• Aucun résultat trouvé

On the Synthesis of General Petri Nets

N/A
N/A
Protected

Academic year: 2021

Partager "On the Synthesis of General Petri Nets"

Copied!
32
0
0

Texte intégral

(1)

HAL Id: inria-00073668

https://hal.inria.fr/inria-00073668

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,

On the Synthesis of General Petri Nets

Eric Badouel, Philippe Darondeau

To cite this version:

Eric Badouel, Philippe Darondeau. On the Synthesis of General Petri Nets. [Research Report] RR- 3025, INRIA. 1996. �inria-00073668�

(2)

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

On the synthesis of general Petri nets

Eric Badouel and Philippe Darondeau

N ˚ 3025

novembre 1996

TH `EME 2

(3)
(4)

#$%'&)(+*-,.0/1324*-5,768%92'%'::;1=<>*-$.05,13*-/

?;@BA

CEDFCHG+I JKCELNMOCPRQTSUMWVXMRCEP

CEYZVE[P\VX]NPB^`_3DbacQTPRM\de]NC

fg

QhiCEYZjMWVE[U^

k

[mlnloQ

g

YHpqC

g

CV

@ C g V @

CrL+setUuTGUvwI LNQxeCEDa

g

CzyE{T{U|I GT{l}[mSUC~^

F€X‚ƒ„N…U‚e† ‡

lcQUPO_qLNQTDFM\[P[mPOSUQ

g

MRY

@

D‰ˆŠ[U^SUMOxeCEL‹a3_>Y

@

CF[]NY

@ Q g

^[LcpŒ;C

g

Lc[

gŽ

pqMRLnCEPRPOQ‘’Q

g

^_qL3Y

@

C^`MO“EMRLNSzlN]

g

C‘ˆ”CEMRS

@

Y•Cp

f

C–Y

g

M0LNCEY—^˜

g

QTDš™cLNMOYiCPW[macCEPOCpFY

g

[Lc^`MOYiMOQUL

^`_n^`Y•CED=^X›

?;@

CFPRMODFMRY—[mY•MRQUL>Y•Q>lN]

g

CFLNCEY—^Xœ^`C

g

MRQT]c^‘MOLl

g

[UVXY•M\VXCFC›žSN›=’Q

g

DFQ3pqC–PRPRMOLNS

ˆŠ[MRYiMOLNSPRQeQTlc^ MOLVŸQUDFD]NLNMOVE[YiMRQTLbl

g

QUY•Q3VXQUPW^XœcD=[E_acC

g

C–DFQxeCp aq_¡[DFMOLNQ

g

[UpN[l

Ž

Y¢[YiMRQTLQY

@

C+[mPOSUQ

g

MRY

@

D>œqˆ”Q g•£

MOLNS’Q

g

STCELNC

g

[mP

f

C–Y

g

M¤LnCEY¢^;™

g

C~pw^Cde]NCEL3YiM\[PRPO_e›

?;@

C

g

]NPOCQ^Cde]NCEL3YiM\[P;™

g

MOLNS

g

Cpq]cVXC~^b[P\^`Q¥Y

@

C>CE¦3l

g

C^i^MRx3MRY_‹Q

f

CEY

g

M LnCEY¢^Ÿœ ^MRLcVŸCwMOY

’Q

g

VXC^;[zVXQUL}VX]

gig

CEL3YMRL3YiC g l g

C–Y¢[mY•MRQTLbQTLFCExeC

g

_pqMW[mDFQTLcp-›

?;@

M\^PRMODFMRY—[mYiMOQULzD=[E_[mPW^`Q

acC

g

C–DFQxeCpa3_FPOC[ExqMOLNS^Cd§]nCELqY•M\[P-Y

g

[mLc^MRY•MRQUL¨^`_n^`Y•CED=^;[LcpwPOM©’Y•MRLNSY

@

Cz[mPRSTQ

g

MRY

@ D

YiQ=^YiCEl=Y

g

[mL}^`MRY•MRQTLª^`_n^`YiC–D=^Xœ3ˆ

@

M\V

@

[mDFQT]NLqY—^;YiQFC–¦qY

g

[UVŸYŠY

@

CCX«0CVXY•MRxeCVŸQUL3YiCEL3Y¢^ŠQm

Y @ CVXQ

g

CX¬}CVXYiMOQULacCEYˆ”CECEL

f

CEY

g

MŠ^YiCEl­Y

g

[mLc^MRY•MRQUL®^`_3YiCED=^z[mLcpSTCELNC

g

[mP

f

CEY

g

M;LNCEY—^

C^`Y—[maNPOM\^

@

Cpba3_Fj]

