHUDQWR´ (VSHUDQWRORJLDM .DMHURM , SS ± )DEUL]LR $ 3HQQDFFKLHWWL  ³&RPH FODVVLILFDUH OH SUHSRVL]LRQL" 8QD QXRYD SUR SRVWD´ 4XDGHUQL GHO /DERUDWRULR GL /LQJXLVWLFD  ± )DEUL]LR $ 3HQQDFFKLHWWL  ³7KH 3UHSRVLWLRQDO 6\VWHP RI &ODVVLF 6\ULDF DQG WKDW RI 6XUHWK´ ,Q 6KDPXHO   SS ± 0DWL 3HQWXV  ³/DPEHN *UDPPDUV DUH &RQWH[W )UHH´ ,Q ³3URFHHGLQJV RI (LJKWK $QQXDO ,((( 6\PSRVLXP RQ /RJLF LQ &RPSXWHU 6FLHQFH´ SS ± ,(((

%LEOLRJUDSK\



&KDwP 3HUHOPDQ DQG /XFLH 2OEUHFKWV7\WHFD  7UDLWp GH O¶DUJXPHQWDWLRQ /D QRX YHOOH UKpWRULTXH %UX[HOOHV (GLWLRQV GH O¶8QLYHUVLWp GH %UX[HOOHV 'DYLG 0 3HUOPXWWHU  ³,PSHUVRQDO SDVVLYHV DQG WKH XQDFFXVDWLYH K\SRWKHVLV´ %/6  ± 'DYLG 0 3HUOPXWWHU DQG 3DXO 0 3RVWDO  ³7KH $GYDQFHPHQW ([FOXVLYHQHVV /DZ´ ,Q 3HUOPXWWHU DQG 5RVHQ   SS ± 'DYLG 0 3HUOPXWWHU DQG &DURO * 5RVHQ HGLWRUV  6WXGLHV LQ 5HODWLRQDO *UDPPDU ,, &KLFDJR &KLFDJR 8QLYHUVLW\ 3UHVV *HUPDQR 3URYHUELR DQG $QQD 7URFLQL &HUULQD  (OHPHQWL GL VLQWDVVL VWUXWWXUDOH 7RULQR 5RVHQEHUJ 6HOOLHU :LOODUG YDQ 2UPDQ 4XLQH  4XLGGLWLHV $Q ,QWHUPLWWHQWO\ 3KLORVRSKLFDO 'LFWLRQDU\ &DPEULGJH 0$ +DUYDUG 8QLYHUVLW\ 3UHVV $DUQH 5DQWD  ³*UDPPDWLFDO )UDPHZRUN $ 7\SHWKHRUHWLFDO *UDPPDU )RUPDO LVP´ 7KH -RXUQDO RI )XQFWLRQDO 3URJUDPPLQJ    ± $DUQH 5DQWD  ³*) $ 0XOWLOLQJXDO *UDPPDU )RUPDOLVP´ /DQJXDJH DQG /LQJXLV WLFV &RPSDVV    ± *LRYDQQL 6DPELQ DQG 6LOYLR 9DOHQWLQL  ³%XLOGLQJ D 7RROER[ IRU 0DUWLQ/|I¶V 7\SH 7KHRU\ 6XEVHW 7KHRU\´ ,Q *LRYDQQL 6DPELQ DQG -DQ 6PLWK HGLWRUV ³7ZHQW\)LYH


