Vérification de propriétés temporelles à la volée

HAL Id: inria-00098698

https://hal.inria.fr/inria-00098698

Submitted on 26 Sep 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

To cite this version:

Laurent Kaiser. Vérification de propriétés temporelles à la volée. RENPAR’10 - Rencontres Franco- phones du Parallélisme, 1998, Strasbourg/France, pp.210-213. �inria-00098698�

.0/21436587:9;43=<'>@?BADCE14<'CB143"/:;F/2GH;FA2I@CJ<'14A2K"K=A:GML@K=9ONP<'K"/2ARQ

SUTVWYXZ+[2\)]_^a`bdc

e cf^hgPi+j2k[alnm&XZ+[oSqpc2^h]ri e TsmutVv:`+wlnXZ+[alyx{z+VX'j2|~}€

s‚ƒ„…oTsZ†‡+XVˆ+WaXŠ‰‹X6v2g)TZŒwiŽŒWTsZwX

bU‘hmETsln‰’‰n“Tsl‹vYXW”_‰n‡WYl$T•–W

—™˜›š6œ4*˜

žŸXt‰nVv:XZBt‰nVv:†Xva+va[Y muX6volnZ+[a ¡WaXZ+[2†X6v2w‡Z+[aWTlnZ+[aXv2[YXmut‡WYX‰n‰nXvo†TZv:‰nXVW2vat¢wlyx{w"T[aln‡Zq+^h‰Xva[2lnm&t{‡Wh‘

[TZ+['†X&t{‡Vˆ‡l‹Wˆ¢Walyx{XWrz+Vq£VZX&‡V*t‰nVvYl‹X6VWavrtWa‡tWaln¢[Y¢vr†¢valnWY¢Xv¤va‡Z+[P¥lnXZ*WYXvatXw[Y¢Xvdg_¢=TZŒmu‡lnZv"iwX[Y[aX

ˆ¢Walyx{w=Ts[aln‡ZBXvY[Ÿw‡Z+•–WY‡Z+[a¢XrTVBtWa‡¥‰n muX†X‰h£X¦+t‰n‡vYl‹‡Zuw‡m¤¥lnZ{T[Y‡lnWaX2X6Z¡XZŒ†Wa¢X¤tTW2‰nXv)TsttWY‡w§X6vŸX¦+§{TsVvh‘

[Yl‹ˆXv=

e £XvY[Ÿ†{TsZv2‰nX¥V[2†q£¢ˆ+ln[aXW2w6X[a[YXPX¦+t‰n‡valn‡Z&X[Ÿ†‡Zw†Xt{‡Vˆ‡lnWo[YWTln[YXWŸ†X6vŸtWY‡¥‰n m&XvotŒ‰‹VŒv2w‡m&t‰nX¦+Xv

z+VXZ‡Vv2tWa¢6vaXZ+[a‡Zv†{TZŒv2wX[)TsWa[Yl‹w6‰‹XVZŒX)m&¢[a§Œ‡†ŒXŸ†X'ˆ¢Walyx{w"T[aln‡ZE¨r‰$T'ˆ‡‰n¢X†XtWY‡tWYl‹¢6[a¢v_[aXm&t{‡WaX‰n‰nXv=

©Hª«š¬­s®–˜šr¯…Ÿ¢6Walyx{w=Ts[aln‡Z°¨r‰$T'ˆ‡‰n¢Xi+w6‡Z+[aWTlnZ+[aX[aXm&t{‡WaX‰n‰nXiTsV[a‡mET[YXŸ¨rXZ+[aWY¢Xvh‘hva‡Wa[Yl‹X6v

±²u³´ «"µªq¶Uœ·­s«=¸¹ª ´

SqTJˆ¢6Walyx{w=Ts[aln‡Zº†XBtWa‡tWaln¢[Y¢vu[YXmut‡WYX‰n‰‹X6vPXvY[uVZŒXEtŒWa‡¥Œ‰‹¢6mET[YlnzVŒX¤[aWa 6vutWY¢vaXZ+[YX°†{TZŒv¤‰‹X6v¤†‡mBTlnZXv'†ŒX

‰h£lnZ[YXWa‡t{¢6WT¥Œl‹‰nln[a¢i†X‰$TŠw‡m&m¤VZl»w"T[aln‡Zqi"†Xv2va+vY[a m&XvŸXm¤¥TWaz+V¢6v=iX[aw^h‰UXva[2lnmut‡WY[TsZ["ivYl‰h£‡Z¤†¢vYl‹WYX'V[Yl‹‰nly‘

vYXW†Xvw‡Z+[YWTlnZ+[aX6v)[YXmut‡WYX‰n‰nXvŸ†{TsZvŸVŒZXPvYt{¢6wlyx{w=T[Yln‡Z°†Xrt‡Vˆ‡lnW2ˆ¢WYlyx{XWz+Vq£VZX'‡V°t‰nVvalnXVŒWavtWa‡tWaln¢[Y¢v