£

]NL}p-›Œ;_bY

@

Cˆ"[~_œqY

@

CVE[mY•CESUQ

g

MWVE[mPBVXQ g•g

C^loQTLcpqCEL}VXC^;acCEYˆ;CEC–L

Y g

[mLc^MRYiMOQUL¯^`_n^`YiC–D=^‘Q

g

^YiCEl­Y

g

[mLc^MRY•MRQUL¯^`_n^`Y•CED=^ [Lcp°LnCEY¢^[

g C g C Ž

CE¦n[mDFMOLNCpª[mLcp

^`MODFlNPRM±™cCpYiQ=JH[mPRQTM\^ŠVXQTLNLNCVŸYiMRQTLc^ŠMRLFY

@

C]c^`]c[P^CEYiY•MRLNSQQ

g

pqC

g

Cp=^`CEY—^X›

²³e´¤µi¶z·cƒ¸¹U† º

_3LqY

@

C^M\^

f˜g

QUaNPOCED»’Q gF¼

C–Y¢^Xœ”½ MOS

@ C gŽ¾

MRDFCEL}^`MRQTLc[mP

‡

]NY•QUD=[Y¢[qœ

f

QUPO_qLnQUDFMW[mP

‡

PRSUQ

g

MOY

@

D>œNJH[mPOQUMW^ ¿QULNLNC~VXYiMOQUL

ÀOÁbÂ

Ã`ďÅEÆ

Â

Ã;ÇȱďÉËʟÌ

ͤÎÏÑФÒ0ÓXԒՊҤ֢Ф×TÖØԒÙÛÚÝÜ Ð’Þ×m×TÓXԒْß`àáE܊ْÎßâ0ãåäcãæ"ãoçß`Ù\Ò0ÓXԒÕHèoé

Êeê’Ã`Ä9ďë

ìíNî

ÖØÏÑÚWï}ð

í

ÔÛÏÝñ

ëò

Ö¢àmӟÞߏÚ\óôNÎmÏÝÚÑÏÑ××Uß

ëöõ

֢ԒÓX÷àߕÖØÞeø—ù¹ÏÑԒÏÑÐ'Ö

ëúÔ

(5)

³3³†

C^F[m]nYiCE]

g

^FQUL3Yp3QULNL"KC¥[ExeCV

]}VE[­Œ;C

g

Lc[

g

pqMOLNCEPOPRQ]NL7[PRSTQ

g

MOY

@ D C

lcQUPR_3LNQTDFM\[PŠloQT]

g

PW[^`_3LqY

@¤A

C^Cp3C

g KC~^`C[]N¦pqC

f

C–Y

g

MŠln]

g ^ A

[>lc[

g

YiM

g

pqC¨^`_n^`Y

A

C–DFC^

pqCY

g

[mLc^MRY•MRQUL}^X›

[ g

C^Y

g

MWVXYiMOQUL¨[m]N¦

g KC~^`C[]N¦lN]

g

^Z^Ñ[Ex

A

C g CzY

g

C^ VŸQUL3Y

g

[MRSTLc[mL3YiCzlc[

g

CE¦3CEDFlNPOC POQ

g

^•d§]nCPQUL=xeCE]NY”DFQ3p;KCEPOM\^`C

g

pqC^;acQT]cVXPRC~^ŠpÑ[YiYiC–LqY•CpN[mL}^ pqC~^;l

g

QTYiQ3VXQTPRC^

pqC=VXQTDFD]NLNM\V–[mYiMOQUL¤›=¿CEYiY•CbPOMRDFMOY¢[YiMRQTL>lcCE]NYC–Y

g

CPRC–x”KCEClc[

g

]NLNC¡[UpN[lNY¢[YiMRQTL­DFM

Ž

LNCE]

g

CpqC PÑ[PRSUQ

g

MOY

@

DFCœN]NYiMOPRM\^•[maNPOCloQT]

g

pqC^

g KC^`C~[m]N¦¨pqC

f

C–Y

g

MS!KC–LŠKC g

[]N¦C–¦”KCVŸ]NYnKC^

pqCD=[mLNM

A

C g

C+^3KCde]NCEL3YiMOCEPRPOCe›

[ g–A

CESTPRCpqCY•M

g

[mSUC ^3KC~d§]NC–LqY•MRCEPOPRCC^YCEPRPOC

Ž

DCEDbCHPRMRD MRY¢[

Ž

YiMOxeC‘ln]NM\^•d§]CEPRPOCMRL3YiC

g l g KCEYiCzVXQTDFDFCZMRLcp”KC–loC–LcpqCEL3YiC^ŠCEL]NL KCEY—[mYZYiQT]NYiC^ZPRC^Z[UVXY•MRQTLc^

d§]nM‘_7^QUL3YCE¦”KCVX]nY¢[manPRC^Fpn[mLc^=]NL Q g p g C¥[

g

aNMRY

g

[M

g

C› ¿CEY•YiC¥^`CVXQTLcpqCªPRMODFMRY—[mYiMOQUL

lcCE]NY”[m]c^•^`MCEY

g

CŠPRCEx”KCEC;C–L[UpN[lNY¢[LqY”PÑ[PRSTQ

g

MOY

@ D C;[]N¦^`_n^`Y

A

CEDFC^p

@

_3lcC g Y g

[mL}^`MRY•MRQTLc^

"!$#&%'(#)+*-,.!0/1#/32-,4!056!$#&%$78!:9

œ3VXCHde]NM

g

CEx3MRCEL3Y

A

[CE¦qY

g

[M

g

CZPRCHVXQTLqY•CELq][PRSTQ

g

MOY

@ D M\de]NCZpqC

P\[=VXQ

g

CX¬cC~VXYiMOQUL CEY¢[aNPRMOClc[K

g

j]

£

]NLcp>CEL3Y

g

CPOC^

g KC^C[m]n¦>pqC

f

CEY

g

MCEYPOC^^`_n^`Y

A

C–DFC^

p

@

_3loC g Y g

[mLc^MRY•MRQUL}^pqC

f

CEY

g

M'›

¼

QU]c^MRL}pqM\de]NQUL}^KCESe[PRCEDFC–LqYzVXQTDFDFCEL3YPRC~^VXQ g•g

C^

Ž

lcQULcpN[LcVXC^VE[YnKCESTQ

g

M\de]NC^ŠCELqY

g C g KC~^`C[]N¦=CEY[]NYiQTD=[mY•C^ŠloC–]NxeCEL3YZ^`C l

g KC^CELqY•C

g

lNPO]c^

^`MODFlNPRC–DFCXL3YCEL=Y•C

g

DFC pqCzVXQULNLnCE¦qMOQULc^;S[mPOQUM\^MRCELnLNC^X›

;·}‚~Xµ¢…-<=³ † º

_3L3Y

@BA

C^CFp3C

g KC^C[m]n¦-œ[m]nYiQUD¡[mYiC¡pqCFp3MRDFCEL}^`MRQTLª^`]Nl"KC g

MOCE]

g

Cœ¹[PRSTQ

Ž

g

MOYiDFC^lcQUPR_3LNQTDFM\[]N¦-œnVXQULnLNCE¦3MRQUL=S[mPRQTM\^MRCELNLnC

(6)

t

! (;–b

QUPRPOQˆŠMRLNS

@Ng

CELq’CE]}V

@

Y=[mL}p

k

QU“EC–LqacC

g S Ñ^ ^`CEDFMOLc[mPZˆ;Q gi£

QUL

) %-/32-,.!

