buyer has been registered) in such a way that the car broker agent and personal assisa tant agents can interact. The specified system configuration is then ...
/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH1
$5HTXLUHPHQW6SHFLILFDWLRQ/DQJXDJHIRU &RQILJXUDWLRQ'\QDPLFVRI0XOWL$JHQW6\VWHP 0HKGL'DVWDQL&DWKROLMQ-RQNHUDQG-DQ7UHXU 9ULMH8QLYHUVLWHLW$PVWHUGDP'HSDUWPHQWRI$UWLILFLDO,QWHOOLJHQFH 'H%RHOHODDQD+9$PVWHUGDP7KH1HWKHUODQGV {jonker, treur}@cs.vu.nl URL: http://www.cs.vu.nl/{~jonker,~treur}
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
/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH2
EHKDYLRXU HJ µH[HUFLVH LPSURYHV VNLOO¶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
L
Q
M
[
\
/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH3
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
5HTXLUHPHQW/DQJXDJH ,Q WKLV VHFWLRQ ZH ILUVW GHILQH DQ RUGHUHGVRUWHG ODQJXDJH FDOOHG 'HVLJQ /DQJXDJH '/ WKHH[SUHVVLRQVRIZKLFKVSHFLI\WKHFRQILJXUDWLRQVRIDJHQWPHGLDWLQJV\VWHP 7KHVH H[SUHVVLRQV ZLOO EH XVHG WR VSHFLI\ WKH UHTXLUHG V\VWHP FRQILJXUDWLRQ 7KHQ EDVHG RQ WKH '/ H[SUHVVLRQV ZH GHILQH DQRWKHU RUGHUHGVRUWHG ODQJXDJH FDOOHG 'H VLJQ$FWLRQ/DQJXDJH '$/ WKHH[SUHVVLRQVRIZKLFKPRGLI\V\VWHPFRQILJXUDWLRQ LHWKHH[SUHVVLRQVLQGLFDWHDFWLRQVWKDWFKDQJHRQHV\VWHPFRQILJXUDWLRQWRDQRWKHU )RU H[DPSOH WKH PDLQWHQDQFH DJHQW LQ RXU H[DPSOH JHQHUDWHV VXFK H[SUHVVLRQV ,Q RUGHUWRPRGLI\WKHV\VWHPFRQILJXUDWLRQWKHPRGLILFDWLRQDFWLRQVQHHGWREHFRPPX QLFDWHG ,Q RXUH[DPSOHWKHPDLQWHQDQFHDJHQWFRPPXQLFDWHVVXFKPRGLILFDWLRQDF WLRQV ZLWK WKH HQYLURQPHQW FRPSRQHQW ,Q RUGHU WR VSHFLI\ WKHVH FRPPXQLFDWLRQ H[ SUHVVLRQV ZH GHILQH D WKLUG RUGHUHGVRUWHG ODQJXDJH FDOOHG &RPPXQLFDWLRQ $FWLRQ /DQJXDJH &$/ WKDW XVHV WKH '$/ H[SUHVVLRQV DQG JHQHUDWHV VXFK FRPPXQLFDWLRQ H[SUHVVLRQV )LQDOO\ WKH H[SUHVVLRQV RI WKHVH