†¢6valnWa¢X6vPvY‡Z+[¥lnXZ¼ˆ¢Walyx{¢6Xv=½_ZX¤tWY¢‡+wwVt{Ts[aln‡ZJ¥lnXZJw‡ZŒZVŒX¤Xva['‰$T™†¢[aX6WamulnZ{Ts[aln‡ZB†X¤‰h£X¦+lnva[YXZwX¤†Xrw‡m¤‘

t‡WY[aXm&XZ+[av2vTs[alnvh•hTlnvTsZ[VZX'tWY‡tWYln¢[a¢†‡ZZ¢Xp_ZE†Œl‹vY[alnZ¡VX†XvŸTtŒtWa‡+w§Xv_¥{TvY¢XvŸvYVW2‰$T'vYlnm¤V‰$T[aln‡ZqiTlnZval

z+VX'†ŒXv'TttWY‡+w§ŒXv¥{TvY¢XvvaVW‰nXw=T‰nwVŒ‰FX6¦§TVvY[aly•o†q£VZB¡WTt§ŒX'†Xrw‡m&t{‡Wa[aX6muXZ+[=¾RTlnv=iŒ‰Trˆ¢Walyx{w"T[aln‡Z°Xva[

w‡Z+•–WY‡Z+[a¢X¤TVRtWa‡¥‰n muX'†U£X6¦tŒ‰‹‡valn‡ZBw‡m¤¥lnZ{T[Y‡lnWaX†VJ¡WTt§ŒX'X¦+t‰n‡WY¢qSX6v)[YXw§Zlnz+VXv'†ŒXPˆ¢Walyx{w=Ts[aln‡ZJ¨¤‰$T

ˆ‡‰n¢Xrt{XWYmuX[Y[aXZ+[†q£¿TZT‰n+vaXWVZXrtWY‡tWYl‹¢6[a¢¤vTsZvPT"ˆ‡lnW)¨™w‡ZvY[aWYVlnWaX¤‰nXP¡WTst§X¤XZJ[a‡[T‰nln[a¢™À‚sÁaÂ`›‡“‡‰nva“+JÀÄ6Á

lnZ†lnz+V{Tsl‹[Uz+VXŸwX6vo[YXw§Zlnz+VXv:Zq£¿T"ˆTlnXZ+[ÄTmBTlnv¢[a¢'Tstt‰nlnzVŒ¢Xvo¨_†Xv:va+vY[a m&Xvo[YXmutŒvdWa¢X6‰ÂTsVt{TWT"ˆTZ+[4X[:tWa‡s‘

t‡vTln[ŸVZŒXPm&¢[a§‡+†Xr¥{Tsva¢X¤vYVW†Xv'X¦+[YXZvaln‡Zv[aXm&t{‡WaX‰n‰nXv†V°m¤V+‘hw=Ts‰‹w6V‰hgŸ‡v[aWT"ˆTsV¦Bv=£¿TtŒtVlnXZ+[ŸvYVW'†Xv

m&‡†Œ ‰nXvo†U£TsV[a‡mETs[aXvd[YXmut‡WYlnva¢v"ivaVŒW2VZX'm&¢[a§‡+†X_†X'ˆ¢Walyx{w=Ts[aln‡Z&X¦+§{TVŒva[alnˆX'z+VXZ‡VvŸT"ˆ‡Zv:†¢ˆX‰n‡tt¢X

À»6Á·TslnZvalUzVŒX'vaVW_‰nXvŸWY¢vaV‰n[T[av_†X'Ő{Æ4‡VvavTlnZ+[ŸÀ»Ç"ÁaiÀ»È6Áag_‡Vv_tWa‡t{‡va‡ZŒvŸ†{TsZvŸwX6[)TWY[alnw‰nX'VZŒX'Z‡VŒˆX‰n‰nX[aXw§+‘

Zlnz+VXr†Xrˆ¢WYl»xw=T[Yl‹‡Z¼†ŒX¤tWa‡tWaln¢[Y¢v'[aX6mut‡WaX6‰‹‰nXv"

e

X[a[YXumu¢6[a§‡+†X'tXWYmuX[†X¤[YWa‡VŒˆXWP¨™‰$Tuˆ‡‰n¢Xr‰h£X6¦lnvY[aXZw6X

†Xw§Xm&lnZvovT[Yl‹vɕÊTlnvTZ+[av2VZŒX)tŒWa‡tŒWaln¢[a¢Š†‡ZZŒ¢X'XZB†lnmulnZ+V{TsZ[4†{TsZv2wXWY[Tsl‹ZŒvŸw=Tsv2‰Ê£X¦+t‰n‡valn‡Z&w‡m¤¥lnZ{Ts[a‡l‹WYX

ž)TsZvrwX[uTWY[alnw‰nXi4Z‡VvŠ•–XWa‡Zv¤[a‡V[r†q£¿T¥‡Wa†ºVZË¥ŒWaX•'WTsttX‰2vaVW¤‰nX&mu‡+† ‰nX¤z+VXuZŒ‡Vv¤T"ˆ‡ZvPVŒ[aln‰nl‹vY¢d’q‰nXv

ÌUÍ"ÎoÏ+м e Xumu‡+† 6‰‹XѕÊTln[t{TWY[alnX¤†X&‰T™•ÊTsmuln‰n‰»X'†ŒXvÒTsV[a‡mETs[aXv_[aXm&t{‡Walnva¢vŠ†q£]Ÿ‰nVW'X[ržŸln‰n‰:À

-

ÁaiX['tXWYmuX['†ŒX

†¢6wWalnWaXŠ‰‹X6vovYvY[a m&XvŸ¨ŠXZ+[aWa¢6Xvh‘hva‡Wa[alnXv"gŸ‡Vv2tWY¢vaXZ+[YXWa‡ZvŸXZŒvaVln[aXŠ‰Ê£¿Ts‰‹¡‡WYl‹[Y§m¤X:†Xˆ¢WYl»xw=T[Yl‹‡ZE¨Š‰$T'ˆ‡‰n¢XŸ†ŒX

tWY‡tWYln¢[a¢v_[aXm&t{‡WaX‰n‰nXv:z+VX'Z‡VvŸT"ˆ‡Zvo†Œ¢ˆX‰n‡tt{¢

Ó² ©Hªq¶q˜+®Ô¸Êš6Õ«"¸–ª ´

ž)TsZvqw6X[a[YXovYXw[aln‡Zqi"Z‡Vv4T‰n‰n‡Zv[Y‡V[†U£Ts¥{‡Wa†'tŒWa¢vYXZ+[aXWd‰nX4mu‡+† 6‰‹X4†X6v)ÌUÍ=Î:ÏÐJi"tVlnvZ‡VvqˆXWaWY‡Zv4w‡mum&XZ+[

m&‡†Œ¢‰nl‹vYXW:VZXtWa‡tWaln¢[Y¢iX6[ŸXZ+xZqiZ‡Vv2†¢xZlnWa‡ZŒv2‰‹X6v2Wa ¡‰‹X6vŸV[Yl‹‰nlnva¢6Xv2t{‡VW2WaX6w§ŒXWaw§XWŠ‰TŠtWY‡tWYl‹¢6[a¢

