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Problmatique du test 8  `Test = analyse dynamique de programmes pour dtecter des fautes par rapport une spcification. `" vrification de modle : exhaustivit impossible en pratique Slectionner les tests : partir du code : test bote blanche/structurel partir de la spcification : test bote noire Activit coteuse et souvent artisanale Formaliser est incontournable pour Amliorer la qualit des tests Diminuer le cot du testnan)n#Z"ZZ-7%1033(3"                                                                        'Test de conformit de systmes ractifs(((Z        2. Gnration de tests la vole [CAV96-99,SCP97-00,IWTCS96,Cfip97, IDPT02,TSI03, & ]*V!(4fZ        5 Motivations: viter l explosion combinatoire Traiter des systmes non dterministes Cadre thorique: Thorie du test des IOTS [Tretmans 95-96] Origines: LTS [DeNicola-Henessy84, Abramsky87, Philips87, Brinksma88] Contribution: Formalisation des objectifs de test Slection de tests la vole ! vrification la vole H+H] ___Hf  8  f       C a                           `                    Le modle: les IOLTS(&    LIOLTS (input/output LTS) : ~ IOTS [Tretmans96], IOA [Lynch88] smantique de systmes ractifs non-dterministes spcifications, implmentations, tests, objectifs" f___ ff 332?                   W"Comportements visibles par le test##(4      \Le test permet de contrler les entres et observer sorties et blocages (timers) distinguer les blocages spcifis dans S des autres ! calculer les blocages sur S j\4\3c*     /                      GRelation de conformit(&      TCas de test et excutions  X)#Principes de la gnration de tests$$(4       ~Dtapes de la gnration(  UProprits des tests gnrs  V Correction: possibilit de rejet non conformit  Exhaustivit : non-conformit possibilit de rejet Tests arborescents ! adapts au non-dterminisme observable< (()   (                                  IGnration la vole   Constat : S trs grand ou infini |S| k" |TC| Ide: viter de construire S construction paresseuse de S, D(S), Vis(S), Vis(S)xTP,CTG pilote par TP utilisation d une reprsentation implicite des IOLTS algorithmes bass sur DFS &)&C2?2    s Implmentation: TGV   `Exprimentations dans des domaines varis. Distribution: CADP, Agedis Transfert: ObjectGodeaxa@B       Rsum de la contribution(  Algorithmique de la gnration de tests sur des modles numrs Fonde sur une thorie du test bien tablie Implmentation efficace: gnration la vole (TGV) Largement publi Transfert industriel (Telelogic)DBB+i <                                                    %#"3. Test asynchrone et test rparti##( #  W4. Gnration de tests symboliques [RBJ-IFM00, CJRZ-Tacas01, CJRZ-Esmart01,CJRZ-Esec01]$X#(5f@       6 LMotivations: viter l explosion combinatoire ! donnes numres  Programmes de test gnriques (non instancis) Approche Modle symbolique: IOSTS (~ autres modles similaires) Smantique IOLTS ! thorie du test identique Gnration symbolique: S , TP " IOSTS TC " IOSTS Slection par utilisation de l interprtation abstraite [Cousot77] Excution : Instanciation des entres ! rsolution de contraintes g 81c 8 i Cc     B  CccCB9    f  8                                                     "                       Modle IOSTS   ^Smantique [[.]]: IOSTS IOLTS M [[M]]x0(C(((C(((((  & _/Gnration symbolique  Oprations syntaxiques dont la smantique commute avec les oprations sur les IOLTS : Produit: xs Calcul des blocages: Ds Dterminisation: dets Vis(PS) = dets(Ds(S xsTP )) Traces([[ dets(Ds(S xsTP)) ]]) = Traces(det(D([[ S ]] xe [[ TP ]])) Slection : reach, coreach non calculables de manire exacte ! sur-approximations reacha et coreacha2VZ;ZZaZZfZ@ f3f3f3Gf3f3f3f3f3f3f3  f3 E f3  f3  f3  f3  f3 E f3  f3  f3 E f3  f3  f3 E f3  f3     f3  f3  f3 G f3  f3  f3 G f3  f3  f3 G f3  f3    3   G 3   G    G   3  3   G       0  3  cK K`                                  %       h5&Consquences de la sur-approximation ''(&   NExemple: calcul du produit   LSlection du graphe de test  V@Excution: instanciation des constantes et rsolution des gardesAA( A #Outillage: STG   Gnration Oprations symboliques Analyse approche par interprtation abstraite (NBAC) Excution Compilation C++/Java Rsolution de contraintes (Omega) Exprimentations : CEPS Distribution : prvue fin 2004 PNP P8PP "N" "8"" ""  "1Contributions la gnration de tests symbolique22(Z          ,Originalit : Gnration de programmes de test Traitement de systmes non-dterministes Thorie indpendante de l approximation Cadre formel : ! garantie de proprits des tests : correction, exhaustivit Outillage (STG) : gnration et excution Publications y7 F8 y; !&K   ) 5. Bilan (&   Contribution originale l algorithmique de la gnration de tests Techniques numratives la vole Techniques symboliques Non dterminisme Asynchronisme et rpartition Cadre formel proprits des tests Outillage et exprimentations Passage l chellelEZjZZZEj 3  }CTravaux connexes  Modles voisins : FSM, EFSM (voir e.g. [Lee-Yannakakis 96]) contrle et donnes Autres techniques base d objectifs : MSC [Grabowski et al 93] Utilisation de model-checkers (e.g. [Engels et al-97, Hong-Lee et al. 01]) limits dans le traitement du non-dterminisme Autres techniques symboliques : Simulation symbolique + rsolution de contraintes (pb de chemins) Smile [Eertink94] TVeda [Clatin et al. 95], Agatha [Lugato et al. 02], Gatel [Marre], BZ-TT [Legeard et al] + spec algbriques [Gaudel-James99, Lestiennes-Gaudel02], Abstractions: EFSM [Petrenko et al 99-04]CZ?P"PB  + 3f)3f%3f0!B 3f3f3f 3f 3f&3f3fb)    L             )  V                           J     *!FDfis de la gnration automatique de tests pour les systmes ractifsGG(            Accrotre l usage industriel des mthodes formelles pour le test : ! qualit ! cots L automatisation du test est un levier pour une meilleure introduction des mthodes formelles dans l industrie. Passage l chelle de l automatisation traiter efficacement des systmes plus complexes en taille et expressivit Mthodologies d utilisation et de combinaison des mthodes formelles Ca  c ofK 8                                                                        k9 Perspectives (  Accrotre l expressivit