MOL f [ g

YiM\[P

G

Ž•º

Y g ]cVXY•]

g

C^

k

{UuU[9œexU[

g

MOQU]c^VXQ gig

C~^`lcQULcp3CELcVXC^acCEYˆ;CECEL[]NYiQTD=[mY—[ [LcpLnCEY”^`_n^

Ž

YiCED¡^Xœeac[U^CpFQUL

g

CESUMOQULc^;MOL=[m]nYiQUD¡[mY¢[3œ

@

[ExeCZacCECELFC^Y¢[aNPRMW^

@

Cp [mLcp=[mL}[mPR_n^`C~p-›

?;@

C

g

CX’C

g

CELcVŸClc[mlcC g ^ ’Q

g Y @

C a}[U^`MWVVXQ g•g

C^loQTLcpqCEL}VXC^Z[

g

C

k

{Uuma¤Q g

¼k?

{TG¤MOLwY

@ C

g

[DFC Q ¿

Ž

LNC–Y¢^Q

g

CEPOCEDFCEL3Y¢[

g

_LNCEY¢^Ÿœ¤[mL}pžj]c{TGMOL>Y

@

g

[mD C Qm

f

LNCEY—^X›

[ g

MW[mL3YFVŸQ gig

C^`lcQTLcpqCELcVŸC^

@

[~xeCacCECEL ^Yi]cp3MRCp

g

C^loC~VXYiMOxeCEPR_>MOL

¼

{ !žŒ

¾

{UvU["

[mLcp>MRL#

¾‘º

{Tt

¾‘º

{U|9›

‡

VEVXQ

g

pqMOLNSFY•QFY

@

C]nLNM©™cC~pl

g

C^CEL3Y¢[mY•MRQTL>Qm

g

CESTMRQTLc^SUMRxeC–L

MRL$Œ ¾

{Uva%'œŠ[

g

CESTMRQULMRL¯[)™c¦3Cp []NYiQTD=[mY•QUL ˆ›

g

›žY–›[>™c¦qC~p°Y_qlcCQmzLNCEY—^MW^F[

DFQ g l @

MW^`D

g

QUD‰Y

@

CF]NLcpqC

g

PR_3MRLnSY

g

[mLc^MRY•MRQUL^_N^YiCED‰YiQ>Y

@

CFD=[

gi£

MRLNS=S

g

[ml

@

Qm [

QULNC

Ž

lNPW[UVXC LNCEY QZY

@

[YY_qlcCeœˆŠMRY

@

QULNCFC–xeCELqY

g

CEl

g

C^`C–LqY—[mYiMOxeCQmHC[UV

@

Y`_3lNMWVE[mP g C Ž

P\[YiMRQTLc^

@

MRl acCEYˆ”CECEL­lNP\[TVXC^[mLcp C–xeCELqY—^X›

k

C–SUMRQTLc^D=[E_acC>^`C–CEL [T^lNPW[UVXC~^ˆŠMOY

@

[mY•Y¢[UV

@

Cp¬cQˆ[

g

VE^Xœ¤Y

@

]c^LNC–Y¢^D=[E_acC [U^i^CEDaNPRCpF

g

QTD‰^`]Nac^CEY¢^Q

g

CESTMRQUL}^X›

‡ L

[m]NY•QUD=[YiQTLSUMOxeC^

g

M\^CbMOL‹Y

@

M\^ˆ"[~_ªYiQ[LQ

g

pqC

g

C~p)9[mDFMOPR_=QmH^]NaNLNC–Y¢^‘QZ[=D=[m¦3M

Ž

D=[mP!LNCEYˆ

@

Q^`C ^`CEYQ;lnP\[UVŸC^M\^hi]c^YY

@

C^CEYQm

g

CESTMRQTLc^QmŠY

@

C[m]nYiQUD¡[mYiQTL¤›

?;@

C

lcQUMRL3YŠM\^;Y•QpqCVXMWpqCZˆ

@

CEY

@ C g Y @

M\^;D=[¦qMOD=[mP3LNCEYŠQ

g

^`QTDFC QMOY¢^Š^]NaNLNCEY—^

g

CEl

g

Q3pq]cVŸC^

MRLªYi]

g

L‹Y

@

CQ

g

MOSUMOLc[mP”[m]nYiQUD¡[mYiQTL ]NlªYiQMW^`QTDFQ g l @

M\^D

9

[U^Y

@ C [U^•^`Q3VXMW[mY•Cp‹S

g

[ml

@

Qm

g

C~[UV

@

[maNPOC D=[

gi£

MRLNS^X›

?;@

CC^i^CELqY•M\[PVXQUL3Y

g

MRaN]NY•MRQTLQm&'

k

{Uua%![mLcp

¼k?

