123456nothereisastrategyforthecontrollertowinthegameandcanprovidethestrategyasanoutputifaskedoptiont0L0L1L2L3L4Goalxxxx0000xx1x0xFig1AnexampleofTimedGameAutomatonThegraphicaluserinterfacehasbeenaugm ID: 857581
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1 UppaalTigaUser-manualGerdBehrmann1,Agne
UppaalTigaUser-manualGerdBehrmann1,AgnesCougnard1,AlexandreDavid1,EmmanuelFleury2,KimG.Larsen1,DidierLime31CISS,AalborgUniversity,Aalborg,Denmark2LaBRI,Bordeaux-1University,CNRS(UMR5800),Talence,France3IRCCyN,EcoleCentraledeNantes,CNRS(UMR6597),Nantes,FranceAbstract.UppaalTigaisatooltoperformautomaticsynthesisofcontrollersfortimedsystems.Thisdocumentistheuser-manualofUp-paalTigabutshouldbereadjointlywiththeUppaaltutorial[BDL04].1IntroductionTigaispartoftheUppaaltoolboxforvericationofreal-timesystemswhichprovidesseveralvericationtoolssuchas:Uppaal1[BDL04](Real-timeVer-ication),Cora2[BLR05](Real-timeScheduling),TROn3[LMN05](OnlineReal-timeTesting),Tiga4(TimedGames),CoVer5(Test-caseGeneration)andTimes6(SchedulabilityAnalysis).Tigaisimplementingarealon-the-\ryalgorithmtosynthesizewinningstrate-gies[LS98,CDF+05].Sinceourrstprototypein2005[CDF+05],Tigahasim-provedofseveralordersofmagnitudeandisnowreadytodealwithindustrialcasestudies.Moreover,allthefeaturesofUppaalarenowsupportedallowingtheusertohavearichspecicationlanguage(integervariables,templates,arrayofvariables,...)tocreateitsmodels.OurinputmodelsarespeciedthroughanetworkofTimedGameAu-tomata[MPS95](TGA)whereedgesaremarkedeithercontrollableoruncontrollable(seeFig.1).Thisdenesatwoplayersgamewithononesidethecontroller(masteringthecontrollableedges)andontheothersidetheenvironment(mas-teringtheuncontrollableedges).WinningconditionsofthegamearespeciedthroughTCTLformulae.Bynow,Tigasupportsbothreachabilityandsafetygames.Givenamode
2 landwinningconditions,Tigaisabletosayif'
landwinningconditions,Tigaisabletosayif'yes'or 123456 'no'thereisastrategyforthecontrollertowinthegameandcanprovidethestrategyasanoutputifasked(option-t0). L0 L1 L2 L3 L4 Goal x x x x x1;x:=0 xFig.1.AnexampleofTimedGameAutomaton.Thegraphicaluser-interfacehasbeenaugmentedtodealwithgamesmodels.Amongotherthings,thesimulatorallowstheusertoplayagainstthestrategiessynthesizedbyTigainordertogivetheunderstandingofwhatthestrategyis.Thisuser-manualiscoveringthespecicitiesofTigacomparedtotheba-sicUppaaltool.Itis,then,stronglyadvisedtostartwiththeUppaaltuto-rial[BDL04]toknowaboutthebasicsofUppaalbeforereadingthisdocument.Werstdeneourgamemodel(section2)andhowtospecifygames(sec-tion3),thenweexplainwhatarestrategies,howtoqueryforacontrollerahowtoplaywithitandhowtointerpretresults(section4).2TimedGameModelOurformalismisbasedonnetworksofTimedGameAutomata(TGA)asde-scribedin[CDF+05,MPS95].Givenanetworkoftimedgameautomatawedenetwotypesofgames,namelyreachabilityandsafetygames.Thissectionbrie\ryre-callsthedenitionofnetworksoftimedgameautomata,reachabilityandsafetygamesandthenotionofstrategyoveragame.Wesupposeherethatthereaderisalreadyfamiliarwithtimedautomataasdenedin[BDL04].2.1TimedGameAutomataLetCbeanitesetofreal-valuedvariablescalledclocks.Wenote(C)thesetofrectangularconstraints'generatedbythegrammar:'::=xkj''wherek,xCand2f;;0.4;䍕 ;g.ATimedGameAutomaton(TGA)isatimedautomatonasdenedin[BDL04]suchthatA=(L;l0;C;Act;E;I)withitssetofactionsActActccActupar-titionedintocontrolla
3 ble(Actc)anduncontrollable(Actu)actions.
ble(Actc)anduncontrollable(Actu)actions.Listheset2 oflocations,l0Ltheinitiallocation,ELActB(C)2CLthetran-sitionsoftheautomatonandI:L!B(C)thelocationinvariants.Fig.1.givesanexampleofatimedgameautomaton.ThesemanticsofatimedautomatonA=(L;l0;C;Act;E;I)isdenedasalabelledtransitionsystemhS;s0;!iwhereSLRCisthesetofstates,s0=(l0; 0)istheinitialstate(where 0isaclockvaluationinwhicheveryclockvalueis0)andSfR00ActgSisthetransitionrelationsuchthat:{(l;u)d !(l;ud)ifd0:0d0dud0jI(l){(l;u)a !(l0;u0)ife=(l;a;g;r;l0)Es.t.ujandu0=[r0]uandu0jI(l0).TimedgameautomatacanbecomposedintonetworksoveracommonsetofactionsandclocksconsistingofntimedgameautomataAi=(Li;li0;C;Act;Ei;Ii)wherethesetofactionsoverthenetworkisgivenby ActActActandissuchthat Act Actc Actuwhere ActcActcfActc[fggand Actu Actn Actc.Notethatthiswayofdeningcontrollableanduncontrollableactionsonthenetworkgivesprecedencetotheenvironmentoverthecontroller.Wealsonotealocationofthesystemasavector l=(l1;:::;ln).WeextendtheinvariantfunctionssuchthatI( l)=inIi(li).Andwewrite l[l0i=li]todenotethevectorwheretheithelementliof lisreplacedbyl0i.SemanticsofanetworkofntimedgameautomataAi=(Li;li0;C;Act;Ei;Ii)isdenedasatransitionsystemhS;s0;!iwhereS(L1Ln)RCisthesetofstates,s0=( l0; 0)where l0=(l10;:::;ln0),istheinitialstateandSfR0 ActgSisthetransitionrelationsuchthat:{( l;u)d !( l;ud)ifd0:0d0dud0jI( l);{( l;u)(a;) !( l0;u0)ifla;g;r !l0s.t.ujandu0=[r0]uandu0jI( l);{( l;u)(ai;aj) !( l0[li=l0i;lj=l0j];u0)ifliai!;gi;ri !l0iandljaj?;gj;