Ó²$±² —™ÕÖ4Öd×+®oš6œFµ¤®ÔךPØ ³"ÙuÚ © Ûظԝ*׶ ³´ Ö4œ4« Ù œ4«"ÖFœ4« Ú «"Õ«"×E©HÕ{­"Ü4¸´ ×Ý

Þ&˜ß ´ ¸Ô«"¸$ª ´ËÓ²$±áàFâ ÌUÍ=Î:ÏÐãÀ»6ÁŸä6åæ:ç â æÔç6è{énä'êìëîíÔï:í–êMðñò2íÔêMðñó¤í–êMð6ñô"õíÔêMðñó2õ"í–êMðñYö'í–êMðYðr÷øuï:í–êMð

ä6åæFç â ä â åä"ùPú6é‹äû âü ä"æ â ÷ âBý"ü$þ ä þUÿ ææ¹åÂò2íÔêMðŸä6åæ4ç â ä â åä=ùrú6é‹ä4û âü4þqÿü$â æÔä =æü÷ â åó¤í–êMð_ä6åæ4ç â ä â åä"ùPú6é‹ä

û âŒüoþUÿ ÷ aén÷ä6ådô"õíÔêMðPä6åædé ÿ ææ ü$âŒüæüé þ ä'êFó2õíÔêMð ó¤íÔêMðräåæ:ç â ä â åä=ùrúénä2û âü:þqÿ ÷Yé‹÷äåhä=ù üåä6å

h÷¤é‹÷ Yå þ äré ÿü¹âüæüéüåæü÷ â ä=æUö'í–êMðä6åæoç â ä â åä"ùPú6é‹ä:û âüþ äræ â å üæü÷ â å

àFâ ä°æ â å üæü÷ â ö'í–êMðBä6åæ þ û âŒüä¤è ë íÔôí ðñ°ñBí ð6ñŠí ðñ í ðYðB÷ø*ôí ðBäåæ_éÿ ææ_å÷ç!ä"

í$#&%nñ' (*)Jò2í–êMðYð,+-#/.0(¼ä6åæŸç â ä1"æ ü÷ â*ü$â æÔä â äBí.ðŸç â ä ù üåå ü÷ â í2%43+ðP÷ç*ç â ä5häähèæü÷ â í'76ð8Bí ð&ä6åæ_ç â

ä â åä"ùrúénäoû âŒüoþUÿ ÷ aén÷ä6å1hä=ùrä"æ–æhä

h÷5è åŠé‹ä'æü þ ä oä"æF í ðŠäåæé ÿ ææ þ ä6åæü¹â æü÷ â 2+û ç!hä

Ó²nÓ² ©Hªq¶U˜+®–¸hšÕŒ«=¸Ôª ´ Õ×­u®Ôך'Ø ³"Ù&Ú ©

|q‡VW:t{‡Vˆ‡l‹W:ˆ¢6Walyx{XW:VZXtWY‡tWYl‹¢6[a¢M†{TsZv:VZXvat¢wlyx{w=Ts[aln‡Z°ï:i+Z‡VvŸT‰n‰n‡Zv[a‡VŒ[o†q£¿Ts¥{‡Wa†uWYXtWY¢vaXZ+[YXW'ï

va‡VvŸ‰$Tѕ–‡WYmuX2†q£VZBÆ2^ap`¾Dösi+tVlnv:•ÊTlnWYX)†ŒX)mmuX2t‡VŒWMXZ°‰$TŠWaXtŒWa¢vYXZ+[TZ+[t{TsW2‰‹X_Æ2^ap`¾ ö{

ž)TsZvd‰$T_vaVln[YXŸ†X_wX[2TWa[Ylnw‰nX2Z‡Vv:w‡Zvaln†¢WYXWa‡Zv2z+Vq£VZX2tWY‡tWYln¢[a¢_Xva[:ˆ¢WYlyx{¢XŸvYl{‡Z¤t{X6V[ Ts[a[YXlnZ†WaX_VZu¢6[T[

†q£¿Tww6Xt[Ts[aln‡ZB†XŠ‰Ê£¿TsV[a‡mET[YXoWYXtWY¢vaXZ+[TZ+[wX[a[YX'tWY‡tWYl‹¢6[a¢

Þ&˜ß

´

¸Ô«=¸Ôª

´*Ó²‹Ó

Û f«=Ռ«Ò¶"!»Õ{­­×+Ö4«=Ռ«=¸Ôª

´ Ý

Î

â*þ

û

âü æ"#$$%&

í¹ö'ðrí(#$$%&

í¹ö'ð ïoí¹ö'ðYð2é

ÿä â

åä"ùrúénä2û

âü2þ ä6å ææ¹å

þqÿ ähèææ

ü÷ â*þ

ç~ÌUÍ=Î:ÏÐOö' ÷ *)

häåÔè÷ âþ â æIç,+ ææ¹å4è÷ç!_é‹ä6å.-"ç+äéyå2é_è h÷è üF æ äåæUåæ üå üæÔä þ â åŸé2û ç!hä/ F÷ âBþû âüæé ÿä â åä"ùPú6é‹ä þ ä6å