ODQJXDJHV ZLOO EH XVHG WR GHILQH WKH 7UDFH5HTXLUHPHQW/DQJXDJH 75/ WKHH[SUHVVLRQVRIZKLFKIRUPDOL]HSURSHUWLHVRI QRWRQO\WKHIXQFWLRQDOEHKDYLRXURIWKHV\VWHPEXWDOVRWKHFRQILJXUDWLRQRIWKHV\V WHPGXULQJH[HFXWLRQWUDFHV 1RWHWKDWWKHILUVWWKUHHODQJXDJHVDUHREMHFWODQJXDJHVLQWKHVHQVHWKDWWKH\DUH XVHG E\ WKH FRPSRQHQWV LQ WKH DJHQWPHGLDWLQJ V\VWHPV WR VSHFLI\ DQG PRGLI\ WKH FRQILJXUDWLRQRIWKHV\VWHPZKLOHWKHWUDFHUHTXLUHPHQWODQJXDJHLVDPHWDODQJXDJH LQ WKH VHQVH WKDW LW LV XVHG E\ DQ H[WHUQDO REVHUYHU WR VSHFLI\ WKH LQIRUPDWLRQDQG FRQILJXUDWLRQ SURSHUWLHVRIWKHV\VWHPEHKDYLRXU&RQVHTXHQWO\WKHILUVWWKUHHREMHFW ODQJXDJHV SUHVXSSRVH FHUWDLQ W\SH RI PXOWLDJHQW V\VWHP DUFKLWHFWXUH VLQFH WKHLU H[ SUHVVLRQVDUHDERXWV\VWHPLQJUHGLHQWV,QWKLVSDSHUZHFRQFHQWUDWHRQV\VWHPVVSHFL ILHGDFFRUGLQJWRVRPHIRUPRIFRPSRVLWLRQDODUFKLWHFWXUH >@7KHVHV\VWHPVFRQVLVW RIDQXPEHURIFRPSRQHQWVWKDWLQWHUDFWZLWKHDFKRWKHUWKURXJKFHUWDLQW\SHVRIFRQ QHFWLRQV &RPSRQHQWV PD\ RU PD\ QRW EH FRPSRVHG RI RWKHU FRPSRQHQWV &RPSR QHQWVWKDWDUHQRWFRPSRVHGDUHVRPHWLPHVFDOOHGSULPLWLYHFRPSRQHQWV7KHVHFRP
/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH4
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
6RUW 63
'HVFULSWLRQ VRUWIRUV\VWHPFRPSRQHQWV SDUWQDPHVLGHQWLI\DVSHFLILF V\VWHPFRPSRQHQWLQWKHKLHUDUFKLFDOV\VWHPVWUXFWXUH
63SULP
VRUWIRUSULPLWLYHV\VWHPFRPSRQHQWV
63,QWHUIDFH
VRUWIRUFRPSRQHQWLQWHUIDFHV LHLQSXWRURXWSXW
6&21
VRUWIRUFRQQHFWLRQVEHWZHHQV\VWHPFRPSRQHQWV
66,*
VRUWIRUVLJQDWXUHVXVHGE\FRPSRQHQWV
6.%
VRUWIRUNQRZOHGJHEDVHVRISULPLWLYHV\VWHPFRPSRQHQWV
7KHVH VRUWV FDQ EH RUGHUHG OLNH IRU H[DPSOH 63 KROGVBLQIRBU VWDWHBU 4 ΓW 7RXWSXW 8$ FRPPXQLFWLRQBIURPBWR 4 6/7(508$0$ WUXH
∧
VWUXFWXUHBUHDOLVHVBVHUYLFH ( '()254 6/7(50
∃W¶ 7!W 7
>KROGVBLQIRBU VWDWHBU 4
⇒
ΓW¶ 7RXWSXW (: ( '()25WUXH @@