%LEOLRJUDSK\

5RELQ %HWK 6KDPXHO HGLWRU  7KH 9ROXPH RI WKH WK 6\ULDF /DQJXDJH &RQIHUHQFH 'XKRN ,UDT  %HWK 0DUGRRWKD 0DUN 6WHHGPDQ DQG -DVRQ %DOGULGJH  ³&RPELQDWRU\ &DWHJRULDO *UDPPDU´ ,Q 5 %RUVOH\ DQG . %RUMDUV HGLWRUV ³1RQ7UDQVIRUPDWLRQDO 6\QWD[´ /RQGRQ %ODFN ZHOO 'UDIW  7R DSSHDU *DEULHOH 6WHLQ  $ 'LFWLRQDU\ RI (QJOLVK $IIL[HV ± 7KHLU IXQFWLRQ DQG PHDQLQJ 0QFKHQ /LQFRP (XURSD -RKQ 5 7D\ORU  &RJQLWLYH *UDPPDU 2[IRUG 2[IRUG 8QLYHUVLW\ 3UHVV /XFLHQ 7HVQLqUH  eOHPpQWV GH V\QWD[H VWUXFWXUDOH  UXH GH OD 6RUERQQH 3DULV (GLWLRQV .OLQFNVLHFN 3DXO 7KDJDUG  ³%HLQJ ,QWHUGLVFLSOLQDU\ 7UDGLQJ =RQHV LQ &RJQLWLYH 6FLHQFH´ ,Q 'HUU\ HW DO  0LFKHO 7RPDVHOOR  &RQVWUXFWLQJ D ODQJXDJH $ 8VDJH%DVHG 7KHRU\ RI /DQJXDJH $FTXLVLWLRQ &DPEULGJH 0$ DQG /RQGRQ +DUYDUG 8QLYHUVLW\ 3UHVV 0DGGDOHQD 7RVFDQR DQG 6LPRQ 6HZDQJL  ³'LVFRYHULQJ 8VDJH 3DWWHUQV IRU WKH 6ZDKLOL DPED 5HODWLYH )RUPV F    8VLQJ &RUSXV 'DWD WR 6XSSRUW $X WRQRPRXV /HDUQLQJ RI .LVZDKLOL E\ ,WDOLDQ 6SHDNHUV´ 1RUGLF -RXUQDO RI $IULFDQ 6WXG LHV    ± 0DXUR 7RVFR  ³7RZDUGV D JHRPHWU\ RI DGSRVLWLRQDO V\VWHPV $ SUHOLPLQDU\ LQYHV WLJDWLRQ RI *DZZDGD´ ,Q %RUERQH HW DO   SS ± $QQH 6MHUS 7URHOVWUD  ³$VSHFWV RI &RQVWUXFWLYH 0DWKHPDWLFV´ ,Q -RQ %DUZLVH HGLWRU ³+DQGERRN RI 0DWKHPDWLFDO /RJLF´ YROXPH  RI 6WXGLHV LQ /RJLF DQG WKH )RXQGDWLRQV RI 0DWKHPDWLFV FKDSWHU ' SS ± $PVWHUGDP (OVHYLHUV $QQH 6MHUS 7URHOVWUD DQG +HOPXW 6FKZLFKWHQEHUJ  %DVLF 3URRI 7KHRU\ YROXPH  RI &DPEULGJH 7UDFWV LQ 7KHRUHWLFDO &RPSXWHU 6FLHQFH &DPEULGJH &DPEULGJH 8QL YHUVLW\ 3UHVV QG HGLWLRQ (GGD :HLJDQG  'LDORJXH 7KH 0L[HG *DPH $PVWHUGDP -RKQ %HQMDPLQV -RVHSK :HL]HQEDXP  ³(/,=$ D FRPSXWHU SURJUDP IRU WKH VWXG\ RI QDWXUDO ODQ JXDJH FRPPXQLFDWLRQ EHWZHHQ PDQ DQG PDFKLQH´ &RPPXQ $&0  ± ,661  GRLKWWSGRLDFPRUJ 85/ KWWSGRLDFP RUJ

%HQMDPLQ /HH :KRUI  ³*UDPPDWLFDO &DWHJRULHV´ /DQJXDJH    ± 85/ KWWSZZZMVWRURUJVWDEOH

%LEOLRJUDSK\ $QQD :LHU]ELFND  7KH 6HPDQWLFV RI *UDPPDU $PVWHUGDP -RKQ %HQMDPLQV 6HLN{


Index (QWULHV DUH RUGHUHG DOSKDEHWLFDOO\ *UHHN OHWWHUV DUH RUGHUHG DFFRUGLQJ WR WKHLU SURQXQFLDWLRQ HJ λ LV OLVWHG XQGHU / 6RPH HQWULHV DUH PDUNHG ZLWK ◮  WKLV VLJQ LQGLFDWHV WR VHH DQRWKHU HQWU\ OLVWHG EHORZ 6RPH HQWULHV UHIHUV WR RWKHU UHODWHG HQWULHV WKHVH UHIHUHQFHV DUH LQWUR GXFHG E\ DOVR DQG WKH HQWU\ WKH\ UHIHU WR )LQDOO\ HQWULHV DUH UHIHUUHG WR DV ◮ A ⊲ B ⊲ C  PHDQLQJ WKDW WKH UHIHUUHG HQWU\ LV C ZKLFK LV OLVWHG XQGHU WKH HQWU\ A DQG WKH VXEHQWU\ B

$ $◮ ◮ JUDPPDU FKDUDFWHU ⊲ $ DEODXW                      ± DOVR ◮ JUDPPDU FKDUDFWHU ⊲ FKDQJH DFFXVDWLYH                      DOVR ◮ XQDFFXVDWLYH VXEMHFW                          DFW VSHHFK                         ◮ ◮ VSHHFK DFW DFWDQW                          DFWLYDWLQJ FRQWH[W                  ◮ ◮ FRQWH[W DFWLYDWLQJ DFWLYH                             ◮ ◮ GLDWKHVLV ⊲ DFWLYH DGMHFWLYH                          DOVR ◮ DGMXQFWLYH DWWULEXWLYH                        ◮ ◮ DWWULEXWLYH SUHGLFDWLYH                       ◮ ◮ SUHGLFDWLYH DGMXQFWLRQ                        DGMXQFWLYH                         DGSRVLWLRQ                  FROORFDWLRQDO                      PRUSKHPLF                       ]HURPDUNHG                     DGSRVLWLRQDO FDWHJRU\               ◮