des modles : contrle, donnes, concurrence, communication, temps Amliorer les critres de slection : objectifs, couverture, hypothses de slection Combiner les techniques pour la gnration de tests : model-checking, preuve, analyse statique, interprtation abstraite, rsolution de contraintes, ordres partiels, Combiner les mthodes de validation dans le processus de dveloppement : Vrifications statiques, contrle, testx$6$14rJ)          $                    "                                          .'Quelques travaux en coursN      Vrification et test de proprits de sret Tester violation d une proprit de sret valide sur la spcification [RMTJJ-Testcom04] Couverture en model-checking et gnration de test [Hoskote et al. 99, Chockler et al. 01] Proprits couvrantes tests couvrants Test de robustesse Tester la prservation de proprits de sret en prsence d alas Contrle et test Contrler la conformit d une implmentation [JMRT-MSR03-CDC04-IJPR04]BsPPcP " H c f"31fc""C""5""  f  8         H   !                                                 -&Fin    o:=Systmes infinis: dtection, reprsentation et model-checking>>(h         !Non-bornitude Indcidable [BZ81] Dcidable ds sous-classes [e.g. Fin82] Dtection par CS sur files (CNS pour ss-classe + gnrale) Reprsentation du systme infini par grammaire de graphes Model-checking de CTL sur grammaire de graphe [J-Stacs91, JJ-TCS93, QJ-Segragra95, QJ-FortePSTV96]I5 ff :fi5f                                           6 p;Vrification la vole(N       Motivation: viter l explosion combinatoire Spec S invalider P en construisant S partiellement par DFS + remplacement [Holzmann] Non-bornitude Model-checking de LTL(sq. finies) Bisimulation [FM-CAV91] [JJ-CAV89,JJ-CAV91, FJJM-FMSD93]J! %` ______1   gf  fD                                 - q<Observation de traces d excutions rparties [JJJR-ICDCS94]$D5(f@       &Test asynchrone [JJTV-FP99]" f&    '9Distribution de test pour le test rparti [JJKV-FP98]$:.( f&#   r=Vrification visuelle: dessin 3D de graphes d tats [J-GD94,J-Cfip94] (N:(Gfh        # +$Travaux en cours4    "Couverture en model-checking / test pour S " y, s couvert si mutant(S,s) " y couverture structurelle ! MdF sur FSM couverture de dpliage ! MdF sur Traces, ioco S " y, s couvert pour y, q ssi Ssqq " y Test de robustesse Test de programmes virgules flottantes $*Vn$aa aaa a %$$(a(,,004a44a44`44a44`44h44h44488?" dd@,3ft?d3fd@ @` n?" dd@   @@``PT    @ ` `:p>> {sL (  L L 6t3 " `} 3 _'Cliquez pour modifier le style du titre(( L L 0t3 " `  vCliquez pour modifier les styles du texte du masque Deuxime niveau Troisime niveau Quatrime niveau Cinquime niveau4w  L 03 "6v 3 j*0  B L s *D3fo"z'Yz,$ 0H L 0޽h ? fff̙___PPT10i. η+D=' = @B +  Niveau @  P(  P P 6 9 #" `  9 _'Cliquez pour modifier le style du titre((  P 09 " t4  9 p8Cliquez pour modifier le style des sous-titres du masque99  P 09 "6v 9 j*0  f P 03f3f"  B P <D3fo?"0@NNN?Nqf  P C 0AlogoirisaPt"Y` H P 0޽h ? fff̙___PPT10i. η+D=' = @B +2@ 0 phB(  h h 0> P   > T*   h 0l!>    > V*  d h c $ ?  >> h 0L$>  0 > vCliquez pour modifier les styles du texte du masque Deuxime niveau Troisime niveau Quatrime niveau Cinquime niveau4w  h 6(> _P  > T*   h 6H.> _  > V*  H h 0޽h ? 3380___PPT10. 0ާ 0(l(  l l 0tg P   g `*    l 0g    g b*    l 6g _P  g `*    l 6g _  g b*   H l 0޽h ? 3380___PPT10. `SA_K0 @0(  x  c $x9P  9 x  c $L9P \E 9 H  0޽h ? ̙33___PPT10i.^aՂ+D=' = @B + @@K0    l (  lr l S 4j>L `}  > T l 09 @&,$D 0 Exemples: protocoles tlcom, systmes embarqus, systmes contrle/commande, etc. Complexit, rpartition croissante, criticit Ncessit de fiabilit / matrise des cots mthodes formelles @\r3                 s  l Hl> ?"6@ NNN?N bP100$ $   l Hs> ?"6@ NNN?N. 1 bP200$ $  B l@ BD?"0@NNN?Np r  l B y>G)HM?"0 NNN?NE aEnv 0$  B  l BD?"0@NNN?NbcIB  l BD?"0@NNN?NxyI  l B ?"6@ NNN?NMp(@H l 0޽h ?l fff̙$ TIMING|55.___PPT10n.+ksDB' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*l%(+0 @7K0 y*q*0{)(     B>G3#H]Q?"0 NNN?Ni aEnv 0$  r  S >L `}  >   B ?"6@ NNN?Nh8   B ?"6@ NNN?NH8  %  N> ?"6@ NNN?Np8xh i Transmitter 0     "  NЊ> ?"6@ NNN?NH8 x@ fReceiver 0    B  <D?"0@NNN?Nxhh`B  <D?"0@NNN?N (`B  <D?"0@NNN?N8  H> ?"6@ NNN?N<0C XRQ(data) 0       H> ?"6@ NNN?N\Nt SCNF 0     H> ?"6@ NNN?N,  Y IND(data) 0    2  T> ?"6@ NNN?N @   Uw$0c   2  T> ?"6@ NNN?NH(  Us$0c    "@ <?"0@NNN?N   # <?"0@NNN?N  r $ TGnRHI?"0@NNN?Nc @  &@ <?"0@NNN?N  ' Nh> ?"6@ NNN?Nld Y d:=0 b:=0 0      ( Nģ> ?"6@ NNN?N fK  d?RQ(d)/ !DT(d,b)$0c   t ) N> ?"6@ NNN?N _  <br `" bit ?ACK(br) / !DT(d,b) $0c 4     U * N> ?"6@ NNN?N _  br = b ?ACK(br) / !CNF b:=1-b$0c 4       0 H4> ?"6@ NNN?N4 ,  Tb:=0 0   8  k  z k- 2 ! N> ?"6@ NNN?N   Us$0c  b ,B NZG@pHVI?"0@NNN?N B b - NG0HekI@G?"0@NNN?N B a . Hȼ> ?"6@ NNN?N7\  'br = b ?DT(d,br) !IND(d) !ACK(b) b:=1-b$(0(c 4      / 6?"0@NNN?N ` h  1 H8> ?"6@ NNN?NFu k  Rbr `" bit ?DT(d,br) !IND(d) !ACK(b) b:=1-b$*0*c 4      6 ND> ?"6@ NNN?NG4 +  \ACK(bit)$ 0 c    8 N> ?"6@ NNN?N /  ` DT(data,bit)$ 0 c   8L  8  J# < $ B K 6D?"0@NNN?N @ B L 6D?"0@NNN?N @ x B M 6D?"0@NNN?N B N 6D?"0@NNN?N( 8 8 B O 6D?"0@NNN?N0 B P 6D?"0@NNN?N( 8 8 8L  8  Q# Z  B R 6D?"0@NNN?N @ B S 6D?"0@NNN?N @ x B T 6D?"0@NNN?N B U 6D?"0@NNN?N( 8 8 B V 6D?"0@NNN?N0 B W 6D?"0@NNN?N( 8 8  { <@> ?"6@ NNN?N lM,$D 0 Processus concurrents, communication (interne-externe), structure de contrle, donnes. Langages de spcification : SDL, Lotos, UML, etc00Z23@&  S   H  0޽h ?"#$ & !!, !!-!/ fff̙___PPT10.8Xq+c<D~' = @B D9' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*{Z%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*{Z%(+R @9K0    +ti (  tx t c $<>L `}  > x t c $>LpF > > t HX> ?"6@ NNN?N   "tat: (localits, val(var), files)6#0!cc # b t HH> ?"6@ NNN?NX * ,  Ftat : (localits, val(var), files)6$0"cc $ B t <D?"0@NNN?N PX0  t <> ?"6@ NNN?N$ N  Waction  0  j 't C BA*bitalt_loose_ok_iminZ  (t <<> 3?"6@ NNN?N B,$ 0 ;Explosion combinatoire, voire infinitude (donnes, files) P<0e33e3 <  )t 0>   )Systme de transitions (LTS) S = [[Spec]](*   # B *t BD3>?"0@NNN?Nh  +t Hz ?"6@ NNN?ND jsimulation exhaustive$03  H t 0޽h ? fff̙ & TIMING |62.8___PPT10.Pu+DO' = @B D ' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(t%(+8+0+(tz +p @+pcK0   `  PY (  Px P c $zL `}  z   P <Pz :  !Proprit P (automate, logique)("0 4     XB P 0Do* P 0|z D0    P 6,z L <Vrification de modle S " P ?