1RWH WKDW 6/7(50 LV DQ DVVXPHG VRUW WKDWUHIHUVWRWKHVHUYLFHODQJXDJHWHUPVE\ ZKLFKWKHXVHUGHQRWHVWKHNLQGRIVHUYLFH V KHLVLQWHUHVWHGLQ([DPSOHVWKDWLOOXV WUDWH 6/7(50 H[SUHVVLRQV DUH ³UHTXHVW SHUVRQDODVVLVWDQW ´ DQG ³UHTXHVW FDUEURNHULQJ V\VWHP ´ *5 &UHDWLRQ 6XFFHVVIXOQHVV ,I DW WLPH SRLQWWWKHDJHQW8$JHQHUDWHVDVHU YLFHUHTXHVW 4 HJIRUKDYLQJSHUVRQDODVVLVWDQFH WR0$RQLWVRXWSXWDQG 5LVWKH EHKDYLRXU UHTXLUHG IRU VHUYLFH UHTXHVW 4 WKHQ D WLPH SRLQW W !W H[LVWV VXFK WKDW WKH V\VWHP FRQILJXUDWLRQ FRQWDLQV WKH QHFFHVDU\ VWUXFWXUH HJ SHUVBDVV DQG WKHV\VWHP VKRZVEHKDYLRXU5
∀4 ΓW 74 6/7(50 >KROGVBLQIRBU VWDWHBU 4 ΓW 7RXWSXW 8$ FRPPXQLFDWLRQBIURPBWR 4 6/7(508$0$ WUXH
∧∃( '()25G 7G 7>VWUXFWXUHBUHDOLVHVBVHUYLFH ( '()254 6/7(50 ∧6% ( '()25G 7G 7 @ ⇒ ∃W¶ 7!W 7( '()25G 7G 7 5
>VWUXFWXUHBUHDOLVHVBVHUYLFH ( '()254 6/7(50
∧KROGVBLQIRBU VWDWHBU 4 ΓW¶ 7RXWSXW (: ( '()25WUXH ∧ 6% ( '()25G 7G 7
∧ ∀W 7W 7W 7W 7
5
>W 7±W 7
5 4
≥G 7∧W 7≤W 7≤W 7±G 7∧W 7±W 7≥G 7⇒
ΓW 7W 7SHUVBDVV @
@@
/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH12
7KHWHUPV6% DQG5RFFXUULQJLQWKLVSURSHUW\DUHH[SODLQHGLQ6HFWLRQ 7KHWHUP6% LVDVFKHPHRISURSHUWLHVWKDWUHODWHDVWUXFWXUH( '()25WREHKDYLRXU 57KHRFFXUUHQFHRI5PDNHVLWDVFKHPH 5
5
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∀4 ΓW 74 6/7(50( '()25
>KROGVBLQIRBU VWDWHBU 4
ΓW 7LQSXW 0$ FRPPXQLFDWLRQBIURPBWR 4 6/7(508$0$ WUXH
∧VWUXFWXUHBUHDOLVHVBVHUYLFH ( '()254 6/7(50 ∧¬∃(¶ '()25 >KROGVBLQIRBU VWDWHBU 4
ΓW 7LQSXW 0$ REVHUYDWLRQBUHVXOW (¶ '()25SRV WUXH
∧VWUXFWXUHBUHDOLVHVBVHUYLFH (¶ '()254 6/7(50 @
⇒
∃
W¶ 7!W 7 >KROGVBLQIRBU VWDWHBU 4
@
ΓW¶ 7RXWSXW 0$ WRBEHBSHUIRUPHG DGG ( '()25 WUXH
∧∀(´ '()25
>VWUXFWXUHBUHDOLVHVBVHUYLFH (´ '()254 6/7(50
∧KROGVBLQIRBU VWDWHBU 4 ΓW¶ 7RXWSXW 0$ WRBEHBSHUIRUPHG DGG (´ '()25 WUXH @ ⇒HTXDO ( '()25(´ '()25 @
@