{UG"¹MW^

Y @

CŠMW^`QTP\[mY•MRQTLQm¤Yˆ”QV

@ [ g

[TVXYiC

g

M\^YiMWV[¦qMOQUD=^-’Q

g

[]NYiQTD=[mY—[ M\^QUDFQ g l @

MWVY•QS

g

[ml

@

^Qm

g

C[TV

@

[maNPOC;D=[

gi£

MRLNS^X›

?;@

C^CZ[m¦3MRQUD¡^

g

Cd§]nM

g

g

QUD Y @ CEM

g

DFQ3pqCEPW^ CELnQU]NS

@bg

CESUMOQULc^¹Y•Q

^`CEl}[

g

[YiC[PRPBpqM©«0C

g

CELqY˜^`Y¢[YiC^MRL=[L=[m]nYiQUD¡[mYiQTL=[mL}pbYiQ

g

]NPOC QT]NYŠ[PRPcDFM\^•^`MOLNSCExeCEL3Y¢^

[mYC[TV

@

^`Y¢[YiCe›zŒŠ[U^CpQUL>Y

@

C^`C–lc[

g

[mYiMOQUL¥[m¦3MRQTD=^XœcxT[

g

MOQU]c^HVXQ

g

CX¬cCVXY•MRQTLc^ acCEYˆ;CEC–L

VE[mY•CESUQ

g

MOC^Q[m]nYiQUD¡[mY¢[[LcpbLNCEY—^

@

[ExeC acCECELC^Y¢[manPRM\^

@

CpMRLY

@

CZPRMOYiC

g

[mY•]

g

Ce›

?;@

C~^`C

VXQ

g

CX¬cCVŸYiMRQTLc^D¡[~_[P\^QaoCQTaNY¢[MRLNCpFMOL=[^`_n^`Y•CED=[mY•M\V;ˆ"[~_¡[U^;MRL}pq]cVXCp

g

C^Y

g

MWVXYiMOQULc^

Qm![ STCELNC

g

[mP0[UpEhi]nLcVXYiMOQULFacCEYˆ”CECEL [m]NY•QUD=[Y¢[ [LcpbLNC–YŠ^`_n^`Y•CED=^ŸœUlc[

g

[mDFC–Y

g

MWV;QULFY

@ C

Y_qlcCQmLnCEY¢^Ÿœ

g

C~^`Y

g

M\VXY•CpFQUL=DFQ3pqC–P\^QY

@

C ^CElc[

g

[mY•MRQTL>[m¦3MRQTD=^(Œ ¾ {Uva%'›

?;@

C=CX«0CVŸYiMRxeC Q g [mPRSTQ

g

MRY

@

DFM\VFVŸQUL3YiCEL3Y¢^ QY

@

C[aoQxeC¨VXQ g•g

C^loQTLcpqCEL}VXC^

@

[ExeC

acCECEL>[Lc[mPO_N^CpMRL¨[

@

[mLcp§’]nP¹Q;l}[mlcC

g

^Ÿ›

‡ V g

]cVXM\[P-9[UVXYZˆŠ[T^ QUa}^`C

g

xeCpwMOL)

¾k

{U|+*

[mL3_­^`C–YQm

g

CESTMRQUL}^ P\[

g

SUC=CELNQT]NS

@

YiQ>ˆŠMOYiLNC^•^‘’Q

g

^•[mYiMW^ 9[TVXYiMOQUL­QmY

@

C=^CElc[

g

[mY•MRQUL

[m¦3MRQTD=^XœZ[mL}p Y @ C g CX’Q

g

Cª^i[M\p [Up3DFM\^•^`MRanPRCeœM\^bY

@

Cª^`C–YFQmzlNPW[UVXC^Qm+[LNCEY ^`_n^`YiC–D

ˆ @ M\V

@=g

CEl

g

Q3pq]cVŸC^;Y

@

CHSUMRxeC–L=[m]NY•QUD=[YiQTL>[U^Š[ S

g

[l

@

g

C[TV

@

[maNPOCD=[

g•£

MOLNSe^Ÿ›,¦

Ž

@

MRanMRYiMOLNS Y

@

CLNCEY"^`_n^`YiC–Dšˆ

@

C–LwMOY;CE¦3M\^Y¢^;MW^

£

LNQˆŠL[T^;Y

@ C

!05 , # % !0/! ' )+2.-/%$7

›

?;@

C

^`_3LqY

@

C^M\^ l

g

QUaNPOCED ’Q

g

CEPRCED CELqY—[

g

_FLNCEY—^Xœ¤CE¦n[mDFMOLNCpb’]

g Y @ C g

MOL‹Y

@

CVE[T^`CQm;™}LNMRY•C

[m]NY•QUD=[Y¢[MOL0žŒ;C

g

{Ut1Š[Lcp0ž½ MW{ 2'œ[Lcpl

g

QxeCp

¼f¹Ž

VXQTDFlNPOCEYiCMOL0žŒŠŒ

¾

{TvU["'œ¹ˆ"[U^

(7)