◮ IRUPDO PRGHO ⊲ JUDPPDU FDWH JRU\ ⊲ DGSRVLWLRQDO DGSRVLWLRQDO WUHH                    ◮ ◮ DGWUHH DGWUHH                      ±  DOVR ◮ IRUPDO PRGHO ⊲ DGWUHH FRUUHFW                          ILQDO                            OLQHDU                     ± DGYDQFHPHQW                  DOORPRUSK                         ◮ ◮ PRUSKHPH ⊲ DOORPRUSK DPELJXLW\                           DUURZ                             ◮ ◮ FDWHJRU\ ⊲ DUURZ DVVHUWLYH                          ◮ ◮ SUDJPDWLF FKDUDFWHU ⊲ DVVHUWLYH DWRP                             ◮ ◮ IRUPDO PRGHO ⊲ JUDPPDU FDWH JRU\ ⊲ DWRP DWWULEXWLYH                      DX[LOLDU\ YHUE                      ◮ ◮ YHUE ⊲ DX[LOLDU\ DYDOHQF\                          

% %DONDQ                            ◮ ◮ VSUDFKEXQG ⊲ %DONDQ %DQWX                             ◮



◮ VSUDFKEXQG ⊲ %DQWX ELYDOHQF\                         

& FHTXLYDOHQFH                     ◮ ◮ IRUPDO PRGHO ⊲ FHTXLYDOHQFH FDOFXOXV ODPEGD                          ◮ ◮ λFDOFXOXV λ◮ ◮ λFDOFXOXV /DPEHN                          ◮ ◮ /DPEHN FDOFXOXV &DUWHVLDQ FORVHG FDWHJRU\           ◮ ◮ FDWHJRU\ ⊲ &DUWHVLDQ FORVHG FDWHJRULDO JUDPPDU                ◮ ◮ JUDPPDU ⊲ FDWHJRULDO FDWHJRU\                ±   DGSRVLWLRQDO                     ◮ ◮ IRUPDO PRGHO ⊲ JUDPPDU FDWH JRU\ ⊲ DGSRVLWLRQDO DUURZ                          &DUWHVLDQ FORVHG                  FRGRPDLQ                        DOVR ◮ IRUPDO PRGHO ⊲ FRQVWUXF WLRQ ⊲ FRGRPDLQ FRVLHYH                      GRPDLQ                          DOVR ◮ IRUPDO PRGHO ⊲ FRQVWUXF WLRQ ⊲ GRPDLQ IXQFWRU             ±  FRQWUDYDULDQW                    JUDPPDU                        ◮ ◮ IRUPDO PRGHO ⊲ JUDPPDU FDWH JRU\ SXUH                           ◮ ◮ IRUPDO PRGHO ⊲ JUDPPDU FDWH JRU\ ⊲ SXUH *URWKHQGLHFN WRSRORJ\      ± LGHQWLW\                          OLQJXLVWLF                        ◮ ◮ IRUPDO PRGHO ⊲ FDWHJRU\ ⊲ OLQJXLVWLF

,QGH[ PRUSKHPLF                      ◮ ◮ IRUPDO PRGHO ⊲ FDWHJRU\ ⊲ PRUSKHPLF SUHVKHDI                      VKHDI                           VLHYH                        VLWH                         WRSRV                  FDXVDWLYH                    ± SDVVLYH                         &&*                              FKDQJH JUDPPDU FKDUDFWHU         ◮ ◮ JUDPPDU FKDUDFWHU ⊲ FKDQJH &KRPVN\ QRUPDO IRUP             ◮ ◮ IRUPDO PRGHO ⊲ &KRPVN\ QRUPDO IRUP FLUFXPVWDQWLDO                      &R&$/             ±  FRGRPDLQ                          ◮ ◮ FDWHJRU\ ⊲ FRGRPDLQ FROORFDWLRQ                DOVR ◮ JUDPPDU FKDUDFWHU ⊲ FKDQJH DOVR ◮ OH[HPH ⊲ FROORFDWLRQ PHWKRG                        PLQLPDO SDLU                   &RPELQDWRU\ &DWHJRULDO *UDPPDU   ◮ ◮ &&* FRPPLVVLYH                       ◮ ◮ SUDJPDWLF FKDUDFWHU ⊲ FRPPLV VLYH FRQMXJDWH                         ◮ ◮ IRUPDO PRGHO ⊲ FRQVWUXFWLRQ ⊲ FRQMXJDWH FRQMXJDWH HTXLYDOHQFH              ◮ ◮ IRUPDO PRGHO ⊲ FHTXLYDOHQFH FRQMXQFWLRQ                       FRQVWUXFWLRQ    ±      ± DOVR ◮ IRUPDO PRGHO ⊲ FRQVWUXF WLRQ DEOH                      ± DFWLYH                       

