modelling and verifying recursive workflow models...
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ModellingandVerifying
RecursiveWorkflowModels
usingAttributeGrammars
Roman BartákCharles University in Prague, Czech Republic
Workflow isadescriptionofa(manufacturing,business,…)process
– tasksandrelations betweenthem– weuseaspecificnestedstructure
(obtainedbytaskdecompositions)– extraprecedence,
synchronization,andcausal
constraintscanbeadded– process isasubsetoftasksthat
satisfiestheconstraints
BackgroundonWorkflows
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
workflowisobtainedbytaskdecomposition
Theproblemofselectingavalidprocess
containinggiventasksistractable.
However,ifweaddextraconstraintsthenthe
problembecomesNP-complete.
PAR PARALT ALT
NestedWorkflows
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Extraconstraintssimplifydesignofcomplexworkflows.• Causal constraints– definerelationsrestrictingappearanceoftasksintheprocess
• Precedence constraints– definingorderingoftasksbeyondthenestedstructure
• Synchronization constraints– definetemporalsynchronizationbetweentasks(forexamplestartingatthesametime)
ExtraConstraintsinNestedWorkflows
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Canwerepresentnestedworkflowswithextra
constraintsinsome“standard”framework?
– toexploittechniques(suchasverification)forthatframework
– tounifyvariousworkflowmodelingapproaches
Canwerepresenteasilyrecursioninthe
workflow(taskdecompositioncontainsthetoptaskitself)?– tomodelplanningproblems,wherethenumberofactionsisunknowninadvance
Motivation
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Attributegrammarisacontext-freegrammar
S→A.B.CA→ aA→a.AB→ bB→b.BC→cC→c.C
BackgroundonAttributeGrammars
a+b+c+
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Attributegrammarisa context-freegrammarwhere:• extraattributesareaddedtosymbols
S(n)→A(k).B(l).C(m)A(n) → aA(n) →a.A(m)B(n) → bB(n) →b.B(m)C(n) →cC(n) →c.C(m)
BackgroundonAttributeGrammars
a+b+c+
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Attributegrammarisa context-freegrammarwhere:• extraattributesareaddedtosymbols• constraintsconnecttheseattributes
S(n)→A(k).B(l).C(m) [n=k=l=m]A(n)→ a[n=1]A(n)→a.A(m)[n=m+1]B(n)→ b[n=1]B(n)→b.B(m)[n=m+1]C(n)→c [n=1]C(n)→c.C(m)[n=m+1]
BackgroundonAttributeGrammars
anbncn
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Howtogetanattributegrammarequivalentto
thenestedworkflowwithextraconstraints?
– equivalence:process~word
Coreideas:
• nestedstructure→ context-freestructure• taskrelations→attributesandconstraints
TranslatingNestedWorkflowsto
AttributeGrammars
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
UsingstartandendtimeattributesfortasksParalleldecomposition(asinglerule)
Ti(Si,Ei)→Ti1(Si1,Ei1)...Tik(Sik,Eik)[Si =min{Si1,...,Sik},Ei =max{Ei1,...,Eik}]
Serialdecomposition(asinglerule)aspecialformofparalleldecompositionwithextraprecedenceconstraints[Ei ≤ Si+1 ]
Alternativedecomposition(asetofrules)Ti(Si,Ei)→Tij (Sij ,Eij ) [Si =Sij ,Ei =Eij ]
TranslatingtheNestedStructure
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Allextraconstraintsarebinary(betweenTi andTj)Twopossiblesituations:
Addattribute(M)toeachsymbolonthepathbetweenTi andTj.