SUMOxeCEL>[Lª[mlNl

g

Q¦qMOD=[mY•C ^QUPO]NYiMOQUL>MRL¨[mPOSUQ

g

MRY

@

DFM\VŠ’Q

g D MRL ¿

{Uv9›

?;@

Czl

g

C~VXM\^C

l g

QTaNPRC–DpqCVŸM\pqCp]nloQTLa3_Y

@

C[mPRSTQ

g

MRY

@

DM\^ ˆ

@

C–Y

@ C g Y @

CSUMOxeCEL>[]NYiQTD=[mY•QUL

@

[U^

^`QTDFC

2=#/% , #

M\^QUDFQ g l @

M\VŠYiQY

@ C g

C[TV

@

[maNPOC D=[

gi£

MRLNSS

g

[ml

@

Q^QUDFCZLNCEY"^`_n^`Y•CED>›

?;@

C ^`_3LqY

@

C^`MW^ l

g

QUaNPOCED ’Q

g

' ):%

f

CEY

g

MLNCEY¢^Ÿœ-CE¦n[mDFMOLNCpF’]

g Y @ C g

MOL#žŒ

¾f,

{T|!MRL

Y @

g

[DFCQmŠ™}LNMRY•C[m]NY•QUD=[Y¢[qœˆŠ[T^ ^`QTPRxeCpMOL ŒŠŒ

¾

{Uva%MOL‹Y•MRDFCzloQTPR_3LNQUD M\[mP!MRL

Y @

Cz^MR“ECQm˜[m]nYiQUD¡[mY¢[3›

?;@

C g

C~^`]NPOYiMRLnS[mPOSUQ

g

MRY

@ D @

[T^;aoC–CELb]}^`CpbMOLF[‘’C–ˆ CE¦3lcC

g

MODFCEL3Y¢^XœTVE[

gig

MOCpQU]NY”MRL

xqMOCEˆ Q;Y

@

C[]NYiQTD=[mY•Cpp3M\^`Y

g

MOaN]NYiMOQULQm”l

g

QTYiQ3VXQTP\^Ÿ›LY

@

MW^ VŸQUL3YiCE¦3YEœcY

@ C g

Cde]NM g C Ž

DFCEL3Y;Y•Ql

g

CEl

g

Q3VXC^•^ Y @

CSUCEL3]NMOLNC[m]nYiQUD¡[mYiQTLˆ

@

MWV

@ g

CEl

g

C^`C–LqY—^Š[ SUMRxeC–Lwl

g

QUY•Q3VXQUP9œ

^`Qª[T^‘YiQª^lNPRMOYMRY¢^POQeQUlc^ MOLqY•Q>VX_nVXPRC~^Xœ¤ˆŠ[T^ ’QU]nLcp‹MRL}VXQUL3xeCELNMOCELqY–›ZLNCSUQ[mPŠQmZY

@ C

l g

C~^`CEL3Ylc[loC

g

M\^ Y•QFPRM±’Y Y

@

M\^ZMRDFl

g

[UVXY•M\VE[P¤VXQTLc^`Y

g

[MRL3Y1* ˆ”C l

g

QxqMWpqC[L[TpN[mlNY—[mY•MRQUL

QmZY

@

CF^_qL3Y

@

C^`MW^[mPOSUQ

g

MRY

@

Dˆ;Q gi£

MRLNSMRL>lcQUPO_qLNQTDFM\[PYiMODFC‘’Q

g % , %$)+*

f

CEY

g

MLNCEY—^

ˆŠMRY

@ Y @

C¡^`Cde]NCEL3YiMW[mP™

g

MOLNS

g

]NPRC›

?;@

C QUY

@ C g

STQe[mPŠQZY

@ C lc[mlcC

g

MW^ Y•Qª^

@

QˆY

@

[Y

Y @ C [mPRSTQ

g

MRY

@

DšMW^

g

QUaN]}^`YEœNa3_Zhi]NDFlnMRLNS

g

QTD^`Cde]NCEL3YiMW[mPcY

g

[mLc^MRY•MRQUL¡^`_n^`YiC–D=^¹YiQ

!$#"%'

#) *-,.!0/1#/32-, !056!$#&%$78!

œc[U^ZpqCX™cLnCpFaq_=j]