,QGH[

DOVR ◮ FRQVWUXFWLRQ ⊲ SDVVLYH DX[LOLDU\                 ±  FRQVWUXFWLRQ V\VWHP               HUH                              HVVH                         JHQLWLYH                          JUDPPDU                        ◮ ◮ IRUPDO PRGHO ⊲ FRQVWUXFWLRQ KDEHUH                      LPSHUDWLYH                   LQFUHGXOLW\                      LQILQLWLYH                         ◮ ◮ YHUE ⊲ LQILQLWLYH LQJ                             ◮ ◮ YHUE ⊲ JHUXQG OLQJXLVWLF                         ◮ ◮ FRQVWUXFWLRQ QRXQSOXVQRXQ                   ◮ ◮ QRXQSOXVQRXQ SDVVLYH             SVHXGRUHIOHFWLYH                UHGXFHG                          UHVXOWDWLYH                 ± VDWXUDWLRQ                      YDOHQF\                          ◮ ◮ YDOHQF\ FRQVWUXFWLRQ V\VWHP                ◮ ◮ FRQVWUXFWLRQ ⊲ FRQVWUXFWLRQ V\VWHP &RQVWUXFWLYH FRQYHUVDWLRQDO DQDO\VLV ◮ ◮ &R&$/ FRQVWUXFWLYH GLFWLRQDU\             ◮ ◮ GLFWLRQDU\ ⊲ FRQVWUXFWLYH FRQVWUXFWLYH PDWKHPDWLFV          FRQWHQW                           FRQWH[W DFWLYDWLQJ                 FRQWH[WIUHH JUDPPDU              ◮ ◮ IRUPDO PRGHO ⊲ JUDPPDU ⊲ FRQWH[WIUHH FRQWH[WIUHH ODQJXDJH              ◮ ◮ IRUPDO PRGHO ⊲ ODQJXDJH ⊲ FRQWH[WIUHH FRUUHFW DGWUHH                      ◮



◮ DGWUHH ⊲ FRUUHFW FRUUHODWLYH         ± DGMXQFWLYH                       DQVZHU                          FLUFXPVWDQWLDO                   VWDWLYH                          FRVLHYH                            ◮ ◮ FDWHJRU\ ⊲ FRVLHYH

' GDWDEDVH                    ± DOVR ◮ GLFWLRQDU\ ⊲ FRQVWUXFWLYH GHFODUDWLRQ                        ◮ ◮ SUDJPDWLF FKDUDFWHU ⊲ GHFODUD WLRQ GHFODUDWLYH V\PERO                 ◮ ◮ V\PERO ⊲ GHFODUDWLYH GHL[LV                             GHSHQGHQF\                 ± DGMXQFWLYHVWDWLYH                 FLUFXPVWDQWLDODGMXQFWLYH          FLUFXPVWDQWLDOYHUEDQW             VWDWLYHYHUEDQW                    GHSHQGHQW                    DOVR ◮ IRUPDO PRGHO ⊲ FRQVWUXF WLRQ ⊲ GHSHQGHQW GHULYDWLRQ                  ± DOVR ◮ JUDPPDU FKDUDFWHU ⊲ FKDQJH GHULYDWLRQ UXOH                     ◮ ◮ IRUPDO PRGHO ⊲ SURGXFWLRQ GLDWKHVLV DFWLYH                           DOVR ◮ FRQVWUXFWLRQ ⊲ DFWLYH SDVVLYH                          DOVR ◮ FRQVWUXFWLRQ ⊲ SDVVLYH GLFWLRQDU\             ± FRQVWUXFWLYH          ± DOVR ◮ GDWDEDVH PDWKHPDWLFDO              ± WUDGLWLRQDO                 ± GLUHFWLRQ RI ILW               ±

 PLQG ZRUOG                   PLQGWRZRUOG                   SUHVXSSRVHG                     ZRUOGWRPLQG                   GLUHFWLYH                          ◮ ◮ SUDJPDWLF FKDUDFWHU ⊲ GLUHFWLYH GRPDLQ                            ◮ ◮ FDWHJRU\ ⊲ GRPDLQ '\QDPLF 6\QWD[                   

( (  ◮ ◮ JUDPPDU FKDUDFWHU ⊲ ( HSVLORQ                            ◮ ◮ DGSRVLWLRQ ⊲ ]HURPDUNHG ǫ                                 ◮ ◮ DGSRVLWLRQ ⊲ ]HURPDUNHG ǫ WUDQVIRUPDWLRQ                   ◮ ◮ WUDQVIRUPDWLRQ ⊲ HSVLORQ HTXLYDOHQFH                       ◮ ◮ IRUPDO PRGHO ⊲ FHTXLYDOHQFH HUJDWLYH                           ◮ ◮ XQHUJDWLYH HUJDWLYLW\                           DOVR ◮ HUJDWLYH DOVR ◮ XQHUJDWLYH H[DPSOHV $PHULFDQ (QJOLVK             %UD]LOLDQ 3RUWXJXHVH           %ULWLVK (QJOLVK                &DWDODQ                      &KRFWDZ                      'XWFK                           (QJOLVK                      ±      ± ±   ±     ±  ±     ±       ±   ± ± ±  ± ± DOVR ◮ H[DPSOHV ⊲ $PHULFDQ (QJOLVK

,QGH[

DOVR ◮ H[DPSOHV ⊲ %ULWLVK (Q JOLVK )UHQFK         ± *HUPDQ         +HEUHZ                         ,QGRQHVLDQ                      ,WDOLDQ               ±              ± ±  -DSDQHVH            .DONDWXQJX             .LVZDKLOL                       /DWLQ                  /LKLU                            /LWKXDQLDQ                      3ROLVK                       3RUWXJXHVH            DOVR ◮ H[DPSOHV ⊲ %UD]LOLDQ 3RU WXJXHVH 7RIL                          7VXQJD                    7XUNLVK                   H[SUHVVLYH                        ◮ ◮ SUDJPDWLF FKDUDFWHU ⊲ H[SUHV VLYH

) IDFHW LOORFXWLRQDU\      DOVR ◮ LOORFXWLRQ ORFXWLRQDU\               SHUORFXWLRQDU\               IDFWLWLYH                          ILQDO DGWUHH                        ◮ ◮ DGWUHH ⊲ ILQDO IL[HG SRLQW                         ◮ ◮ IRUPDO PRGHO ⊲ IL[HG SRLQW IRUPDO PRGHO ±   ± DGSRVLWLRQDO FDWHJRU\             ◮

,QGH[

◮ IRUPDO PRGHO ⊲ JUDPPDU FDWH JRU\ ⊲ DGSRVLWLRQDO DGWUHH                    ± DOVR ◮ DGWUHH ILQDO                           ◮ ◮ DGWUHH ⊲ ILQDO DWRP FDQFHOOHG                      VSHFLDO                        FHTXLYDOHQFH                    FDWHJRU\ OLQJXLVWLF                      PRUSKHPLF                  &KRPVN\ QRUPDO IRUP           FRQVWUXFWLRQ     ±  DOVR ◮ FRQVWUXFWLRQ FRGRPDLQ                     DOVR ◮ FDWHJRU\ ⊲ GRPDLQ FRPSRQHQW                     FRPSRVLWLRQ                   FRQMXJDWH          ± GHSHQGHQW                     DOVR ◮ GHSHQGHQW GRPDLQ                       DOVR ◮ FDWHJRU\ ⊲ GRPDLQ JRYHUQRU                      DOVR ◮ JRYHUQRU SURGXFW                       DOVR ◮ IRUPDO PRGHO ⊲ SURGXFW FRUUHFW DGWUHH                     ◮ ◮ DGWUHH ⊲ FRUUHFW FRVLHYH                          ◮ ◮ FDWHJRU\ ⊲ FRVLHYH GHULYDWLRQ UXOH                   ◮ ◮ IRUPDO PRGHO ⊲ SURGXFWLRQ IL[HG SRLQW                      JUDPPDU                        FRQWH[WIUHH                    JUDPPDU FDWHJRU\          ± DGSRVLWLRQDO                   DWRP                          SXUH                           JUDPPDU FKDUDFWHU             



DOVR ◮ JUDPPDU FKDUDFWHU JUDPPDU FRQVWUXFWLRQ            ◮ ◮ IRUPDO PRGHO ⊲ FRQVWUXFWLRQ JUDPPDU SURGXFW                 ◮ ◮ IRUPDO PRGHO ⊲ SURGXFW *URWKHQGLHFN WRSRORJ\           ◮ ◮ FDWHJRU\ ⊲ *URWKHQGLHFN WRSRORJ\ LQGLFDWRU                         ◮ ◮ LQGLFDWRU ODQJXDJH FRQWH[WIUHH              ± JHQHUDWHG                      OLQHDU DGWUHH                      ◮ ◮ DGWUHH ⊲ OLQHDU SURGXFW              DOVR ◮ IRUPDO PRGHO ⊲ FRQVWUXF WLRQ ⊲ SURGXFW GHJUHH                         SURGXFWLRQ                      UHGXQGDQF\ WUDQVIRUPDWLRQ        ◮ ◮ WUDQVIRUPDWLRQ ⊲ UHGXQGDQF\ VLHYH                            ◮ ◮ FDWHJRU\ ⊲ VLHYH VLWH                              ◮ ◮ FDWHJRU\ ⊲ VLWH V\PERO QRQWHUPLQDO                   VWDUW                           WHUPLQDO                       IXQFWRU                            ◮ ◮ FDWHJRU\ ⊲ IXQFWRU

* JHQHUDWHG ODQJXDJH                ◮ ◮ IRUPDO PRGHO ⊲ ODQJXDJH ⊲ JHQHUDWHG JRYHUQPHQW                    ± DGMXQFWLYHVWDWLYH                 FLUFXPVWDQWLDODGMXQFWLYH          FLUFXPVWDQWLDOYHUEDQW             VWDWLYHYHUEDQW                    JRYHUQRU                    