TranslatingExtraConstraints
A"
Ti" Tj"
X" Y"B" C"
D" E"Alterna2ve"rules"
Ti"
X"
D"
Tj"
A"
Alterna2ve"rules"
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
AssumeconstraintTi ó TjGrammarrules:
Tj(...,M)→...,A(...,M),... [M=1]X(...,M)→... [M=0]D(...,M)→...,Ti,... [M=1]
TranslatingExtraConstraints(1)
A"
Ti" Tj"
X" Y"B" C"
D" E"Alterna2ve"rules"
Ti"
X"
D"
Tj"
A"
Alterna2ve"rules"
Tj=>T
iTimutex T
jTi→T
jTiss T
jTiseT
j
Tj(...,M)→...,A(...,M),... M=1 M=1 M≤Sj M=Sj M=EjX(...,M)→... M=0 M=1 --- --- ---D(...,M)→...,Ti,... M=1 M=0 Ei ≤M M=Si M=Si
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
TranslatingExtraConstraints(2)
A"
Ti" Tj"
X" Y"B" C"
D" E"Alterna2ve"rules"
Ti"
X"
D"
Tj"
A"
Alterna2ve"rules"
Grammarrules:ParalleldecompositionofA:A→...,B(...,M),...,C(...,M),...[]
AlternativedecompositionofA:A→B(...,M) [M=0]A→C(...,M) [M=0]
X(...,M)→... [M=0]Y(...,M)→... [M=0]
D(...,M)→...,Tii,... [M=1]E(...,M)→...,Tj,... [M=1]
AssumeconstraintTi ó Tj
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Wecanrepresentnestedworkflowswithextra
constraintsusingattributegrammars.
Canweverifytheworkflow/planningdomain
modelrepresentedasanattributegrammar?
–Whatdoesitmeantoverifytheattributegrammar?
– Howcanwerealizetheverificationalgorithminthecaseofrecursivegrammars?
Nextsteps
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Whereisthebuginthefollowinggrammar?
S(NS)→A(NA).B(NB) [NS=NA,NS=NB]A(N)→a [N=1]A(N)→a.a [N=2]B(N)→b.b [N=2]
Theattributegrammarverificationproblemconsistsofdetectingnon-terminalsandrulesthatcannotbeusedinanysuccessfulderivation.
AttributeGrammarVerificationProblem
A(N)→a [N=1]
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Attributegrammarverificationissimilartoreductionofacontext-freegrammar.
1. translatetheattributegrammartoaCFGbygroundingallattributes
2. reduceCFG
VerificationviaTranslationtoCFG
original grounded generating
non-terminals
reachable
non-terminals
S(NS) → A(NA).B(NB)[NS = NA,NS = NB]
A(N) → a [N = 1] A(N) → a.a [N = 2] B(N) → b.b [N = 2]
S1 → A1.B1S2 → A2.B2A1 → a A2 → a.aB2 → b.b
S2 → A2.B2A1 → a A2 → a.aB2 → b.b
S2 → A2.B2
A2 → a.aB2 → b.b
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
SimulatethereductionalgorithmontheattributegrammarandcalculatepossiblevaluesofattributesbysolvingunderlyingCSPs.
S(NS)→A(NA).B(NB)[NS=NA,NS=NB]A(N)→a [N=1]A(N)→a.a [N=2]B(N)→b.b [N=2]
DirectVerificationviaCSP
Bottom-up
SAB
Top-down
SAB2
21,2
222
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Editorofattributegrammarswithlinearconstraints.Push-buttonverificationwithhighlightingallerrorsinthegrammar.
Implementation
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
Wecantranslatenestedworkflowswithextra
constraintstoattributegrammars.
WecantranslateSTRIPSplanningdomainmodelstoattributegrammars.Wecanfullyverifytheattributegrammars:
• bytranslationtoaCFG
• directlybysolvingunderlyingCSPs
Thedownside:• verificationiscomputationallydemanding
Summary
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
• translationofothermodels(suchashierarchicaltasknetworks)
• automatedlearningofgrammars(fromexampleplans/schedules)
• visualizationandsupportforinteractiveediting
Thisisjustthebeginning…
WorkflowModelingandVerificationusingAttributeGrammars RomanBarták
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