£

]NL}p)žj]}{UG *ˆ;Cl

g

Qmx3M\p3C [^`C~VXQULcp[UpN[l

Ž

Y¢[YiMRQTL­QmZY

@

CF^_qL3Y

@

C~^`M\^z[mPOSUQ

g

MRY

@

D>œ¤ˆ;Q gi£

MRLNSMRLlcQUPO_qLnQUDFMW[mPY•MRDFC ’Q gf

CEY

g

MLNCEY—^

ˆŠMRY

@ Y @ C

!$#"%' )/3,).1%

›

?;@

C g

CED=[MRLNMOLNS>^CVXY•MRQUL}^‘QmHY

@

Cwl}[mlcC g [ g

C=Q

g

S[mLNMO“ECp­[U^ ’QUPOPRQˆZ^X›

º

C~VXYiMOQULG

g

CV–[mPRPW^

g

QTD žŒ

¾

{Tvma ¤Y

@

C‘STCELNC

g

[mPpqCŸ™cLNMRY•MRQTLwQ

g

C–SUMRQTLc^XœNl}[

g

[DFCEY

g

M\VZQULY

@

CY_qlcC

QmBLNCEY¢^Ÿœe[mL}p

g

CVE[T^`Y—^¹MRLY

@

M\^¤DFQU]nP\p‘Y

@

CZ[ma}^`Y

g

[UVXY˜VXQ g•g

C^loQTLcpqCEL}VXCŠacCEYˆ;CECEL+^`Cde]NCEL

Ž

YiMW[mPNY

g

[mL}^`MRY•MRQTLF^_N^YiCED=^[mL}pLNC–Y¢^¹ˆŠMOY

@ Y @

CZ^Cd§]nCELqY•M\[P§™

g

MRLNS

g

]NPOCe›

?;@

CZV–[mYiC–SUQ

g

M\VE[P

VXQ g•g

C^lcQULcpqC–LcVXCC^Y¢[aNPRMW^

@

Cp MOLŒ ¾

{Uva%cM\^l

g

C^`CEL3YiC~p

@ C g

CŠMOLbY

@

CH^`MRD lNPRC

g

’Q g D Qm

[wJH[mPOQUM\^HVXQULNLnCVXYiMOQUL¤›

º

C~VXYiMOQUL>t’Q3VX]c^`C~^ QUL

f

CEY

g

M¹LnCEY¢^Ÿ›

‡

lcQUPR_3LNQTDFM\[P^`_3LqY

@

C^`MW^

[mPOSUQ

g

MRY

@ D M\^l

g

Q3p3]cVXCp-œa}[U^`C~p®QTL­Y

@

C=[TpN[mlnY¢[mY•MRQTL QmZl

g

MRL}VXMRlNPOC^MRL

@ C g

MOYiCp

g

QTD

Y @ Cˆ”C[

£ C g

[mPRSTQ

g

MRY

@ D ’Q

g

' ) % f

CEY

g

M¹LNC–Y¢^ZpqCX™cLNC~pwMRL#ŒŠŒ

¾

{Uva

º

C~VXYiMOQUL ¡VE[

gŽ

g

MOC^ Y @ C[ma}^`Y

g

[UVXY VXQ g•g

C^loQTLcpqCEL}VXCacCEYˆ;CECEL=Y

g

[mL}^`MRY•MRQTLª^`_n^`YiC–D=^Š[mLcpLnCEY¢^ Y•Q=^`Y•CEl

Y g

[mLc^MRYiMOQUL^`_n^`Y•CED=^[mL}p®LnCEY¢^ ˆŠMOY

@ Y @

C=^`Y•CEl‹™

g

MRLNS

g

]NPRC›

º

CVXY•MRQTL­vwl

g

C^`C–LqY—^ [mL

]NlNS

g

[Up3Cp)xeC

g

^`MOQULQm”Y

@

C[PRSTQ

g

MOY

@ D ˆ @

M\V

@

^QUPOxeC^ Y @ C^`_3L3Y

@

C^M\^Šl

g

QTaNPRC–D MRLY

@

MW^

g

MWV

@ C g

VXQTLqY•CE¦qY–›

(8)

v

Eb "b> ”–b š‰=! ‘! (

¨B

‡

p3]c[mP0[Up–hi]NLcVXY•MRQUL aoC–Y`ˆ”CECEL[]NYiQTD=[mY—[‘[LcpbLNC–Y;^_N^YiCED¡^XœUlc[

g

[DFCEY

g

M\VQULFY

@

CŠY_qlcC

QmLNC–Y¢^Xœ

@

[U^acCECEL=VXQTLc^`Y

g

]cVŸYiCpbMOLŒ ¾

{Uva%'› Z]

g

lN]

g

lcQe^C‘MOLbY

@

M\^”^`CVŸYiMRQTLbMW^Y•Q[UV

Ž

VXQU]nLqY¤’Q g Y @

MW^¤VXQ g•g

C^lcQULcpqC–LcVXC;ˆŠMOY

@

QT]NYY

@ C @

CEPOlQm0VE[YiCESTQ

g

MRC^Ÿ›

C;^

@

[mPOPqY

@ C g

CX’Q g C

VXQUL}^`Y

g

]cVXY+[¨JH[PRQUMW^ VXQTLNLNCVŸYiMRQTL‹acCEYˆ”CECELª[m]nYiQUD¡[mY¢[[mLcpªLNCEYz^`_n^`Y•CED=^X›

CF^

@

[mPOP

M\pqC–LqY•M©’_ªY

@ C £ C g

LNCEPQmY

@

CVXQULnLNCVXY•MRQULBœ_3MRCEPWpqMRLnS>[

g

C–P\[mY•MRQTL°Qzpq]c[PRMOY`_ªacCEYˆ;CEC–L

^`CEl}[

g

[YiCp­[]NYiQTD=[mY—[[mL}p°^•[mY•]

g

[YiCp‹LnCEY^_N^YiCED=^Ÿ›JZMRxeCEL¥[^CElc[

g

[mY•Cp­[m]NY•QUD=[

Ž

YiQTL¤œoY

@

Cp3]c[mP¤LNC–Y^_N^YiCED MW^Š[U^•^`CEDaNPRC~p

g

QTD

g

CESUMOQULc^ŠMRL=Y

@

Cz[m]NY•QUD=[YiQULBœ-^CECEL[U^

lNP\[TVXC^;QY

@

CLNC–YE›

C ^

@

[mPOP[mPW^`QM\^QUPW[mYiCz[TpqDFM\^•^`MOaNPRCH^`]Na}^`CEY—^

g

CESTMRQTLc^ŠV

@ [ g

[TVXYiC

Ž

g

MW^`YiMWV;Qm!^CElc[

g

[mY•Cpb[]NYiQTD=[mY—[qœn[mLcpY

@ C g

CEa3_ PW[~_Y

@

CZS

g

QT]NLcpN^’Q g Y @

C MOLqxeC^YiMOSe[mY•MRQTL

Qm”[PRSTQ

g

MOY

@ D M\VZ^`QUPO]NYiMOQULc^ŠYiQY

@

C ^_qL3Y

@

C^`MW^l

g

QUaNPOCED>œqln]