DOVR ◮ IRUPDO PRGHO ⊲ FRQVWUXF WLRQ ⊲ JRYHUQRU JUDPPDU  ± ±           DOVR ◮ IRUPDO PRGHO ⊲ JUDPPDU FDWHJRULDO                         FDWHJRU\                         ◮ ◮ IRUPDO PRGHO ⊲ JUDPPDU FDWH JRU\ SXUH                           ◮ ◮ IRUPDO PRGHO ⊲ JUDPPDU FDWH JRU\ ⊲ SXUH FKDUDFWHU VWDWLYH                          ◮ ◮ VWDWLYH YHUEDQW                         ◮ ◮ YHUEDQW FRQVWUXFWLRQ                     ◮ ◮ IRUPDO PRGHO ⊲ FRQVWUXFWLRQ FRQWH[WIUHH                     ◮ ◮ IRUPDO PRGHO ⊲ JUDPPDU ⊲ FRQWH[WIUHH SURGXFW                          ◮ ◮ IRUPDO PRGHO ⊲ SURGXFW XQLYHUVDO                         ◮ ◮ 8QLYHUVDO *UDPPDU JUDPPDU FDWHJRU\                 ◮ ◮ IRUPDO PRGHO ⊲ JUDPPDU FDWH JRU\ SXUH                            ◮ ◮ IRUPDO PRGHO ⊲ JUDPPDU FDWH JRU\ ⊲ SXUH JUDPPDU FKDUDFWHU   ±  DOVR ◮ IRUPDO PRGHO ⊲ JUDPPDU FKDUDFWHU $                                FKDQJH        ±  (                                ,                                 LPSRVLWLRQ           DOVR ◮ JUDPPDU FKDUDFWHU ⊲ FKDQJH 2                               

,QGH[ UDLVLQJ                    VWDWLYDWLRQ                        VWDWLYH                           ◮ ◮ VWDWLYH 8                                YHUEDQW                          ◮ ◮ YHUEDQW YHUELILFDWLRQ                      JUDPPDU FRQVWUXFWLRQ              ◮ ◮ IRUPDO PRGHO ⊲ FRQVWUXFWLRQ JUDPPDU SURGXFW               ◮ ◮ IRUPDO PRGHO ⊲ SURGXFW *UDPPDWLFDO )UDPHZRUN            JUDPPDWLFDOL]DWLRQ         OH[LFDOL]DWLRQ                     *URWKHQGLHFN WRSRORJ\             ◮ ◮ FDWHJRU\ ⊲ *URWKHQGLHFN WRSRORJ\ *URWKHQGLHFN WRSRV                 ◮ ◮ FDWHJRU\ ⊲ WRSRV

+ KLGLQJ                             ◮ ◮ LQIRUPDWLRQ KLGLQJ KRPRQ\P\                        ◮ ◮ PRUSKHPH ⊲ KRPRQ\P K\SHURQ\P\                      K\SRQ\P\                       

, ,◮ ◮ JUDPPDU FKDUDFWHU ⊲ , LGLROHFW                           LOORFXWLRQ                   ± DOVR ◮ IDFHW ⊲ LOORFXWLRQDU\ UHVSRQVLELOLW\                    LOORFXWLRQDU\                       ◮ ◮ IDFHW ⊲ LOORFXWLRQDU\ LPSRVLWLRQ                        ◮ ◮ JUDPPDU FKDUDFWHU ⊲ LPSRVL WLRQ

,QGH[ LQGLFDWRU                       LQILQLWLYH                          ◮ ◮ YHUE ⊲ LQILQLWLYH LQIRUPDWLRQ KLGLQJ            ±    ±       LQIRUPDWLRQ SURPLQHQFH           LQJ                               ◮ ◮ YHUE ⊲ JHUXQG LQVWLWXWLRQ                    

MRLQW DWWHQWLRQDO IUDPH          

/ /DEHOOHG 'HGXFWLYH 6\VWHP          λFDOFXOXV                         /DPEHN FDOFXOXV                   ODQGPDUN                         ODQJXDJH FRQWH[WIUHH                     ◮ ◮ IRUPDO PRGHO ⊲ ODQJXDJH ⊲ FRQWH[WIUHH JHQHUDWHG                        ◮ ◮ IRUPDO PRGHO ⊲ ODQJXDJH ⊲ JHQHUDWHG QDWXUDO                          OH[HPH                      ± FROORFDWLRQ                 VHOHFWLRQ                        OH[LFDOL]DWLRQ                      ◮ ◮ JUDPPDWLFDOL]DWLRQ ⊲ OH[LFDO L]DWLRQ OH[LFRQ                       OLQHDU DGWUHH                       ◮ ◮ DGWUHH ⊲ OLQHDU OLQHDU ORJLF                         OLQJXLVWLF FDWHJRU\                 ◮ ◮ IRUPDO PRGHO ⊲ FDWHJRU\ ⊲ OLQJXLVWLF OLQJXLVWLF FRQVWUXFWLRQ              ◮



◮ FRQVWUXFWLRQ ORFXWLRQDU\                        ◮ ◮ IDFHW ⊲ ORFXWLRQDU\ ORJLF OLQHDU                            ◮ ◮ OLQHDU ORJLF WHUP                           

0 PDWKHPDWLFDO FDWHJRU\              ◮ ◮ FDWHJRU\ PDWKHPDWLFDO GLFWLRQDU\            ◮ ◮ GLFWLRQDU\ ⊲ PDWKHPDWLFDO PDWKHPDWLFV FRQVWUXFWLYH          ◮ ◮ FRQVWUXFWLYH PDWKHPDWLFV PHDQLQJ                    ± PHQWDO VWDWH                       PHWKRG FROORFDWLRQ                ◮ ◮ FROORFDWLRQ ⊲ PHWKRG PLQG                             PLQGWRZRUOG                     ◮ ◮ GLUHFWLRQ RI ILW ⊲ PLQGWR ZRUOG PLQLPDO SDLU                      ◮ ◮ FROORFDWLRQ ⊲ PLQLPDO SDLU PRGHO IRUPDO                      ◮ ◮ IRUPDO PRGHO PRQRYDOHQF\                       PRUSK                      PRUSKHPH                DOORPRUSK                       KRPRQ\P                   K\SHURQ\P\                      ◮ ◮ K\SHURQ\P\ K\SRQRP\                       ◮ ◮ K\SRQRP\ PRUSK                           ◮ ◮ PRUSK PRUSKHPLF FDWHJRU\               ◮ ◮ IRUPDO PRGHO ⊲ FDWHJRU\ ⊲ PRUSKHPLF PRUSKRORJ\                        ILQDO PRUSKHPH               



,QGH[

1 QDWXUDO ODQJXDJH                    ◮ ◮ ODQJXDJH ⊲ QDWXUDO QRPLQDOL]DWLRQ                     QRQWHUPLQDO V\PERO               ◮ ◮ IRUPDO PRGHO ⊲ V\PERO ⊲ QRQWHUPLQDO QRUPDOLVDWLRQ                      QRXQSOXVQRXQ              

2 2◮ ◮ JUDPPDU FKDUDFWHU ⊲ 2 RQWRORJ\                         

3 SDLU PLQLPDO                      ◮ ◮ FROORFDWLRQ ⊲ PLQLPDO SDLU SDUVLQJ                    ± SDVVLYH VHHGLDWKHVLV ⊲ SDVVLYH            SUDJPDWLF FKDUDFWHU                DVVHUWLYH                   ± FRPPLVVLYH            ± GHFODUDWLRQ             ± GLUHFWLYH                     H[SUHVVLYH             ± SUDJPDWLFV HPSKDVLV             SUHGLFDWLYH                     SUHSRVLWLRQDO V\VWHP                 SUHVKHDI                           ◮ ◮ FDWHJRU\ ⊲ SUHVKHDI SUHVXS                             ◮ ◮ GLUHFWLRQ RI ILW ⊲ SUHVXSSRVHG SURGXFW                            ◮ ◮ IRUPDO PRGHO ⊲ SURGXFW SURGXFWLRQ                         ◮ ◮ IRUPDO PRGHO ⊲ SURGXFWLRQ SURPLQHQFH                        ◮ ◮ LQIRUPDWLRQ SURPLQHQFH SXUH JUDPPDU FDWHJRU\             ◮

◮ IRUPDO PRGHO ⊲ JUDPPDU FDWH JRU\ ⊲ SXUH

4 TXDGULYDOHQF\                      TXLQYDOHQF\                       

5 UDLVLQJ                            ◮ ◮ JUDPPDU FKDUDFWHU ⊲ UDLVLQJ UHGXFWLRQ                        UHGXQGDQF\            ±  DOVR ◮ WUDQVIRUPDWLRQ ⊲ UHGXQ GDQF\ UHODWLRQ DGMXQFWLYHVWDWLYH          ± FLUFXPVWDQWLDODGMXQFWLYH    FLUFXPVWDQWLDOYHUEDQW      ± LGHQWLW\                          VWDWLYHYHUEDQW            ±  UHVXOWDWLYH                         ◮ ◮ FRQVWUXFWLRQ ⊲ UHVXOWDWLYH UKRWUDQVIRUPDWLRQ                 ◮ ◮ WUDQVIRUPDWLRQ ⊲ UHGXQGDQF\ ρWUDQVIRUPDWLRQ                   ◮ ◮ WUDQVIRUPDWLRQ ⊲ UHGXQGDQF\ UXOH GHULYDWLRQ                    ◮ ◮ IRUPDO PRGHO ⊲ SURGXFWLRQ

6 VDWXUDWLRQ                          ◮ ◮ FRQVWUXFWLRQ ⊲ VDWXUDWLRQ VFHQH              VHOHFWLRQ                           VHPDQWLF IUDPH                    VHPHPH                   VHQVH                             VKHDI                              ◮ ◮ FDWHJRU\ ⊲ VKHDI VLHYH                              ◮ ◮ FDWHJRU\ ⊲ VLHYH VLWH                               ◮

,QGH[

◮ FDWHJRU\ ⊲ VLWH VSHHFK DFW      GLUHFW                           LQGLUHFW                ± VSUDFKEXQG %DONDQ                          %DQWX                           6WDQGDUG $YHUDJH (XURSHDQ                 7XUNLVK                       6WDQGDUG $YHUDJH (XURSHDQ         ◮ ◮ VSUDFKEXQG ⊲ 6WDQGDUG $YHU DJH (XURSHDQ VWDUW V\PERO                       ◮ ◮ IRUPDO PRGHO ⊲ V\PERO ⊲ VWDUW VWDWH PHQWDO                       ◮ ◮ PHQWDO VWDWH VWDWLYDWLRQ                         ◮ ◮ JUDPPDU FKDUDFWHU ⊲ VWDWLYD WLRQ VWDWLYH                             VWULQJ                             ◮ ◮ ZRUG ⊲ DV VWULQJ VXEMHFW                              DOVR ◮ XQDFFXVDWLYH DOVR ◮ XQHUJDWLYH DFFXVDWLYH                        ◮ ◮ DFFXVDWLYH ⊲ VXEMHFW VXSSOHWLRQ          ±  DOVR ◮ JUDPPDU FKDUDFWHU ⊲ FKDQJH V\PERO GHFODUDWLYH                      QRQWHUPLQDO                     ◮ ◮ IRUPDO PRGHO ⊲ V\PERO ⊲ QRQWHUPLQDO VWDUW                             ◮ ◮ IRUPDO PRGHO ⊲ V\PERO ⊲ VWDUW WHUPLQDO                         ◮ ◮ IRUPDO PRGHO ⊲ V\PERO ⊲ WHUPLQDO V\QWDFWLFL]DWLRQ                  

 V\QWD[                             V\VWHP FRQVWUXFWLRQ                     ◮ ◮ FRQVWUXFWLRQ ⊲ FRQVWUXFWLRQ V\VWHP SUHSRVLWLRQDO                     ◮ ◮ SUHSRVLWLRQDO V\VWHP

7 WDXWUDQVIRUPDWLRQ                 ◮ ◮ WUDQVIRUPDWLRQ ⊲ WUHH τWUDQVIRUPDWLRQ                   ◮ ◮ WUDQVIRUPDWLRQ ⊲ WUHH WHUP ORJLFDO                       ◮ ◮ ORJLF ⊲ WHUP WHUPLQDO V\PERO                   ◮ ◮ IRUPDO PRGHO ⊲ V\PERO ⊲ WHUPLQDO 7RSRORJLFDO GHSHQGHQF\ JUDPPDU   WRSRORJ\                          ◮ ◮ FDWHJRU\ ⊲ *URWKHQGLHFN WRSRORJ\ WRSRV                              ◮ ◮ FDWHJRU\ ⊲ WRSRV WUDGLWLRQDO GLFWLRQDU\               ◮ ◮ GLFWLRQDU\ ⊲ WUDGLWLRQDO WUDMHFWRU\                       WUDQVIHU       ±    DOVR ◮ WUDQVIHUHQFH PDUNHG                         WUDQVIHUHQFH       ±   WUDQVIRUPDWLRQ   ±    ±  HSVLORQ                      ± SHUPXWDWLRQ                      UHGXQGDQF\           ± ±  DOVR ◮ UHGXQGDQF\ WUHH             ±   YHUEDQWWRVWDWLYH                 WULYDOHQF\                          7XUNLVK                            ◮



,QGH[

◮ VSUDFKEXQG ⊲ 7XUNLVK

8 8◮ ◮ JUDPPDU FKDUDFWHU ⊲ 8 XQDFFXVDWLYH   ±      XQHUJDWLYH          ±    8QLYHUVDO *UDPPDU                DOWHUQDWLYH YLHZ                   

9 YDOHQF\              ±   DFWDQW                            ◮ ◮ DFWDQW DGYDQFHPHQW                     ◮ ◮ DGYDQFHPHQW YHUE DX[LOLDU\                    DOVR ◮ FRQVWUXFWLRQ ⊲ DX[LOLDU\ FRSXOD                           HVVH  ± ±      DOVR ◮ FRQVWUXFWLRQ ⊲ HVVH JHUXQG                     ± KDEHUH                  ±  DOVR ◮ FRQVWUXFWLRQ ⊲ KDEHUH LPSHUDWLYH                       DOVR ◮ FRQVWUXFWLRQ ⊲ LPSHUDWLYH LQILQLWLYH                        SDUWLFLSOH                     SHUIHFW                           SUHVHQW SURJUHVVLYH                YHUEDQW                            YHUELILFDWLRQ                      ◮ ◮ JUDPPDU FKDUDFWHU ⊲ YHUELIL FDWLRQ

: ZRUG                            DV VWULQJ                          ZRUGDVVWULQJ                     ◮

◮ ZRUG ⊲ DV VWULQJ ZRUOG                            ZRUOGWRPLQG                     ◮ ◮ GLUHFWLRQ RI ILW ⊲ ZRUOGWR PLQG

= ]HURYDOHQF\                       ◮ ◮ DYDOHQF\