$0f4      D  P 6"z ( ,$ 0 $Test: Imp conforme S ? I conf S ?"%0%f@      v  P < 'zA  nSpcification Spec S = [[Spec]] comportementaleD80 4     B  P@ 6Do! | ,$@ 0j P H /z?"6@ NNN?N  ,$@ 0 Implmentation Imp$0&    P HD4z ?"6@ NNN?N ,$ 0 Hyp: Imp modlisable par I(0gf4    H P 0޽h ? fff̙7 & TIMING |34.4 ___PPT10.nPO)+[=D ' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* P%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* P%(++0+ Pz ++0+Pz ++0+Pz +| @ЩK0 7:/: 6J@8(  r  S DzL `}  z    fGNHvd @?"6@ `NNN?N;y  HFz?"6@ NNN?Nl$D 0U 0U 0 hVrification la vole 0   r   HJz?"6@ NNN?N,$D 0 Non bornitude de files de CFSM 0 &      HpOz?"6@ NNN?N X ,$@ 0 ;Gnration de tests symbolique (IOSTS) (E. Zinovieva, 00->) <0< &+    b  H0Tz?"6@ NNN?N6 ,$D 0 xModel checking 0 &   W  HXz?"6@ NNN?N ) ,$D  0 mGen. test (FSM) 0    "  NG*HI___)?"0@NNN?N2  ,$@  0"  HH`;I___)?"0@NNN?N ,$@ 0"  HH@I___)?"0@NNN?NWZ,$D 0v # HP^z?"6@ NNN?N*TE,$@ 0 "Test et contrle (V.Tschaen, 01->) #0# &    8  .8  <cz ?"6@ NNN?N P880     <gz ?"6@ NNN?N P920      <tkz ?"6@ NNN?N P910      <oz ?"6@ NNN?N  P930     <rz ?"6@ NNN?N@ Q  P960    ! <`vz ?"6@ NNN?N P890    " <zz ?"6@ NNN?N P900    $ <}z ?"6@ NNN?N (  P940    % <Lz ?"6@ NNN?N+ <  P950    & <z ?"6@ NNN?NT e  P970    ' <z ?"6@ NNN?Nh y P980    ( <8z ?"6@ NNN?N} P990    ) <܏z ?"6@ NNN?N P000    * <z ?"6@ NNN?N P010    + <$z ?"6@ NNN?N P020    , <Țz ?"6@ NNN?N P030    - <lz ?"6@ NNN?N P040      <z?"6@ NNN?N{ SADP 0      Hz3?"6@ NNN?N{ WAAR$0     <z?"6@ NNN?N{ UPAMPA 0   / <4z?"6@ NNN?N{ eVerTeCS 0   0 B ?"6@ NNN?N{6V 1 Nذz?"6@ NNN?Nay_ ,$@ 0 f Vrification* 0    l 2 Ntz?"6@ NNN?Ne vs,$D 0 |"Test de conformit & Observation*#0"  #  4@ TZGwH|Iw___)?"0@NNN?N ,$@  0" 5 NGHI2___)?"0@NNN?N % ,$@ 0" 6 NGHiI___)?"0@NNN?N ? ,$D 0" 7 NGHIh___)?"0@NNN?N ,$@ 0T 8 Hĺz?"6@ NNN?N 5 ,$D  0 j Repr. 3D LTS 0      l R > GR >,$@ 0  NLz?"6@ NNN?Np > BReprsentation model-checking de syst. infinis (YM Quemener,93-96) C0C @      : H ?"6@ NNN?NR )@U 0U 0l <N 7  D  S ,$D 0#  H' = @B DV>' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*1%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*G%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D ' =%(D ' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'9%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(DY' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*5%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*6%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(Dq' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*6%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*7%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*7%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*7%(D# ' =%(D ' =%(D!' =4@BBBB%(D' =,543*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D!' =4@BBBB%(D' =,543*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D!' =4@BBBB%(D' =,543*3>Bfillcolor=@BPB<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*++0+z ++0+ z ++0+z ++0+z ++0+z ++0+#z ++0+1z ++0+2z ++0+8z ++0+z ++0+z ++0+Hz + @K0 x@(  xr x S x L `}    x c $LL `  "P@08XH x 0޽h ? fff̙___PPT10i.@[+D=' = @B +  @ pK0 @0V(  0r 0 S L `}    0 c $L `<$D 0  H 0 0޽h ? fff̙___PPT10.p+YD' = @B DQ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0)Q%(DL' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0Qt%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0t%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(+" @@K0 @+P(  r  S TBL `}     c $C  Pb: tester qu une implmentation I (bote noire) est conforme sa spcification S (suppose correcte).hg  g  h   6h>3[   gSpcification S n     6O  lImplmentation I f    <T 1  T I conf S ?  =  z       !,$D 0   <X   OVerdict   ZB   s *D  X  @ 01  XB  0Dox + x XB @ 0Do    <,R] W  \S!*      <`   \S?*      <+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =-o6Bwipe(up)*<3<*!++0+ ++0+ ++0+ ++0+( +N @mK0 l(  r  S L `}     c $L `<$@ 0  "  @H  0޽h ? fff̙  ___PPT10 .+ED ' = @B Di ' = @BA?%,( < +O%,( < +DL' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Vg%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*g%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DL' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* E%(+N  @K0  LP(  r  S hL `}      0  L"6 ? `  X2  0O  Bo N?A3f  X2  0k O X2  0 3 X2   0 O; X2  @ 0?X2   0 ?; dB  @ <D++{ dB  @ <D + dB  <D C+ dB  <D#  dB  <D3 3[ dB  <D ck  Bā _  N?Bf    B|Ɂ ou O! Z3f    BĹ   O! Y3f    B<3   O! X3f    BЁf   Kt3f    6ՁT3$  ]S,3f 3f    <|ف ?"6@ NNN?Nb ,$ 0 non-dterminisme observable : Les entres ne dterminent pas les sorties non-contrlabilitT`0g,cct           r  <h ?"6@ NNN?N m ;,$ 0 non-dterminisme (au sens des automates) incertitude supprim par dterminisationTU0)gfc*ct           @ <?"6@ NNN?N WN ,$D 0 @ <f?"6@ NNN?N R ,$D 0^B G@ 6D+  R2 H s * 3 ^B I 6D+  J <b OoI  N?Bf   K <H o} O! X  R2 L@ s *H  0޽h ? fff̙ T TIMING8|37.2|9.8|15.1|24.9|72.4|15.l ___PPT10L .@V+?fD' = @B Dk' = @BA?%,( < +O%,( < +D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+p+0+ ++0+ +} @;K0 ijaj=Cxi(  xx x c $L `}    x  6  L"6 ? `  @ F j  x lZ2 x s *e x <|  N?A3f  Z2 x s *aeZ2 x s * ) Z2  x s * e1 Z2  x s *]  Z2  x s *E 9 fB  xB 6DAAqfB  xB 6D A fB x 6DYA  x  BCDE F0@1 1) fB x 6D Y fB x 6DI) q fB x 6Dy)   x <do /  N?B3f   x <w 7  O! Z3f   x <P  O! Y3f   x <U   Mt3f   x <   O! X3f   x <" + %  Mt3f   x 0jI ]S,3f 3f  L x <* 3?"6@ NNN?NY ,$@ 0 nComportements visibles de rfrence. 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Zt?"0@NNN?NlG { f,$  0 \TP* f  C  ZD?"0@NNN?N y ' ,$ 0 MCTG   B  TDo?"0@NNN?No ( ,$@ 0B  ZZDo?"0@NNN?N  ,$@ 0R  T ?"6@ NNN?N! ,$ 0 \TC0    6 _"`  NVis(S)  W  Zx?"0@NNN?N  ,$ 0 a Vis(S)xTP      B  ZZDo?"0@NNN?N' L ,$@ 0B  ZZDo?"0@NNN?N ,$@ 0B ' BD?"0@NNN?N,$@ 0R ( T ?"6@ NNN?NP ,$ 0 \TC0   ) H$ ?"6@ NNN?NL  ,$ 0 ?Algorithme non-dterministe [Tretmans96] [Lestiennes-Gaudel02],@0#f&   $ El    5* @,$D 0B B BD?"0@NNN?N@ P  ! N ?"6@ NNN?N   V!A$0c  !R , Z ?"6@ NNN?N' H  Q? 0  B - BD?"0@NNN?NX@ `  . 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