g

^]NCpFMRL^`C~VXYiMOQULtq›

Œ;CX’Q

g

C^Y¢[YiMRLnSSUCELnC

g

[P3pqCX™cLNMOYiMOQULc^o’Q

g

[]NYiQTD=[mY—[qœULNC–Y¢^¤[mL}p

g

CESTMRQUL}^ lc[

g

[DFCEY

g

M\V

QULªY

@

CzY_qlcC Q”LNCEY¢^Ÿœ-PRC–YŠ]c^ MRL}pqM\VE[YiC+[F^`POMRS

@

YHpqM©«0C

g

CELcVXCzaoC–Y`ˆ”CECEL=Y

@

CVXQ g•g

C^loQTL

Ž

pqCELcVŸC^ C~^`Y¢[aNPRMW^

@

C~p acCEPOQˆ­[mLcp MOL žŒ

¾

{Tvma '›JZMRxeCELz[ŠLNCEY!^`_n^`Y•CED ˆŠMRY

@

^CEY¹QcCExeCEL3Y¢^

œNY

@

Cz^`CEYZQm!CExeCEL3Y¢^QmY

@

Czpq]c[mP![m]nYiQUD¡[mYiQTL=M\^ MRL=Y

@

Cl

g

C^`C–LqY”lc[mlcC

g

œoˆ

@

MOPRCMOY

ˆŠ[T^[bde]NQTYiMRC–LqYŠQ MRLY

@

C’Q

g

DFC

g

ˆ;Q g•£

›

?;@

C MODFlcQ

g

Y”QmY

@

M\^ZpqMW^`YiMOLcVXY•MRQUL=MW^;LNQUY

_eCEYZVXQTDFlNPRC–YiCEPO_VXPOC[

g ›

"!#$%$& ' (*)+

C g

C^`C

g

xeC Y

@

C[mlnloC–PRP\[YiMOQULªQm

*.#2-7*=#*

Y•Q=MRLNMOYiM\[PRMO“ECpFY

g

[mLc^MRYiMOQULª^_N^YiCED=^,.-

0/1 1324135769

œ ˆŠMOY

@

^`CEYHQm

#)+*-,-!0/1#/32-,.!82+9:/; ;</

[mLcp

/3, /1#/3* !$#*=#&%=576?>/

›

?;@

C , %$) 5=/3, Y g

[mLc^MRY•MRQUL7^_N^YiCED @8, -

/1 132 9

M\^[mPRˆ"[E_N^F[T^i^]NDFCp­YiQacC

%:#&%$)7/3, /!$#/BA

œDFC[LNMRLnSwY

@

[mY ’Q

g

[mL3_

!$#*=#&%C5D>E/

[Lcp

%GF %$, #IHJ>

œ

%5LK

M

57N19

>D2PO %5QK

M

5RNSN9>D2UT 57N

-

57NSN

› k

CVE[PRP0Y

@

[YZ[DFQ g l @

M\^`D QY

g

[mLc^MRY•MRQUL^_N^YiCED=^

%VW1YX 9 *

/1 1Y2 9 M

/ N1 N132 N9

M\^[bl}[mM

g

QmŠD¡[mlc^

V * / M / N

[Lcp

X * M N

^`]cV

@ Y @

[mY Z5

K

M 5 N

9[>D2\T ZV %5=9^]`_

Kba

M V %5 N9 9c>D2

N› ‡

]NY•QUD=[Y¢[[

g

CZ[mPOˆŠ[E_n^[U^•^`]NDFC~p

YiQaoC

*dA3A%+!:!0/-/%

œ¹DFC~[mLNMOLNSFY

@

[mY

/

M\^Y

@

CbMOLcpq]cVŸYiMRxeC+VXPRQ^`]

g

CQm"Y

@ C ^`MOLNSUPOCEYiQTL^CEY

ef5 67g

ˆ›

g

›žYE› ’Q

g

ˆŠ[

g

p­Y

g

[Lc^`MOYiMOQULc^bMOL

2 › jQ

g l @

MW^`D=^Qmz[]NYiQTD=[mY—[‹[

g

Chi]c^YbY

@ C

DFQ g l @

MW^`D=^¹Q¤Y

@

C ]nLcpqC

g

PR_3MRLNSY

g

[mLc^MRY•MRQUL ^`_n^`Y•CED=^¹Y

@

[mY”l

g

C~^`C

g

xeCŠMRLNMOYiM\[Pc^`Y—[mY•C^X› 'L

Y @

C+^`Cde]NCEP9œqLNQTY¢[YiMRQTLc^

5QK

M

[mL}p 5 K

h

M

[mlNlcC[

g

[U^Z^

@ Q g Y @

[mL}pN^ ’Q gji

5 N >k/ %5lK

M 5 N9

>D2

[Lcpnm

5 N >o/ Z5QK

M 5 N9 h>J2

›

(9)

|

C g

C^`C

g

xeCZY

@

C[lNlcCEPRPW[mY•MRQUL Qm

, %:# !05!$#"%$78!

Y•QMRLNMOYiMW[mPRMO“ECpLNCEY¢^-

c1 1 1

6 9

œeˆŠMOY

@ , %$) 5=/3,

LNCEY4@ -

c1 19

[mL}p

/3, /1#/3* 7*-) /3,

6 › LQ

g

pqC

g

Y•Q

SUMOxeCŠ[]NLNM±’Q

g

Dl

g

C^`C–LqY—[mYiMOQUL ’Q

g

[mPOPNY_qlcC^¤QmBLNCEY¢^ŸœUˆ;C"pqCElc[

g

Y¹

g

QUD Y @ CŠY

g

[Up3MRYiMOQULc[P

pqCX™cLnMRYiMOQUL QLNCEY—^F[mLcp l g

QUlcQ^`CªLNQˆ [ªSUCELNC

g

[mP pqCX™cLNMOYiMOQUL C–LcVXQUD lc[U^•^`MRLnS

f

C–Y g M

LNCEY—^ [T^[F^`lcCVŸM©™0VY_qlcCzQmLNC–Y¢^ ’]NPOPR_=pqCŸ™cLNCp[~’YiC

g

ˆŠ[

g

pN^

9 › ‡

7*-) /3,

M\^Z[bD=[l

* M /  g

QTD Y @ C^`CEY

' *dA%+!