:RUOGSURSHUWLHV 7KHUHTXLUHGSURSHUWLHVRIWKHEHKDYLRXURIWKHHQYLURQPHQWFRPSRQHQWDUHVSHFLILHG DVIROORZV (5 (:$FWLRQ([HFXWLRQ6XFFHVVIXOQHVV ,IDWWLPHSRLQWWWKHZRUOGFRPSR QHQW(:KDVWRBEHBSHUIRUPHG α RQLWVLQSXWDQGβLVWKHHIIHFWRISHUIRUPLQJαWKHQD WLPHSRLQWW !WH[LVWVVXFKWKDW(:KDVβRQLWVRXWSXW
/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH13 ∀4 ΓW 7α $&7,21β '()25 >KROGVBLQIRBU VWDWHBU 4
ΓW 7LQSXW (: WRBEHBSHUIRUPHG α $&7,21 WUXH ⇒
∃W¶ 7!W 7 >KROGVBLQIRBU VWDWHBU 4
@
ΓW¶ 7RXWSXW (: β '()25WUXH
∧LVBHIIHFWBRI β '()25α $&7,21 @
:KHUHWKHSUHGLFDWHLVBHIIHFWBRI βα LVGHILQHGDVIROORZV ∀[ '()25 ∀[ '($7
LVBHIIHFWBRI [DGG [ LVBHIIHFWBRI
¬[GHOHWH [
:RUOGSURSHUWLHV 7KHWUDQVIHUSURSHUWLHVVSHFLI\WKDWLQIRUPDWLRQWUDQVIHUEHWZHHQDJHQWVWDNHVSODFHLQ D SURSHU PDQQHU 7ZR LPSRUWDQW WUDQVIHU SURSHUWLHV DUH VSHFLILHG DV WKH IROORZLQJ UHTXLUHPHQWV 75 7UDQVIHU 8$0$ ,IDWWLPHSRLQWWWKHDJHQW8$JHQHUDWHVDUHTXHVWIRU 0$ RQ LWV RXWSXW WKHQ D WLPH SRLQW W !W H[LVWV VXFK WKDW 0$ KDV WKLV UHTXHVW RQ LWV LQSXW ∀4 ΓW 7ϕ )25 >KROGVBLQIRBU VWDWHBU 4
ΓW 7RXWSXW 8$ FRPPXQLFDWLRQBIURPBWR ϕ )258$0$ WUXH ⇒
∃
W¶ 7!W 7 >KROGVBLQIRBU VWDWHBU 4
ΓW¶ 7LQSXW 0$ FRPPXQLFDWLRQBIURPBWR ϕ )258$0$ WUXH @
@
75 7UDQVIHU 0$(: ,I DW WLPH SRLQW W WKH DJHQW 0$ JHQHUDWHV α IRU(:RQLWVRXWSXW 1RWHWKDW αLVRIW\SH $&7,21VXFKWKDWLWLV HLWKHU DGG ( RU GHOHWH ( WKHQ D WLPH SRLQW W !W H[LVWV VXFK WKDW (: KDV WRBEHBSHUIRUPHG α RQLWVLQSXW
WRBEHBSHUIRUPHG
∀4 ΓW 7α $&7,21 >KROGVBLQIRBU VWDWHBU 4
∃
W¶ 7!W 7
ΓW 7RXWSXW 0$ WRBEHBSHUIRUPHG α $&7,21 WUXH ⇒
ΓW¶ 7LQSXW (: WRBEHBSHUIRUPHG α $&7,21 WUXH @
>KROGVBLQIRBU VWDWHBU 4 @
6HPDQWLF3URSHUWLHV 7KH VHPDQWLF SURSHUWLHV VSHFLI\ WKH DVVXPHG JHQHULF SURSHUWLHV RI WKH V\VWHP 7KH IROORZLQJVHPDQWLFSURSHUWLHVDUHGLVWLQJXLVKHG
/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH14
6HPDQWLF3URSHUWLHV 7KLVSURSHUW\JXDUDQWHHVWKDWLIDV\VWHPGHVFULSWLRQKROGVLQ WKHLQIRUPDWLRQDOVWDWH RI WKHHQYLURQPHQWWKHQWKHDFWXDOV\VWHPFRQILJXUDWLRQ LWVVWUXFWXUDOVWDWH LVLQGHHG GHVFULEHGE\WKDWGHVFULSWLRQ 5$ ,IDWWLPHSRLQWWLQWUDFH 4WKHZRUOGFRPSRQHQW(:KDVGHVFULSWLRQ(RQ LWV RXWSXW WKHQ DW WLPH SRLQW W LQ WUDFH 4WKHV\VWHPKDVVWUXFWXUH( LHWKHV\VWHP GHVFULSWLRQKROGVBLQIRBU VWDWHBU 4 ΓW 7LQWHUIDFH & 63 ) ,)25WY 79 ⇒ ∃Σ 6,* >ROGVBVWUXFWBU VWDWHBU 4 ΓW 7V\VWHP H[LVWVBFRPS & 63 WUXH ∧KROGVBVWUXFWBU VWDWHBU 4 ΓW 7V\VWHP KDVBLQWHUIDFHBVLJQDWXUH Σ 6,*& 63 WUXH ∧KROGVBVWUXFWBU VWDWHBU 4 Γ""W 7V\VWHP LVBIRUPXODBRI ) ,)25Σ 6,* WUXH @ @
&$ $W DQ\ WLPHWLQDQ\WUDFH 4LIWKHV\VWHPKDVDFHUWDLQVWUXFWXUH LQLWVVWUXF WXUDOVWDWH WKHQWKHIRUPXODHWKDWFDQEHHYDOXDWHGLQWKLVV\VWHPVWUXFWXUHKDYHWUXWK YDOXHV LQWKHV\VWHP VLQIRUPDWLRQDOVWDWH
∀4 ΓW 7& 63) ,)25( '()25∃Σ 6,* Γ"W 7V\VWHP H[LVWVBFRPS & 63 WUXH ∧ KROGVBVWUXFWBU VWDWHBU 4 Γ"W 7V\VWHP KDVBLQWHUIDFHBVLJQDWXUH Σ 6,*& 63 WUXH ∧ KROGVBVWUXFWBU VWDWHBU 4 Γ""W 7V\VWHP LVBIRUPXODBRI ) ,)25Σ 6,* WUXH @ ⇒ ∃WY 79KROGVBLQIRBU VWDWHBU 4 ΓW 7LQWHUIDFH & 63 ) ,)25WY 79 @ >>KROGVBVWUXFWBU VWDWHBU 4
/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH15
6WUXFWXUH%HKDYLRXUSURSHUWLHV ,Q WKLV VHFWLRQ UHTXLUHG EHKDYLRXU LV UHODWHG WR VWUXFWXUH SURSHUWLHV DQG VHUYLFH UH TXHVWV,QWKHIROORZLQJ 5 4 Γ W 7 W 7 & 63 VWDQGVIRUDFHUWDLQEHKDYLRXUDOUH TXLUHPHQW$VDQH[DPSOH SHUVBDVVBUHT 4 Γ W 7 W 7 & 63 GHQRWHVWKHIROORZLQJ UHTXLUHPHQW KHUH,1)2LVDVRUWIRUWKHFRQWHQWRIUHTXHVWVDQGDQVZHUV
∀$ ,1)2>KROGVBLQIRBU VWDWHBU 4 ΓW 7LQSXW & 63 UHTXHVW $ ,1)2 WUXH
⇒
∃W 7∃% ,1)2>W 7≤W 7≤W 7W 7∧ KROGVBLQIRBU VWDWHBU 4
ΓW 7RXWSXW & 63 DQVZHUBIRU % ,1)2$ ,1)2 WUXH @@
%\ GHILQLQJ VXFK DEEUHYLDWLRQV IRU WKH UHTXLUHPHQWV RI LQWHUHVW IRU WKH V\VWHP LQ TXHVWLRQDSRZHUIXOVFKHPHRIVWUXFWXUHEHKDYLRXUSURSHUWLHVFDQEHIRUPXODWHG 6% DQG6% /HW 6% ( '()25 G 7 G 7 GHQRWH WKH IROORZLQJ VFKHPH RI VWUXFWXUH EHKDYLRXU SURSHUWLHV ,I EHWZHHQ WLPH SRLQWV W DQG W WKH V\VWHP KDV VWUXFWXUH ( '()25 WKHQ 5 LV WUXH EHWZHHQ W DQG W ± G IRU DOO SHULRGV RI VXIILFLHQW OHQJWK G PLQLPXP 5
5
5
∀4 Γ∀W 7W 7W 7W 7 ≥
>>W 7±W 7 G 7
∧∀W∈>W 7W 7@KROGVBVWUXFWBF VWDWHBF 4 ΓW 7 ( '()25WUXH ∧W 7≤W 7≤W 7±G 7∧W 7±W 7≥G 7@ 5 4
⇒
ΓW 7W 7SHUVBDVV @
,Q WKH QH[W VWUXFWXUHEHKDYLRXU VFKHPH RI SURSHUWLHV 6% WKH OLQN LV PDGH EH WZHHQDVHUYLFHUHTXHVW 4WKHEHKDYLRXU 5WKDWVDWLVILHV 4DQGWKHSRVVLEOHVWUXFWXUHV ( '()25WKDWFDQUHDOLVH56% GHQRWHVWKHIROORZLQJVFKHPHRIVWUXFWXUHEHKDYLRXU SURSHUWLHV 5
5
∀4 6/7(50
>LPSOLHGBVHUYLFH5 4 6/7(50
⇒
∃( '()25G 7G 7 >6%5 ( '()25G 7G 7
∧
VWUXFWXUHBUHDOLVHVBVHUYLFH ( '()254 6/7(50 @
@
6\VWHP(YDOXDWLRQ ,Q RUGHU WR HYDOXDWHWKHV\VWHPEHKDYLRXUZHQHHGWRYHULI\WKDWWKHV\VWHPKDVWKH UHTXLUHG SURSHUWLHV ,Q 6HFWLRQ ZH KDYH LQWURGXFHG FHUWDLQ SURSHUWLHV IRU WKH SUR SRVHGVFHQDULR+RZHYHUYHULI\LQJVXFKSURSHUWLHVPD\EHTXLWHFRPSOH[7KHUHIRUH ZHPD\GHILQHVRPHLQWHUPHGLDWHSURSHUWLHVE\PHDQVRIZKLFKJOREDOSURSHUWLHVFDQ
/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH16
EHSURYHGHDVLO\DQGPRUHHIILFLHQWO\DQGZKLFKE\WKHPVHOYHVFDQEHGHULYHGIURP EDVLFSURSHUWLHV ,QWHUPHGLDWH3URSHUWLHV ,QWHUPHGLDWHSURSHUWLHVFDQEHGHULYHGIURPEDVLFSURSHUWLHV+RZHYHULWLVXVHIXOWR IRUPXODWH WKHP H[SOLFLWO\ 7KHVH SURSHUWLHV VSHFLI\ WKH RXWSXWRXWSXW UHODWLRQV EH WZHHQ GLIIHUHQW V\VWHP FRPSRQHQWV 7ZR LPSRUWDQW LQWHUPHGLDWH SURSHUWLHV DUH DV IROORZV ,5 8$0$,QWHUDFWLRQ ,IDWWLPHSRLQWWWKHDJHQW8$JHQHUDWHVDVHUYLFHUH TXHVW 4 IRU 0$ RQ LWV RXWSXW WKHQ D WLPH SRLQW W !W H[LVWV VXFK WKDW 0$ KDV WRBEHBSHUIRUPHG DGG ( UHODWHGWRWKLVUHTXHVWRQLWVRXWSXW ∀4 ΓW 74 6/7(50( '()25 ΓW 7RXWSXW 8$ FRPPXQLFDWLRQBIURPBWR 4 6/7(508$0$ WUXH
>>KROGVBLQIRBU VWDWHBU 4
∧VWUXFWXUHBUHDOLVHVBVHUYLFH ( '()254 6/7(50
∧¬∃(¶ '()25
>KROGVBLQIRBU VWDWHBU 4
ΓW 7RXWSXW (: REVHUYDWLRQBUHVXOW (¶ '()25SRV WUXH
∧VWUXFWXUHBUHDOLVHVBVHUYLFH (¶ '()254 6/7(50 @@
⇒
∃W¶ 7!W 7
>KROGVBLQIRBU VWDWHBU 4
ΓW¶ 7RXWSXW 0$ WRBEHBSHUIRUPHG DGG ( '()25 WUXH
∧ ∀(´ '()25
>VWUXFWXUHBUHDOLVHVBVHUYLFH (´ '()254 6/7(50
∧KROGVBLQIRBU VWDWHBU 4 ΓW¶ 7RXWSXW 0$ WRBEHBSHUIRUPHG DGG (´ '()25 WUXH ⇒HTXDO ( '()25(´ '()25
@
@
@
,5 0$(: ,QWHUDFWLRQ ,I DW WLPH SRLQW W 0$ KDV DQ DFWLRQ HJ WRBEHBSHUIRUPHG DGG ( RUWRBEHBSHUIRUPHG GHOHWH ( RQLWVRXWSXWWKHQDWLPHSRLQWW !W H[LVWVVXFKWKDW(:KDVWKHHIIHFWRIWKHDFWLRQ HJ(UHVSQRW( RQLWVRXWSXW
∀4 ΓW 7α $&7,21β '()25
>>KROGVBLQIRBU VWDWHBU 4
∧
β
ΓW 7RXWSXW 0$ WRBEHBSHUIRUPHG α $&7,21 WUXH
LVBHIIHFWBRI '()25
∃W¶ 7!W 7
KROGVBLQIRBU VWDWHBU 4
α $&7,21 @ ⇒
ΓW¶ 7RXWSXW (: β '()25WUXH @
7KH8VHRI3URRI3DWWHUQV 7KHIROORZLQJORJLFDOUHODWLRQVKLSVKROGEHWZHHQWKHGLIIHUHQWSURSHUWLHV
/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH17
,QWHUPHGLDWHSURSHUWLHVDUHLPSOLHGE\WUDQVIHUSURSHUWLHVDQGDJHQWRUZRUOGSUR SHUWLHV 75 $5⇒,5 75 (5⇒,5 ,QWHUPHGLDWHSURSHUWLHVFDQEHFKDLQHGWRLQGLUHFWLQWHUDFWLRQSURSHUWLHVH[SUHVV LQJLQGLUHFWLPSDFWRIRQHFRPSRQHQWRQDQRWKHURQH ,5 ,5⇒*5
,QGLUHFWLQWHUPHGLDWHSURSHUWLHVLPSO\WKHJOREDOSURSHUWLHVDVVXPLQJ5HSUHVHQ WDWLRQDQG&RKHUHQFHSURSHUWLHVDQG6WUXFWXUH%HKDYLRXUUHODWLRQVKLSV *5 5$ &$ 6%⇒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µH[HUFLVHLPSURYHVVNLOO¶ZKLFKDUHUHODWLYHWR FRPSDULQJ WZRDOWHUQDWLYHVIRU WKHKLVWRU\FDQEHH[SUHVVHGLQWKLVODQJXDJH LQVWDQGDUGIRUPV RIWHPSRUDOORJLFGLIIHUHQWDOWHUQDWLYHKLVWRULHVFDQQRWEHFRPSDUHG $ WKLUG DQGPRUHVRSKLVWLFDWHGXVHLVWRVSHFLI\UHTXLUHPHQWVRQWKHG\QDPLFVRI WKHSURFHVVRIPRGLILFDWLRQRIWKHV\VWHPVWUXFWXUHRYHUWLPHIRUH[DPSOHDVLQLWLDWHG DQGSHUIRUPHGE\WKHV\VWHP HJRQHRILWVDJHQWV LWVHOI+HUHUHTXLUHPHQWVRQIRU H[DPSOHDJHQWEHKDYLRXUDQGWKHG\QDPLFVRIWKHV\VWHPVWUXFWXUHDQGWKHLUUHODWLRQ
/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH18
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¶ 'XERLV (