ææ¹å þqÿ äÉèÂææü÷ â°þ ä_ö è102#$3%*& í$ö'ðdë #ï5476 ($

Ó²98² —/:;®–ךr¶U×8­sª ´ š6«=µœd­s«=¸Ôª ´

|q‡VW4t{X6WamuX6[a[aWYXŸ‰$T_WaXw§X6Waw§X†q£VZrw§ŒXmulnZr†{TZvö ˆ¢WYlyxÂTZ+[d‰$T2tŒWa‡tŒWaln¢[a¢_ö iZ‡VvoTs‰‹‰n‡Zv4†¢x{ZlnWd†ŒXvdWa 6¡‰nXv

t{X6WamuX6[a[TsZ+[q†Xdw6‡ZvY[aWaVŒl‹WYXd‰nXPÌUÍ=Î:ÏÐ ö .<=< ë ö ?>9>ö A@T"ˆX6woï:í$ö B<=< ðN ï:í¹ö ð7)dï:í$ö ði=òfí$ö B<=< ðdë òfí$ö ð2+dòfí$ö ði

ó¤í$ö

B<=<

ðdë ó™í$ö1ð +¤ó™í$öðX[Ÿó2õí¹ö

.<=<

ðdëHó2õí¹öð0+¤ó2õí$öðC e X[Y[aX‡t¢WTs[aln‡Z&†Xw‡ZŒva[aWYVw[Yl‹‡ZBXva[:tWa‡+w§X'†ŒX

‰$T'Z‡[aln‡Z&†Xw‡m&t{‡valn[aln‡Z¤†X e2e `i+X[=i+‰nXv2WY ¡‰nXv2w6l»‘h†XvYva‡VvŸ‡Z[:¢[Y¢'¢wWYl‹[YXvŸ†ŒX)mBTZln WYX)¨Št{‡Vˆ‡lnW)æh÷ç

ý

ä:‰$T

tWa‡tWaln¢[Y¢DMz+VX6‰qz+VXva‡l‹[2‰h£XZ†ŒWa‡ln[:‡?EBX‰n‰nXŸvYX'[aWY‡VˆX)†TZv2‰$TŠvat¢wlyx{w=Ts[aln‡Z¼ïB’

‘ c2 ¡‰nXGFõ4’ e X[Y[aXrWa ¡‰nX)vYXWa['¨rw‡Zva[YVlnWaX'‰nXtWYXmulnXW2¢[T[2†XŠö

.<=<

¨rt{TWY[alnW2†Xv_¢[Ts[av_l‹ZŒl‹[Yl$TV¦¤†XŠö_X[_ö'

@

‡ZEw6‡ZvYl‹†Œ WaX'z+VX‰nXv_†XV¦&Æ2^ap)`Œ¾0w6‡mum&XZwX6Z[:XZBm6muX2[aX6mutvBC

ô õ í$ö

B<=<

ð4ë íÔô õ í$ö ð6ñô õ í¹ö ðYð

ïoí¹ö

.<=< ð

‘cf ¡‰nXFH4’

e

X[a[YXWa ¡‰‹X[YWTln[YX)‰nXv2w"Tv2‡?EB‰h£‡Z¤ZXtXV[_[alnWaXW2†ŒXv2[aWTZvYl‹[Yln‡Zv2z+VX†{TsZv2ö b4Z&•ÊTln[=iln‰{ZU£X6va[

t{Tv2t‡vYvaln¥‰nX†q£" ý â ä :†{TZv2ö 

í–ôIHñôKJ=ð ï:í$ö B<=< ð*L

íÔô H ñMdñ H ñ H ñô3NH ð ö'í$ö1ðOLRí–ô J ñ*Mdñ J ñ J ñô3NJ ðQP ö'í$öð

í–ô

NH ñôKJð

ï:í$ö

B<=<

ð1LJíaíÔô,Hñô7J"ðñMdñRH=ñ5H=ñ"í–ô

NH

ñôKJ=ðYð

ö'í¹ö

.<=< ð

‘)c2 ¡‰‹X/F J ’ e X[a[YX¤Wa ¡‰‹X¤vYXWa[Š‰‹‡WavYzVŒX¤‰Ê£‡Z°t{X6V['[alnWYXWvalnm¤V‰n[TsZ¢muX6Z[2VŒZX¤[aWTZvYl‹[Yln‡Z°†X¤ö1ŠX['ö{qp_ZJvaX

[aWY‡VˆX)X6ZB•ÊTln[:†{TZŒv2‰TŠvaln[YV{T[Yl‹‡Zu‡SEEVŒZX_è æüä2†ŒX'‰$T'tWY‡tWYln¢[a¢D Xva[_ˆ¢WYlyx{¢X

í–ô H ñô J ð ï:í$ö B<=< ð*L

íÔô H ñMdñ H ñ H ñô3N

H ð ö'í$ö1ðOLRí–ô J ñ*Mdñ J ñ J ñô3N

J ð ö'í$öð

í–ô NH ñô NJ ð ï:í$ö B<=< ð1LJíaíÔô

H

ñô

J

ðñMdñ H + J

ñ H + J

ñ"í–ô NH ñô NJ ðað ö'í¹ö .<=< ðL

í–ô NH

ñô J ð ï:í$ö B<=< ð1LJíaíÔô H ñô J ðñMdñ H ñ H ñ"í–ô

NH

ñô J ðYð ö'í¹ö .<=< ð

8² ©H˜+«"ÜFªq¶U×°¶U×{˜+µ¸¹ß­sÕ«"¸–ª ´UT ®ÔÕVª{®Ô˜+×

SqTrmu¢6[a§‡+†X†X'ˆ¢Walyx{w"T[aln‡ZE[YXmut‡WYX‰n‰nXŸz+VX'Z‡Vv)T"ˆ‡Zv2†Œ¢ˆX‰n‡tt{¢6X'v=£lnZvatŒl‹WYX'†X‰h£¿TttWY‡+w§ŒX'¢Z+Vmu¢6WT[YlnˆX

†XvPcf†{|4Æ'gŸ‡Vv'¼T"ˆ‡ZvTćV[a¢r‰nXv[aXw§Zlnz+VXvr†Xrˆ¢WYlyx{w=T[Yln‡Z*¨u‰$T™ˆ‡‰n¢Xrz+VXrZ‡Vv'T"ˆ‡Zv¢[YXZ†VX6vPt‡VW

t{‡Vˆ‡lnW2tWaXZŒ†WaXrXZBw‡m&t[aX†X6vŸw‡Z[YWTsl‹Z+[YXvŸ[YXmut‡WYX‰n‰‹X6v'+gŸ‡VŒv)T‰n‰n‡ZŒvo[Y‡V[2†q£¿Ts¥{‡Wa†&•ÊTlnWYX)VŒZEWTttX‰4vaVŒWŸ‰$T

mu¢[Y§‡+†X¢Z+Vmu¢6WT[YlnˆXŸtŒVlnv=i+Z‡Vv2tWa¢6vaXZ+[aX6Wa‡ZŒv'Z‡[YWaX'T‰n¡‡Waln[Y§muX

8²¹±{² —¤ÕŒÖFÖ×®2š6œFµ¤®ÔÕ°*˜+«"ÜFªq¶U×&˜ ´ œ4*˜µÕŒ«=¸{×

Sd£¿TttŒWa‡+w§XP¢6ZVŒmu¢WT[alnˆX¤À»}6ÁÉiUÀ»6ÁaiUÀÃÇ6Ádw‡ZvalnvY[aXu¨¤w6‡ZvY[aWaVŒl‹WYX¤‰h£X6ZvaXm¤¥Œ‰‹XŠ†V¼¡WTst§Xr†q£¿TwwX6vavaln¥ln‰nln[a¢¤¨¤t{TsWa[Yl‹W

†q£VZXw‰$TvYvaX'†U£¢6[T[Yv2lnZln[al$T‰nX)ó2õ:ë í–ô"õí¹ö"ðñô=õsí$öðñBW'õð

Þ&˜ß

´

¸Ô«=¸Ôª

´U8²$±

Û$X®ÔÕ{š=š6×°¶"!»˜+«=Õ«šsÝ

àFâ

ä 6éååä

þqÿ

ææ$åŸóHë íÔô,Hñô7JñBW'ðŠäåæ

þ

û

âŒü ä_è 10

)oô,H¤ä6åæé

ÿ

ææ8÷ç&

â æ þ äŠé

ÿ

ç+æ–÷ù æ–äfö :ä=æFôKJ¤äåæé

ÿ

ææ8÷ç!

â æ þ äŠé

ÿ

ç+æ–÷ù æ–ä_ö

)DW@ä6åærç

â å åæ=ùrä

þUÿü$â -"ç!æ

ü÷ â

å™è›ä ùPä"æ–æ

â æ þ ä ÷

â

åä

ý

äRé‹ä6åhä6éæ

ü÷ â

å¼æÔä"ù2è÷hä6é$é‹ä6å°ä

â

æhäJénäå

þü$ý äYåä6å

æ

â å üæü÷ â åŠåä

â å üú üéüå ä6å þ â

å'é

ÿ

ææ én÷úé4í–ôIHñôKJ=ð

ï:í¹ö

.<=<

ðZYdäŠå

åæ"ùPäräåæI÷ùfè›÷så

¤þ ä þ

ä=ç,+Bæ

è›ä6å

þqÿü¹â

)

-=ç!æ

ü÷ â å[\+í

ðŠäåæé

ÿü$â åæ

â æ þ ä¤æ

ü þ äré¤æ

â å üæü÷ â æ]?0

\+í ð 0æ–ä"ù2èå*häåæ â æè›÷ç!'æühäæ

\+í ðU\+í N–ð

_

0è{énçåU âþ ä þü hä â ä¤ä â æhäŠé‹ä6å ü¹â åæ â æ$å þ äPæü þ äræoä"æ þ ä¤æ ÿ

Uäuå

åæ=ùräW'õ÷ â æüä â æé‹ä6å þ ÷ ââ äå°æÔä=ùfè÷hä6é$é‹ä6å¤åç&™é‹ä6å ü$â åæ â æ$å þ ä°æü þ ä6åEæ â å üæü÷ â åué‹÷ Yå.-"ç+äBé ÿ÷ â åä

æh÷ç ý ä þ â å'é ÿ ææ én÷úé4í–ô"õí¹ö6ðñô=õí$öðYð

qä*sé"çé þ ä_é"PæÔ÷æéüæþ ç è ä þ ä6åK6ésååä6å þqÿ ææ¹å2åä¤æÔäù ü$â én÷Yå$-=ç ÿüé â ä häåæÔä_èé‹çå þ ä'æ â å üæü÷ â å

æ üú6é‹ä6åKBæ üæÔä 2:÷ç dé‹÷ Yå.-"ç+ä'é ÿ÷ âRâ ä hä"æh÷ç ý ä V-"ç+ä þ äå*6éååä6å þUÿ ææ$å þ 1æÔæ–ä ü$â æÔäå

8²‹Ó² ®;ªµ¸–«"Ü4*×Ò¶U×V˜+µ¸$ßo­ÕŒ«=¸Ôª ´ T ®ÔÕV{ª®Ô˜×

Sd£¿T‰n¡‡Waln[a§ŒmuX4†X2Z‡[aWaX2m&¢[a§Œ‡†ŒXo†X2ˆ¢Walyx{w"T[aln‡ZP†X2tŒWa‡tŒWaln¢[a¢6vo[YXmut‡WYX‰n‰‹X6v·¨Ñ‰Tfˆ‡‰‹¢6X2V[aln‰nlnvaX:VZPm&¢w=TsZlnvamuX

†Xt{TsWaw‡VWav_XZBtWa‡s•–‡ZŒ†XVWŸT"ˆXwWaX[Y‡VWTWaWYln WaX'X6ZEw"TvŸ†U£X6w§ŒXw

|q‡VW:wX‰$Ti‡Z¤w=Ts‰nwV‰nXŸ[Y‡V[:†q£¿T¥‡WY†¤‰TÑtWaXm&ln WaX2w‰$TsvavaX_†q£¢[Ts[ ó2õsb4ZŒvaVln[aX'¨tTWa[YlnWd†q£VZX_w‰$TvavYXŸ†q£¢[T[Yv ó¤i

‡Zuw‡Zva[YWaVln[ŸX6[2‡ZBt{TWYw‡VŒWa[ŸX6ZEtŒWa‡•Ô‡Z†X6VW2‰nX)¡WTst§X†Xv_w‰$TvavYXvŸ†U£¢6[T[Yvq’

‘P`+l:‡ZËTs[a[aX6l‹Z+[rVZX&w‰$TvavYXB†q£¢[Ts[av¤óN ë íÔô7sñô{ñBW'ð‡SE ô #3$%*& í$öð'T‰n‡Wavr‡ZËTVŒWTB[YWa‡VŒˆ¢uVŒZ

w§Xm&lnZuˆ¢6WalyxÂTZ+[:‰$T'tWY‡tWYln¢[a¢D @SX'w§XmulnZ¤XvY[q’ó2õ Oó ó óN9C

‘o`+lq‡ZETs[a[aX6l‹Z+[2VZŒX'w‰$TvYvaX†q£¢[Ts[av_†¢–ÄTŠw=T‰nwVŒ‰‹¢6Xi‡ZEX6ZEWYXw§XWYw§ŒX¤VZX'TV[YWaX

‘o`+lq‡ZuZXŠt{XVŒ[ŸT[a[YXlnZ†WYX'VZXZ‡VˆX‰n‰nXw‰$TvYvaX'†q£¢[T[Yv=i+‡ZBWYX[a‡VWaZXŠXZ¼TWYWaln WYX @w‰$TvYvaX'†q£¢[T[Yv)óC

‘o`+lq[Y‡V[YXvŸ‰nXv2w6‰TsvavYXvŸ†q£¢[T[Yv2‡Z+[2¢[a¢Šw=T‰nwV‰n¢X6v=i{Ts‰n‡Wav:‰$TrtWa‡tWaln¢[Y¢ ZU£X6va[2t{Tsv2ˆ¢WYl»x¢X'†{TsZvŸï

&ª«=Õ«"¸Ôª

´b8²$±

)4ö™ä=æUö'Rå÷ â æé‹ä6åuÌUÍ=Î:ÏÐãùr÷ þ éüå â æIhäåÔèä=æü$ý ä=ùrä â ædé"¤åÔè üû8æü÷ â ä=æé_è h÷è ü æ ý üûä

) F%3 ö% & %%í$#íÔô

ñô

ð6ñ "! (+ñ*Mdñ"í–ô

J

ñô J

ðaðCé"=çénäŸénä â ÷ç ý äç&å

åæ "ùPä þqÿü$â -"ç!æ ü÷ â åK_èæü þ äé ÿ â )

üä â å

åæ"ùPä# "!Pä"æ þ äå*÷ â æ ü$â æÔäåPæÔä"ù2è÷hä6é$é‹ä6å*åå÷ üF ä6åçŠè såå ä þ äPíÔô

ñô ð uí–ô

J

ñô J ð

)%$'& ô %=ï ( íYí–ô

ñô

ðñ) "!=ñ"í–ô

J

ñô J

ðYð ý üûdä -=ç+ä é‹ä6å ÷ â æ ü$â æ–ä6å æÔä"ù2è÷hä6é$é‹ä6å¤è÷ç!&èååä þ ä*íÔô

ñô

ð

íÔô

J

ñô J

ð:èä=ç ý ä â æ*"æhä ý üû ä6å þ â å+ "!

)Ÿï( 3$%=ô"ôK%,( íaíÔô

ñô*+ðað1 ä äué ÿä â åä=ùrúénä þ äå ææ$å*sé‹÷úç + æ–æÔä ü â úénäå™è æü þ ä¤éÿ ææIén÷úéoíÔô

ñô ð

ä â

hä6å–èä=æ

â

æ:é‹ä6åKénäåF

õ FAHPä"æOFJ

) ä6åæç

â

ä_è

ü

énä*÷

â

æÔä

â â æ:é

ÿä â åä"ùrúénä

þ

äå*6éååä6å

þUÿ

ææ$åCuæ

ü

æÔä

)dó*3-(.%&äåæé

ÿä â åä=ùrú6é‹ä

þ

äå 6ésååä6å

þUÿ ææ$å

þ

1sé"çé äå

)dó'/2%

äåæ:ç

â ä=ù

ü$â

èäùrä=æÔæ

â æ þ ä ý üû äŠéÑè h÷è üF

æ

10¿ë3254°ó*3-(.%'0¿ë6254¼ó'/2%

0¿ë62

"!

õ

0¿ë F%3 ö% & %%í2ñ)2ñ"í–ô"õ+í$ö1ðñô"õí¹ö'+ðaðYð

#7 ( í$#íÔô=õí$ö1ðñô"õí¹ö'ðYðñ) "!

õ

(ñó*3-(.%"ð

$*& %í$#í–ô"õ+í$ö1ð6ñô"õí¹ö'+ðað6ñ2 (ñó'/2% ð

$*& %í$#í–ô"õ+í$ö1ð6ñô"õí¹ö'+ðað6ñ "!õ ñï( $3%=ô"ô7%"( íaí–ô"õí¹ö6ðñô=õí$öðYðað (ñB'ð

869:<;>=<?-:A@B>CD:<?-CE:6FEGIH"@JD=<K.L:MKON<K.L3P>JE?.LELQK.LRNSH);>:<?-:TLVU6:E=<?T@,:<K-=8

W

?>CE:EFEG<K

í ë2ðYXP

?T@"=MK

#+í–ô

ñô

ð6ñ "!"ñZ('0¿ë~ö%

%í'ð

[ @

í\ZPë62ð

?EJEB>=TL

#íÔô

J

ñô J

ðñM@('0ë ö%

%í\–ð

/%&

%í–ð

"!

J

0¿ë F%3

ö%A&

%\%í#íÔô

ñô

ð6ñ "! (ñMdñ"í–ô

J

ñô J

ðað

[ @ í#+í–ô

J

ñô J

ð6ñ "!

J

(/P ó 3>(<% L]$'&

ô

%"ï

(

íaíÔô

ñô

ðñ) "!ñ=íÔô

J

ñô J

ðað

?EJEB-=TL

8_^-C3B-`E:a@K-CE:6GEC<KDC<B>GEb<KEJEJcKdP>JE?.LcL>KDNSH);-:<?>:TL

#íÔô

J

ñô J

ðñ) "!

J ( 8

$*A&

%í#íÔô

J

ñô J

ð6ñ "!

J

ñïe(2$$%"ô"ô7%"(

íYí–ô

J

ñô J

ðað(+ñ Šð

$*A&

%í#íÔô

J

ñô J

ð6ñ*M@(+ñó'/2%

ð

8 [

@VJEK

ô J K.L:6GEC1;>:<?-:6NSH)?.PcP>K-fE:<?>:A@B-CSgh?EJEB>=TLVB-Ci?jbM;-=A@

X

@;dJc?jfc=<B-fE=A@;-:<;d8

[ @ íÔô

J

#$$%&

í¹ö'+ðað

?cJEB-=TL F%

(

%í–ó'/2%

ð

k

@"C [ @

[

@"C<B-C

/%& %í'ð

/%& %íÔó'/2% ð

k

@"C [ @

k

@,C

W

?-CE:EFEGMK

8Vl<?DfE=<B>fE=A@;-:M;OCSH)?6fEG3m-:E=<KDb<;-=a@

X

@;EK68

F%

(

%í2ð

Etat S7_S10 T12 : !B C5[0;2],C9[0;2] RAZ de {C7}

Etat S5_S9 T11 : !C C3[1;2] RAZ de {C5}

Etat S3_S9 T10 : !A C1[0;2],C8[0;2] RAZ de {C3, C9}

Etat S1_S8 TIOSM : TC RAZ de {C1, C8}

Etat S10 T9 : !B C9[0;2]

Etat S9 T8 : !A C8[0;2] RAZ de {C9}

Etat S8 TIOSM : TP RAZ de {C8}

Etat S11 T5 : !B C3[3;4]

Etat S7 T7 : !B C5[0;2] RAZ de {C7}

Etat S5 T4 : !C C3[1;2] RAZ de {C5}

Etat S3 T2 : !A C1[0;2] RAZ de {C3}

Etat S6 T6 : !E C4[1;3] RAZ de {C6}

Etat S4 T3 : !A C2[0;1] RAZ de {C4}

Etat S2 T1 : !D C1[1;2] RAZ de {C2}

Etat S1 TIOSM : TS RAZ de {C1}

-

’öŸï0Ihähè åä â æ â æé"&å–è üû8æü÷ â ïNoö 0Ihähè åä â æ â æé"'è h÷è ü æ 0ä"ædöŸóîë öŸï >>öb0Ihähè )

åä â æ â æ2ç â ä=ù ü$â°ý üûN â æ þ â å)ï

q² Xª

´

­s®–œdš6¸–ª

´

Sd£¿TttŒWa‡+w§X¤X¦+§{TVŒva[alnˆXuV[Yl‹‰nlnva¢6X¤t{‡VWPˆ¢Walyx{X6WP†X6vPtWY‡tWYln¢[a¢vr[aX6mut‡WaX6‰‹‰nXvŠZ¢wXvYvaln[aXR¢Z‡WYmuXm&XZ+[Ÿ†X&WaXvɑ

va‡VWawX6v)w"TWln‰•ÊTV[2w"T‰nwV‰nXW_‰Ê£XZŒvaXm¤¥‰nX†VB¡WTt§ŒX'†q£¿Tww6XvavYl‹¥Œl‹‰nln[a¢

e £XvY[Ÿt‡VWYz+V‡lhi+Z‡Vv)T"ˆ‡Zv2tWY‡t‡vY¢'VZX

mu¢[Y§‡+†Xr†X¤ˆ¢WYlyx{w=T[Yln‡Z*¨u‰$T™ˆ‡‰n¢Xr†X¤tWY‡tWYln¢[a¢vr[aX6mut‡WaX6‰‹‰nXvz+Vl4[aX6Z[YXu†q£¢ˆ+ln[aX6W)‰h£X¦+t‰n‡vYln‡Z°w‡m¤¥lnZ{T[Y‡lnWaX

XZ¡XZ†WY¢XPtTWŸ‰h£V[Yl‹‰nlnvTs[aln‡Zr†q£VZXŠmu¢[Y§‡+†XX¦+§{TVvY[alnˆXtVŒl‹vYz+Vq£X‰n‰‹XZXŠw‡ZvYlnva[aXŠt{TvŸ¨rw=Ts‰nwV‰nXWŸX6[Ÿmu¢6mu‡WYlnvaXW

‰h£X6ZvaXm¤¥Œ‰‹X¤†ŒV*¡WTst§X&†q£¿TwwX6vavaln¥ln‰nln[a¢4Sd£¿Ts‰‹¡‡WYl‹[Y§muXŠzVŒXuZ‡VvÒT"ˆ‡ZvŠtWa¢vYXZ+[a¢¼T8¢[a¢Blnmut‰$TsZ[Y¢'†{TsZvP‰h£‡VŒ[aln‰

'æ

ü

÷åù ÀÀ6Áaiz+Vl:tXWam&X[PTVŒvaval:†X&Wa¢=Ts‰‹lnvYXWP†U£TsV[aWYXv'‡t{¢WT[Yl‹‡ZvrvaVW'‰nXvrÆ2^ap`¾ @w6‡mut‡vYln[aln‡ZJX['ˆTs‰‹ln†{Ts[aln‡Z

†XBÆ2^ap`¾*i:‹n=CgŸ‡VŒv¤Z‡VvrlnZ+[a¢WYXvavY‡Zvu¨Rmu‡+†¢‰nlnvaX6W'X[rˆT‰nln†XW'†X6v¤tWa‡[a‡+w‡‰nXv¤¨Rw‡Z+[aWTlnZ+[aXvr[aX6mut‡WaX6‰‹‰nXv

w‡m&t‰nX¦+Xv=

'¸4®–¸Ôª2;{µÕÖ4ÜU¸$×

!"$#&%'(#&%'*),+-). #/!102'*3-45)0768456#&%'9):,'*4!1;*6=<&)80?>45',@A;B!1'BC;*'8DFE:GHE8IBJ9K8KLM

EANON='B,4%)0?!1'B$QPR!168S8PT)A3'B!CU-6:C3-V('B5!W;*684!1)CX):.D#&!107'(O'B>Y'BC3'BC4Z@[+A\545'*02\](\!CU2#/!102'O^ '*45!$_O'*45\*`ba a a

#/,6C\56;*4!1):C\):Cc@[)."4d=6:,'aDCU!C'*',5!CUDeMH5Ff8IBgeAhA*K8K8>M>iEj:K:klEf:eM

emnO61):C$J'07)A3oB1',p*\5'*6:q73'^D'*45!Q45'*0?>Y):5!1\5p*\&\545)A;5%68\54!1r8'*\ms'*qA45'BC\!1):C\'*4m6>M>!1;*64!1)8C\(#/%o*\5'3'3)A;*45),684*

#D):1):\5'8D*KKAf[

Lt<Zvu86:,3QD#Du8pB,)CJvuM<O$w'B5C6:C3M'*Sm JPT)MC!1'B/xCy4%'7z+R{8',5!W;*64!1):C|):.WMC!145'-4,6C\!14!1)C}\5+A\545'*07\*Dw):,076

PT'*4%)A3\!Ci@A+A\545'*0~O'*\!1UCJDsEj[,k5Ef:eJ*KKAE

jAm$6:!1\5'B€x?J():Cp8$]C'707p*4%)A3M'3'7{8p,5!W;*64!1):C|3ƒ‚!C45'B,):>YpB,6:„!!…45pT45'90?>Q):,',1'8 <&):1)Ar8'†.…,6C;9):>%)C'‡a _k

^ƒ(‚KJ6\56CMC'8D9K8KAf

Gtx?V@A):ˆ‰):1\ˆ+8$@?@A07):ˆ6QJ)A;*6JPT)A3'Bv<=%'*;5ˆA!CU7.")'*6:k#&!107'2@[+A\545'907\*Q<&)80>M45'B(!13'*3-V 'B5!W;*684!1)CJ>>

E[8,klE8E:LQƒ!1o*U'8J9K8K‰j[

fAtuMM#D)\5\56!C4*PT)A3pB!1\5684!1)Cy45'*0?>\&,p*'BQ,pB>6:,4!1'*\&>Q)M167{6!13M64!1):Cy3'>,):>5!1p*45p*\(45'*0?>Q),'B1'*\*QPTp*4%)A3M)1)8U!1'†3'

;*):C\545;94!1):Ci3M'07)A3oB1'*\O'9461U8)5!14%07'9\3M'{6:!13684!1)CJ€#/%o*\5'3'3M)A;945):,684*Y`b_(^m _O6C;9+8J9K8KAfA

ŠtuMm#D)\5\56!C4* w&&@8!107)C)4kQ!1):C$VOpB5!W;*64!1):C‹."),07'B1'T3'†>,):>5!1p*45p*\-45'90?>Q):,',1'*\-3Q‚C'-6:>>!1;*684!1)CŒ3A!1\545!„Mp*'

45'*0?>\,p*'B"'*6:k#&!107'2@[+A\545'*02\*D#(@Y‚KAfAM>68U'*\je:kG8G^D6:5!1\H"wM,6:C;*'IB56:C{8!1',7*KKAfA

Km6:!1\5',(`ŽC45'B,)>QpB,6:„!!145p45'90?>Q):,',1'‘X"‚6!13M'y3Q‚645)076845'*\‡45'*0?>Q)5!1\5p*\Ty'BC4,p*'h\5):,4!1'8(PTp*07)!,'R3'’(am

]C!1{8'B,\!145p7“('BC5!D^D):!C;*6,p8Q_O6C;*+J*KK8G