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ComparingPetriNetandActivityDiagramVariantsforWorkflowModelling–AQuestforReactivePetriNetsRikEshuis?RoelWieringaDepartmentofComputerScience,UniversityofTwenteP.O.Box217,NL-7500AE,Enschede,TheNetherlands,{eshuis,roelw}@cs.utwente.nlAbstract.Petrinetvariantsarewidelyusedasaworkflowmodellingtechnique.Recently,UMLactivitydiagramshavebeenusedforthesamepurpose,eventhoughthesyntaxandsemanticsofactivitydiagramshasnotbeenyetfullyworkedout.Nevertheless,activitydiagramsseemverysimilartoPetrinetsandonthesurface,onemaythinkthattheyarevariantsofeachother.Tosubstantiateordenythisclaim,weneedtoformalisetheintendedsemanticsofactivitydiagramsandthencomparethiswithvariousPetrinetsemantics.InpreviouspaperswehavedefinedtwoformalsemanticsforUMLactivitydiagramsthatareintendedforworkflowmodelling.Inthispaper,wediscussthedesignchoicesthatun-derliethesetwosemanticsandinvestigatewhetherthesedesignchoicescanbemetinlow-levelandhigh-levelPetrinetsemantics.WearguethatthemaindifferencebetweenthePetrinetsemanticsandourseman-ticsofUMLactivitydiagramsisthatthePetrinetsemanticsmodelsresourceusageofclosed,activesystemsthatarenon-reactive,whereasoursemanticsofUMLactivitydiagramsmodelsopen,reactivesystems.Sinceworkflowsystemsareopen,reactivesystems,weconcludethatPetrinetscannotmodelworkflowsaccurately,unlesstheyareextendedwithasyntaxandsemanticsforreactivity.1IntroductionPetrinetsareapopulartechniqueformodellingthecontrolflowdimensionofworkflows.Whenmodellingworkflows,peopletendtodrawnodesthatrepresenttasksoractivities,andarrowsbetweenthenodesthatrepresentsequencingofactivities.TheresultingdiagramslooklikePetrinets,andsoPetrinetsseemanaturaltechniqueformodellingworkflows[2,22].Thefollowingargumentsareof-tenusedtosupportthis:Petrinetsaregraphical,theyhaveaformalsemantics,theycanexpressmostofthedesirableroutingconstructs,thereisanabun-danceofanalysistechniquesforprovingpropertiesaboutthem,andfinallytheyarevendor-independent.Mostoftheseargumentsdonotrefertothedomainofworkflowmodelling(onlytheroutingargumentdoes)andpointoutadvan-tagesofPetrinetsingeneral.Moreover,sincePetrinetsalreadyexistedbefore?SupportedbyNWO/SION,grantnr.612-62-02(DAEMON).workflowmanagementsystemswereinvented,theirsemanticsisnotspecificallyintendedforworkflowmodelling.SononeoftheseargumentsstatewhyandhowPetrinetsareusefulforworkflowmodelling.Thisisunsatisfactoryforanalysispurposes,sinceanalysingaPetrinetworkflowmodelpresupposesthatthePetrinetmodelstherealworkflowaccurately.Recently,UMLactivitydiagrams[56]havealsobeenusedforworkflowmod-elling.Theytooaregraphical,usebubblesandarrows,arevendor-independent,andcanexpressmostdesirableroutingconstructs.Unfortunately,theOMGse-mantics[56]isnotformal(norprecise),anditisnotintendedforworkflowmodelling[28].WethereforedefinedtwosemanticsforUMLactivitydiagramsthatareintendedforworkflowmodelling[27,28].Thegoalistousethesese-manticsforanalysingworkflowmodelsinactivitydiagramnotationbymeansofmodelchecking[16,25].Thefirstsemanticsisahigh-levelsemantics,basedupontheStatematesemanticsofstatecharts[37],thatiseasytoanalyse(bothforacomputerandforaperson)butsomewhatabstract.Bycontrast,thesecondsemanticsislow-levelandresemblesboththebehaviourofanabstractworkflowsystemandtheinformalOMGsemanticsofUMLstatemachines,butitismoredifficulttoanalysethanthefirstsemantics.WehaveimplementedverificationsupportusingmodelcheckingforthefirstsemanticsinourdiagrameditingtoolTCM[17,25].Inthispaperwediscussthedesignchoicesthatunderliebothourformalexecutionsemantics.Sinceourpurposeistomakeanalysisofactivitydiagramworkflowmodelspossible,thesemanticsmustbeanaccuraterepresentationofworkflowbehaviour.Ourdesignchoicesarethereforemotivatedintermsofthedomainofworkflowmodelling.Usingthesechoicesasayardstick,weinvestigatehowwellPetrinetscanmodelsomeimportantaspectsofworkflowmodelling.WehopethisprovidesrelevantargumentsforandagainsttheclaimthatPetrinetsareusefulforworkflowmodelling.Thisapproachmayseemsubjective,sinceotherpersonsmightmakeotherdesignchoices,andconsequentlytheymightdrawotherconclusionsaboutthesuitabilityofPetrinetsforworkflowmodelling.However,wethinkthatthechoiceswehavemadeinoursemanticsarereasonable,becausetheyaremoti-vatedbythedomainofworkflowmodelling.Evenifonedoesnotagreewiththechoiceswemade,ourdiscussiongives–wehope–moreinsightinpossibleanswerstothequestionwhatactuallyisaPetrinet[20].Ourmostimportantdesignchoiceisthatthesemanticsforactivitydiagramsmustbereactive.Thetoken-gamesemantics,whichischaracteristicforPetrinets,doesnotrepresentreactivity,whichischaracteristicofworkflowsystems.APetrinettransitioncanfireifallitsinputplacesareinthecurrentmark-ing[48,51].Butinareactivesystematransitioncanbetaken(fired)ifallitssourcenodes(inputplaces)areinthecurrentconfiguration(marking)anditstriggereventoccurs[37,56].Thistriggereventisaneventintheenvironmentofthesystem,thatthesystemwillreacttobytakingthetransition.AlthoughPetrinetsinourviewarenotreactive,wewillstudydifferentwaysofsimulatingreactivebehaviourindifferentPetrinetvariants.Inthesequel,wepresupposesomebasicknowledgeofPetrinetsandhigh-levelPetrinets(seee.g.[40,48