Y•Q[ ^`CEY /

Qm

2 A:* !$#*=#"% !

p3CElcCELcpqMOLNS

QUL>Y

@

C Y_3loCzQmLnCEY¢^

9 ›

?;@

ClNPW[UVXC^;MOL

[mLcpY

@ C % F %$, #3!

MOL [ g

CzY

@

CzLNQ3pqC^ZQm"[

VXQUD lNPRCEY•CŠaNM

Ž

lc[

g

YiMOYiCZS

g

[ml

@

œ3ˆ

@

Qe^CCpqSTC^[

g

CD=[mlnloC~pY•Q[^`CEY

2 A:*%GF %$, #3!

pqC–loC–LcpqMRLnSbQTLY

@

C‘Y_3lcC‘QLnCEY¢^

9

a3_bY

@

C

%$/ # 7*=#)$/

*

l;

M ›

?;@

C

^`CEYHQm”PRQ3VE[P^`Y—[mY•C^Xœ-Y

@

C^`C–Y Q;POQ3VE[mP!CExeCEL3Y¢^Xœc[Lcp>Y

@

Czlc[

g

YiM\[P[UVŸYiMRQTL>Qm”Y

@

C P\[YiY•C

g

QULY

@

C’Q

g

DFC

g

œ§D¡[

£

C]Nl[Y_qlcCQm!LNCEY—^X›

=³\‚’· "!# ´%$³·'&(³§‚)+*

#5 ' % 2 , %:#! /! *-, %:#"% )7/3, /!$#/BA/. #)+*-,.!0/1#/32-,

!056!$#&%$71024365798:5;<80>= ?

% ) % / *-,

*-) % ) %+!&' %A#/BF % ! %:#3! 22 A:* !$#*=#&%+! *-,

2 A:*%GF % , # !@? *-,A0CB+5%7EDF5;4DG57 % , %+! # %' *-):#/3* *dA#/32-, 22 A:*% F %$, #3! 2-,

2 A:*!$#*=#&%+!

‡

^S

g

[l

@

^Ÿœ LNCEY—^b[

g

CQm+[^`Y—[mY•M\VwL}[mYi]

g

Ceœ;an]NYFY_qlcC^ QLNCEY—^

9

pqCX™cLnCY

@

CEM

g

pq_

Ž

Lc[mD M\VE^;* Y

@

Clc[

g

YiMW[mP"[UVXY•MRQUL}^ QmZCExeCEL3Y¢^ZQUL­D=[

g•£

MOLNSe^D=[E_aoC MRLq’C g•g

Cp

g

QTD»Y

@ C

lc[

g

YiMW[mPn[UVXY•MRQUL}^¹QmcPOQ3VE[mP3CExeCEL3Y¢^cQULPOQ3VE[mPn^`Y—[mYiC~^Xœ]c^`MOLNSY

@

C;ˆ;C–MRS

@

Y¤D=[Y

g

MO¦ Y•QVŸQUL3Y

g

QTP

^`_3LcV

@Ng

QTLNMR“EC~pl

g

Q3pq]cVXY—^;QmPOQ3VE[mP0CExeCEL3Y¢^X›

?;@

CZ’QUPRPOQˆŠMRLNS+pqCX™cLNMOYiMOQULCE¦qY•CELcpN^MRLY

@

MW^

ˆŠ[E_FY

@

C]c^`]c[P

! % %$, #/3* )$/3,) .1%

›

=³\‚’·HI!KJB³ML³No‚’„ <­„NƒO9 9PQP0ƒm„'$RS)UT

/BF %$,(* , %:#

-

c1 19?

2 #5:' %A02U365798:5;8:0>= ? # %E,3! % %$, #/3*.7*-) /3, -)+*'% 2 /! # %#)+*-,.!0/1#/32-,

!056!$#&%$7V36579W%8;8XY=

/1#! %:# 2 #)+*-,.!0/1#/32-,.!2 % , % -05[Z

36\ K

] \ N=S^CX _a` b'cG^Gd 3H\e36cM=9f _hgji

Ka

k ] \ N 36cN==S^G0

y 9

T

/BF %$,*, %:#!05!$#"% 7 -

c1 1l 1 6 9? # %,3! % %$, #/3*. 7*-) /3, -)+*'%2 /!

# %*.#2-7*=#2-,

m=-

/1 132n$1

69

%$) %j/ /!# % /3, A$#/BF % A/2 ! ) % 2je 6 g

) # 02-)

*-) #) *-,.!0/1#/32-,.! /3, 2A? *-,C2n

-

2po 0/; ;D/9

‡ £

CE_>CE¦n[mDFlNPOCbMW^ Y

@ C Y`_3lcC=Qm

f

CEY

g

M;LNC–Y¢^Xœ

0 W

KHqsrut

-

3wvyxY8SvyxzD-vyxY80

W

KHqsrut

=

›½ZC

g

Ceœ

Y @

CHPRQ3VE[P¤^`Y—[mY•C^;[

g

CLc[Yi]

g

[mP0Lq]NDacC

g

@

MOPRCŠY

@

CPRQ3V–[mP-C–xeCELqY—^[

g

Clc[M

g

^QmLc[Yi]

g

[mP

Lq]nDbacC

g

^XœN[TVXYiMOLNSlc[

g

YiMW[mPOPR_QULY

@

C’Q

g

DFC

g

[TVEVXQ

g

pqMOLNSYiQY

@

CY

g

[mL}^`MRY•MRQTL

g

]nPRC.*

u{ _}|i~ a

 M { N9c>Q€

W

K6qrwt 

{E‚„ƒ O { N -

w{

 ƒ 99…I†

Références

Documents relatifs

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST