Borders of Decidability in Verification of Data-Centric Dynamic Systems

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Borders of Decidability in Verification of Data-Centric Dynamic Systems

  1. 1. Borders of Decidability in Verification of Data-Centric Dynamic Systems Babak Bagheri Hariri, Diego Calvanese, Marco Montali1 , Alin Deutsch2 , Giuseppe De Giacomo3 KRDB Research Centre for Knowledge and Data Free University of Bozen - Bolzano Knowledge Representation and Reasoning (KRR) Meraka Institute - CSIR, Pretoria, South Africa March, 2013 Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 1 / 34
  2. 2. Why Formal Verification? Errors in computerized systems can be costly. Pentium chip (1994) Toyota Prius(2010) Ariane 5 (1996) Bug found in FPU. Intel of- Software “glitch” found in Exploded 37secs fers to replace faulty chips. anti-lock braking system. launch. Estimated loss: 475m $ after overflow exception. 185,000 cars recalled. Cause: uncaught Why verify? “Testing can only show the presence of errors, not their absence.” [Edsger W. Dijkstra] Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 2 / 34
  3. 3. Model Checking System Specification Design/Develop Temporal Properties ¬EF fail Finite State Model Model Checker e.g. NuSMV, Spin Verified The finite state requirement is severe and restrictive Specially for settings that capture data and dynamics simultaneously, (e.g. Artifact-Centric Business Process Systems). Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 3 / 34
  4. 4. Model Checking System Specification Design/Develop Temporal Properties ¬EF fail Finite State Model Model Checker e.g. NuSMV, Spin Verified The finite state requirement is severe and restrictive Specially for settings that capture data and dynamics simultaneously, (e.g. Artifact-Centric Business Process Systems). Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 3 / 34
  5. 5. A Concrete Example! Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 4 / 34
  6. 6. A much more Crucial Example! Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 5 / 34
  7. 7. A much more Crucial Example! Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 5 / 34
  8. 8. A much more Crucial Example! Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 5 / 34
  9. 9. Traditional Process Modeling • Structural modeling of the domain of interest: conceptual models, domain ontologies, database schemas UML, ORM, ER, . . . • Behavioral modeling of the domain of interest: activities, services, business processes BPMN, EPC, UML, BPEL, SOA-related technologies, . . . Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 6 / 34
  10. 10. Traditional Process Modeling • Structural modeling of the domain of interest: conceptual models, domain ontologies, database schemas UML, ORM, ER, . . . • Behavioral modeling of the domain of interest: activities, services, business processes BPMN, EPC, UML, BPEL, SOA-related technologies, . . . Lack of a coherent holistic view: • Two models are loosely connected; • The full combined behavior is never captured. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 6 / 34
  11. 11. Business Artifacts to the Rescue • The artifact-centric approach emerged as a foundational proposal for merging data and processes together. Data must be modeled taking into account that they will be manipulated by processes. Processes must be modeled by considering that they are meant to manipulate data. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 7 / 34
  12. 12. Business Artifacts to the Rescue • The artifact-centric approach emerged as a foundational proposal for merging data and processes together. Data must be modeled taking into account that they will be manipulated by processes. Processes must be modeled by considering that they are meant to manipulate data. • Initial proposals by IBM (Nigam, Caswell 2003), and continued by Rick Hull, Jianwen Su, Victor Vianu, .... Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 7 / 34
  13. 13. Business Artifacts to the Rescue • The artifact-centric approach emerged as a foundational proposal for merging data and processes together. Data must be modeled taking into account that they will be manipulated by processes. Processes must be modeled by considering that they are meant to manipulate data. • Initial proposals by IBM (Nigam, Caswell 2003), and continued by Rick Hull, Jianwen Su, Victor Vianu, .... • ACSI Project for artifact-centric service interoperation. aC   Si   Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 7 / 34
  14. 14. What is an Artifact? Consists of: • information model - relevant data maintained by the artifact • lifecycle model - (implicit) description of the allowed information model evolutions through the execution of a process. Information model Babak Bagheri Hariri Lifecycle Borders of Decidability in Verification of DCDSs Artifact March, 2013 8 / 34
  15. 15. Concrete Models for Artifacts Some concrete information models: • Relational database (with nested records). • (Description Logic) knowledge base. Some concrete lifecycle models: • Finite-state machines. State = phase; events trigger transitions. Implemented in the Siena IBM prototype. • Proclets (interacting Petri nets). Emphasise many-to-many relationships between artifacts. • Guard-Stage-Milestone lifecycles, based on declarative (even, condition, action)-like rules. Implemented in the Barcelona IBM prototype. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 9 / 34
  16. 16. Data-Centric Dynamic Systems (DCDS) • Abstract model behind different variants of artifact-centric business process systems; • semantically equivalent to the most expressive models for business process systems (e.g., GSM). Data Babak Bagheri Hariri Process Data+Process Borders of Decidability in Verification of DCDSs March, 2013 10 / 34
  17. 17. Data-Centric Dynamic Systems (DCDS) peer Schema Customer In Debt Customer owes Instance Cust(ann) peer(mark, john) Gold(john) closed Loan Babak Bagheri Hariri Data Layer Gold Customer Borders of Decidability in Verification of DCDSs March, 2013 10 / 34
  18. 18. Data-Centric Dynamic Systems (DCDS) Data Layer peer Schema Instance Customer Cust(ann) peer(mark, john) Gold(john) In Debt Customer owes closed Loan Gold Customer Process Layer Actions GetLoan(x) : ∃y.peer(x, y) Cust(z) Loan(z) InDebt(z) Gold(z) Babak Bagheri Hariri {owes(x, UInput(x))}, {Cust(z)}, {Loan(z)}, {InDebt(z)}, {Gold(z)} Borders of Decidability in Verification of DCDSs March, 2013 10 / 34
  19. 19. Data-Centric Dynamic Systems (DCDS) Data Layer peer Schema Instance Customer Cust(ann) peer(mark, john) Gold(john) In Debt Customer owes closed Loan Gold Customer Process Layer Actions GetLoan(x) : Service Calls UInput(x) Babak Bagheri Hariri ∃y.peer(x, y) Cust(z) Loan(z) InDebt(z) Gold(z) {owes(x, UInput(x))}, {Cust(z)}, {Loan(z)}, {InDebt(z)}, {Gold(z)} Borders of Decidability in Verification of DCDSs March, 2013 10 / 34
  20. 20. Data-Centric Dynamic Systems (DCDS) Data Layer peer Schema Instance Customer Cust(ann) peer(mark, john) Gold(john) In Debt Customer owes closed Loan Gold Customer Process Layer Condition Action Rules peer(x, y) ∧ Gold(y) −→ GetLoan(x) Service Calls UInput(x) Babak Bagheri Hariri Actions GetLoan(x) : ∃y.peer(x, y) Cust(z) Loan(z) InDebt(z) Gold(z) {owes(x, UInput(x))}, {Cust(z)}, {Loan(z)}, {InDebt(z)}, {Gold(z)} Borders of Decidability in Verification of DCDSs March, 2013 10 / 34
  21. 21. Data-Centric Dynamic Systems (DCDS) Data Layer peer Schema Instance Customer In Debt Customer owes closed Loan Gold Customer Cust(ann) peer(mark, john) Gold(john) owes(mark, @25 ) Process Layer Condition Action Rules peer(x, y) ∧ Gold(y) −→ GetLoan(x) Service Calls UInput(x) Babak Bagheri Hariri Actions GetLoan(x) : ∃y.peer(x, y) Cust(z) Loan(z) InDebt(z) Gold(z) {owes(x, UInput(x))}, {Cust(z)}, {Loan(z)}, {InDebt(z)}, {Gold(z)} Borders of Decidability in Verification of DCDSs March, 2013 10 / 34
  22. 22. Data-Centric Dynamic Systems (DCDS) • Data Layer: Relational databases / ontologies Data schema Data instance: state of the DCDS • Process Layer: Atomic actions Conditions for application of actions Service calls: communication with external environment Deterministic services Nondeterministic services Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 10 / 34
  23. 23. Data-Centric Dynamic Systems (DCDS) • Data Layer: Relational databases / ontologies Data schema Data instance: state of the DCDS • Process Layer: Atomic actions Conditions for application of actions Service calls: communication with external environment Deterministic services: e.g., historical exchange rate of POD/RAND Nondeterministic services: e.g., current exchange rate of POD/RAND Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 10 / 34
  24. 24. Data-Centric Dynamic Systems (DCDS) • Data Layer: Relational databases / ontologies Data schema Data instance: state of the DCDS • Process Layer: Atomic actions Conditions for application of actions Service calls: communication with external environment Deterministic services: e.g., historical exchange rate of POD/RAND Nondeterministic services: e.g., current exchange rate of POD/RAND Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 10 / 34
  25. 25. Data-Centric Dynamic Systems (DCDS) • Data Layer: Relational databases / ontologies Data schema Data instance: state of the DCDS • Process Layer: Atomic actions Conditions for application of actions Service calls: communication with external environment Deterministic services: e.g., historical exchange rate of POD/RAND Nondeterministic services: e.g., current exchange rate of POD/RAND Allow one also to take into account user-input. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 10 / 34
  26. 26. Semantics via Transition Systems P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), I = {P(a), Q(a, a)} Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  27. 27. Semantics via Transition Systems P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), I = {P(a), Q(a, a)} P(a) Q(a,a) Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  28. 28. Semantics via Transition Systems f(a)→ P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), g(a)→ P(a) R(a) Q( , ) I = {P(a), Q(a, a)} P(a) Q(a,a) Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  29. 29. Semantics via Transition Systems f(a)→a g(a)→ P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), P(a) R(a) Q(a, ) I = {P(a), Q(a, a)} P(a) Q(a,a) Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  30. 30. Semantics via Transition Systems f(a)→a g(a)→a P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), P(a) R(a) Q(a,a) I = {P(a), Q(a, a)} P(a) Q(a,a) Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  31. 31. Semantics via Transition Systems f(a)→a g(a)→a P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), P(a) R(a) Q(a,a) f(a)→a g(a)→b I = {P(a), Q(a, a)} P(a) R(a) Q(a,b) P(a) Q(a,a) Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  32. 32. Semantics via Transition Systems f(a)→a g(a)→a P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), P(a) R(a) Q(a,a) f(a)→a g(a)→b I = {P(a), Q(a, a)} P(a) R(a) Q(a,b) f(a)→b g(a)→a P(a) Q(a,a) Babak Bagheri Hariri P(a) R(a) Q(b,a) Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  33. 33. Semantics via Transition Systems f(a)→a g(a)→a P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), P(a) R(a) Q(a,a) f(a)→a g(a)→b I = {P(a), Q(a, a)} P(a) R(a) Q(a,b) f(a)→b g(a)→a P(a) Q(a,a) P(a) R(a) Q(b,a) f(a)→b g(a)→b P(a) R(a) Q(b,b) ... Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  34. 34. Semantics via Transition Systems f(a)→a g(a)→a P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), P(a) R(a) Q(a,a) f(a)→a g(a)→b I = {P(a), Q(a, a)} P(a) R(a) Q(a,b) f(a)→b g(a)→a P(a) Q(a,a) P(a) R(a) Q(b,a) f(a)→b g(a)→b P(a) R(a) Q(b,b) ... Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  35. 35. Semantics via Transition Systems f(a)→a g(a)→a P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), P(a) R(a) Q(a,a) f(a)→a g(a)→b f(a)→a g(a)→b P(a) R(a) Q(a,b) P(a) Q(a,b) I = {P(a), Q(a, a)} f(a)→b g(a)→a P(a) Q(a,a) P(a) R(a) Q(b,a) f(a)→b g(a)→b P(a) R(a) Q(b,b) ... Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  36. 36. Semantics via Transition Systems f(a)→a g(a)→a P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), P(a) R(a) Q(a,a) f(a)→a g(a)→b f(a)→a g(a)→b P(a) R(a) Q(a,b) P(a) Q(a,b) I = {P(a), Q(a, a)} f(a)→b g(a)→a P(a) Q(a,a) P(a) R(a) Q(b,a) f(a)→b g(a)→b P(a) R(a) Q(b,b) ... Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  37. 37. Semantics via Transition Systems f(a)→a g(a)→a P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), P(a) R(a) Q(a,a) f(a)→a g(a)→b f(a)→a g(a)→b P(a) R(a) Q(a,b) P(a) Q(a,b) f(a)→b g(a)→a f(a)→b g(a)→a P(a) R(a) Q(b,a) P(a) Q(b,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) I = {P(a), Q(a, a)} P(a) Q(a,a) ... Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 11 / 34
  38. 38. Borders of Decidability in Model Checking of DCDSs Motivation: verification of artifact-centric business process systems in design phase. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 12 / 34
  39. 39. Borders of Decidability in Model Checking of DCDSs Motivation: verification of artifact-centric business process systems in design phase. Artifacts (DCDSs) pose two challenging problems: 1 properties to be verified need to query over the artifact information model: Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 12 / 34
  40. 40. Borders of Decidability in Model Checking of DCDSs Motivation: verification of artifact-centric business process systems in design phase. Artifacts (DCDSs) pose two challenging problems: 1 properties to be verified need to query over the artifact information model: µL is not expressive enough to compare over time objects created by the process. Verification of µLFO is undecidable, even for very restricted DCDSs! We need to look at fragments of µLFO . µLFO µL LTL PDL CTL HML Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 12 / 34
  41. 41. Borders of Decidability in Model Checking of DCDSs Motivation: verification of artifact-centric business process systems in design phase. Artifacts (DCDSs) pose two challenging problems: 1 properties to be verified need to query over the artifact information model: µL is not expressive enough to compare over time objects created by the process. Verification of µLFO is undecidable, even for very restricted DCDSs! We need to look at fragments of µLFO . 2 Verification of DCDSs is undecidable even for propositional reachability properties. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs µLFO µL LTL PDL CTL HML March, 2013 12 / 34
  42. 42. Borders of Decidability in Model Checking of DCDSs Motivation: verification of artifact-centric business process systems in design phase. Artifacts (DCDSs) pose two challenging problems: 1 properties to be verified need to query over the artifact information model: µL is not expressive enough to compare over time objects created by the process. Verification of µLFO is undecidable, even for very restricted DCDSs! We need to look at fragments of µLFO . 2 Verification of DCDSs is undecidable even for propositional reachability properties. µLFO µL LTL PDL CTL HML We also need to look restrictions on DCDSs themselves. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 12 / 34
  43. 43. Verification Formalisms: µLFO We introduce: µLP and µLA as extensions of µL with (restricted) first order quantification. µL LTL PDL CTL HML Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 13 / 34
  44. 44. Verification Formalisms: µLFO We introduce: µLP and µLA as extensions of µL with (restricted) first order quantification. µLA µLA : FO quantification over current active domain. LTLFO : ∀x. Customer(x) =⇒ F Gold(x) µLA : ∀x. Customer(x) =⇒ µZ .Gold(x) ∨ [−]Z µL LTL PDL CTL HML Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 13 / 34
  45. 45. Verification Formalisms: µLFO We introduce: µLP and µLA as extensions of µL with (restricted) first order quantification. µLA µLA : FO quantification over current active domain. µLP LTLFO : ∀x. Customer(x) =⇒ F Gold(x) µLA : ∀x. Customer(x) =⇒ µZ .Gold(x) ∨ [−]Z µLP : FO quantification only holds over persisting individuals. LTLFO : ∀x. Gold(x) =⇒ G Gold(x) µLP : ∀x. Gold(x) =⇒ νZ .Gold(x) ∧ [−]Z Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs µL LTL PDL CTL HML March, 2013 13 / 34
  46. 46. Restrictions on DCDSs Run-bounded DCDS: runs cannot accumulate more than a fixed bound of different values. • Still infinite-state due to infinite branching. • A semantic condition, whose checking is undecidable. We introduce enough syntactic condition: Weak-acyclicity. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 14 / 34
  47. 47. Restrictions on DCDSs Run-bounded DCDS: runs cannot accumulate more than a fixed bound of different values. • Still infinite-state due to infinite branching. • A semantic condition, whose checking is undecidable. We introduce enough syntactic condition: Weak-acyclicity. • Very restrictive for DCDSs with nondeterministic services. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 14 / 34
  48. 48. Restrictions on DCDSs Run-bounded DCDS: runs cannot accumulate more than a fixed bound of different values. • Still infinite-state due to infinite branching. • A semantic condition, whose checking is undecidable. We introduce enough syntactic condition: Weak-acyclicity. • Very restrictive for DCDSs with nondeterministic services. State-bounded DCDS: states cannot contain more than a fixed bound of different values. • Relaxation of run-boundedness. • Infinite runs are possible. • A semantic condition, whose checking is undecidable. We introduce enough syntactic condition: GR-acyclicity. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 14 / 34
  49. 49. Unrestricted DCDSs (Turing complete) Results on DCDSs Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 15 / 34
  50. 50. Unrestricted DCDSs (Turing complete) Results on DCDSs Unrestricted µLFO U µLA U µLP U µL U D: Verification is decidable; U: Verification is undecidable; N: There is no finite representation. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 15 / 34
  51. 51. Finite-state DCDSs Unrestricted DCDSs (Turing complete) Results on DCDSs Unrestricted Finite-state µLFO U D µLA U D µLP U D µL U D D: Verification is decidable; U: Verification is undecidable; N: There is no finite representation. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 15 / 34
  52. 52. Finite-state DCDSs Unrestricted DCDSs (Turing complete) Results on DCDSs Finite-range DCDSs Unrestricted Finite-state µLFO U D µLA U D µLP U D µL U D D: Verification is decidable; U: Verification is undecidable; N: There is no finite representation. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 15 / 34
  53. 53. Finite-state DCDSs Run-bounded DCDSs Unrestricted DCDSs (Turing complete) Results on DCDSs Finite-range DCDSs Unrestricted Run-bounded Finite-state µLFO U N D µLA U D D µLP U D D µL U D D D: Verification is decidable; U: Verification is undecidable; N: There is no finite representation. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 15 / 34
  54. 54. Weak-acyclic DCDSs Finite-state DCDSs Run-bounded DCDSs Unrestricted DCDSs (Turing complete) Results on DCDSs Finite-range DCDSs Unrestricted Run-bounded Finite-state µLFO U N D µLA U D D µLP U D D µL U D D D: Verification is decidable; U: Verification is undecidable; N: There is no finite representation. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 15 / 34
  55. 55. Weak-acyclic DCDSs Finite-state DCDSs Run-bounded DCDSs State-bounded DCDSs Unrestricted DCDSs (Turing complete) Results on DCDSs Finite-range DCDSs Run-bounded Finite-state µLFO Unrestricted U State-bounded U N D µLA U U D D µLP U D D D µL U D D D D: Verification is decidable; U: Verification is undecidable; N: There is no finite representation. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 15 / 34
  56. 56. Weak-acyclic DCDSs GR-acyclic DCDSs Finite-state DCDSs Run-bounded DCDSs State-bounded DCDSs Unrestricted DCDSs (Turing complete) Results on DCDSs Finite-range DCDSs Run-bounded Finite-state µLFO Unrestricted U State-bounded U N D µLA U U D D µLP U D D D µL U D D D D: Verification is decidable; U: Verification is undecidable; N: There is no finite representation. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 15 / 34
  57. 57. Weak-acyclic DCDSs GR+ -acyclic DCDSs GR-acyclic DCDSs Finite-state DCDSs Run-bounded DCDSs State-bounded DCDSs Unrestricted DCDSs (Turing complete) Results on DCDSs Finite-range DCDSs Run-bounded Finite-state µLFO Unrestricted U State-bounded U N D µLA U U D D µLP U D D D µL U D D D D: Verification is decidable; U: Verification is undecidable; N: There is no finite representation. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 15 / 34
  58. 58. Towards the Decidability Results Sources of infinity in DCDSs: • Infinite branching; ... • Infinite runs. P(a) ... P(b) P(a) ... ... To prove decidability of model checking for a given restriction and verification formalism: • we use bisimulation as a tool; • show the restricted DCDSs have a finite-state bisimilar transition system. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 16 / 34
  59. 59. Bisimulation States s A and s B of transition systems A and B are bisimilar : Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 17 / 34
  60. 60. Bisimulation States s A and s B of transition systems A and B are bisimilar : A B sA sB Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 17 / 34
  61. 61. Bisimulation States s A and s B of transition systems A and B are bisimilar : 1 If s A and s B are isomorphic; A B sA sB Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 17 / 34
  62. 62. Bisimulation States s A and s B of transition systems A and B are bisimilar : 1 If s A and s B are isomorphic; 2 A A If there exists a state s1 of A such that s A ⇒A s1 , A sA Babak Bagheri Hariri A s1 B sB Borders of Decidability in Verification of DCDSs March, 2013 17 / 34
  63. 63. Bisimulation States s A and s B of transition systems A and B are bisimilar : 1 2 If s A and s B are isomorphic; A A If there exists a state s1 of A such that s A ⇒A s1 , then there exists B B a state s1 of B such that s B ⇒B s1 , A sA Babak Bagheri Hariri A s1 B B s1 sB Borders of Decidability in Verification of DCDSs March, 2013 17 / 34
  64. 64. Bisimulation States s A and s B of transition systems A and B are bisimilar : 1 2 If s A and s B are isomorphic; A A If there exists a state s1 of A such that s A ⇒A s1 , then there exists A B B B a state s1 of B such that s B ⇒B s1 , and s1 and s1 are bisimilar; A sA Babak Bagheri Hariri A s1 B B s1 sB Borders of Decidability in Verification of DCDSs March, 2013 17 / 34
  65. 65. Bisimulation States s A and s B of transition systems A and B are bisimilar : 1 2 3 If s A and s B are isomorphic; A A If there exists a state s1 of A such that s A ⇒A s1 , then there exists A B B B a state s1 of B such that s B ⇒B s1 , and s1 and s1 are bisimilar; the other direction! A B A s1 sA sB A s2 Babak Bagheri Hariri B s1 Borders of Decidability in Verification of DCDSs B s2 March, 2013 17 / 34
  66. 66. Bisimulation States s A and s B of transition systems A and B are bisimilar : 1 2 3 If s A and s B are isomorphic; A A If there exists a state s1 of A such that s A ⇒A s1 , then there exists A B B B a state s1 of B such that s B ⇒B s1 , and s1 and s1 are bisimilar; the other direction! A and B are bisimilar, if their initial states are bisimilar. A B A s1 sA sB A s2 Babak Bagheri Hariri B s1 Borders of Decidability in Verification of DCDSs B s2 March, 2013 17 / 34
  67. 67. Bisimulation States s A and s B of transition systems A and B are bisimilar : 1 2 3 If s A and s B are isomorphic; A A If there exists a state s1 of A such that s A ⇒A s1 , then there exists A B B B a state s1 of B such that s B ⇒B s1 , and s1 and s1 are bisimilar; the other direction! A and B are bisimilar, if their initial states are bisimilar. µL invariance property of bisimulation: Bisimilar transition systems satisfy the same set of µL properties. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 17 / 34
  68. 68. Verification Formalisms (continue) µLFO First Order Temporal Logics Bisimulation Invariant Languages CTL Propositional Temporal Logics µL L Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 18 / 34
  69. 69. Verification Formalisms (continue) µLFO Bisimulation Invariant Languages CTL Propositional Temporal Logics Persistence Preserving Bisimulation Invariant Languages First Order Temporal Logics µLP µL LP L Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 18 / 34
  70. 70. Verification Formalisms (continue) µLFO µLP Persistence Preserving Bisimulation Invariant Languages Bisimulation Invariant Languages CTL Propositional Temporal Logics History Preserving Bisimulation Invariant Languages First Order Temporal Logics LP µLA µL LA L Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 18 / 34
  71. 71. Decidability Results for Run-bounded Systems: Theorem Verification of µLA over run-bounded DCDSs is decidable and can be reduced to model checking of propositional µ-calculus over a finite transition system. . . . . . . Idea: use isomorphic types instead of actual values. . . . Remember: runs are bounded! . . . . . . Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 19 / 34
  72. 72. Decidability Results for Run-bounded Systems: Theorem Verification of µLA over run-bounded DCDSs is decidable and can be reduced to model checking of propositional µ-calculus over a finite transition system. non a-bisimilar . . . . . . Idea: use isomorphic types instead of actual values. . . . a-bisimilar Remember: runs are bounded! . . . . . . Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 19 / 34
  73. 73. Decidability Results for Run-bounded Systems: Theorem Verification of µLA over run-bounded DCDSs is decidable and can be reduced to model checking of propositional µ-calculus over a finite transition system. . . . . . . Idea: use isomorphic types instead of actual values. . . . Remember: runs are bounded! Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 19 / 34
  74. 74. History Preserving Bisimulation P(x) P(x) ∧ Q(f (x), g(x)) Q(a, a) ∧ P(x) R(x), I0 = {P(a), Q(a, a)} f(a)→a g(a)→a P(a) R(a) Q(a,a) f(a)→b g(a)→b P(a) Q(a,a) f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→c g(a)→c f(a)→c g(a)→c P(a) R(a) Q(c,c) P(a) Q(c,c) ... Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 20 / 34
  75. 75. History Preserving Bisimulation f(a)→a g(a)→a P(a) R(a) Q(a,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→c g(a)→c f(a)→c g(a)→c P(a) R(a) Q(c,c) P(a) Q(a,a) P(a) Q(c,c) ... Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 20 / 34
  76. 76. History Preserving Bisimulation f(a)→a g(a)→a P(a) R(a) Q(a,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→c g(a)→c f(a)→c g(a)→c f(a)→a g(a)→a P(a) R(a) Q(c,c) P(a) Q(a,a) P(a) Q(c,c) P(a) R(a) Q(a,a) f(a)→a g(a)→b f(a)→b g(a)→a P(a) R(a) Q(b,a) P(a) Q(b,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→b g(a)→c f(a)→b g(a)→c P(a) R(a) Q(b,c) Babak Bagheri Hariri P(a) Q(a,b) f(a)→b g(a)→a P(a) Q(a,a) f(a)→a g(a)→b P(a) R(a) Q(a,b) ... P(a) Q(b,c) Borders of Decidability in Verification of DCDSs March, 2013 20 / 34
  77. 77. History Preserving Bisimulation f(a)→a g(a)→a P(a) R(a) Q(a,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→c g(a)→c f(a)→c g(a)→c f(a)→a g(a)→a P(a) R(a) Q(c,c) P(a) Q(a,a) P(a) Q(c,c) P(a) R(a) Q(a,a) f(a)→a g(a)→b f(a)→b g(a)→a P(a) R(a) Q(b,a) P(a) Q(b,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→b g(a)→c f(a)→b g(a)→c P(a) R(a) Q(b,c) Babak Bagheri Hariri P(a) Q(a,b) f(a)→b g(a)→a P(a) Q(a,a) f(a)→a g(a)→b P(a) R(a) Q(a,b) ... P(a) Q(b,c) Borders of Decidability in Verification of DCDSs March, 2013 20 / 34
  78. 78. History Preserving Bisimulation f(a)→a g(a)→a P(a) R(a) Q(a,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→c g(a)→c f(a)→c g(a)→c f(a)→a g(a)→a P(a) R(a) Q(c,c) P(a) Q(a,a) P(a) Q(c,c) P(a) R(a) Q(a,a) f(a)→a g(a)→b f(a)→b g(a)→a P(a) R(a) Q(b,a) P(a) Q(b,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→b g(a)→c f(a)→b g(a)→c P(a) R(a) Q(b,c) Babak Bagheri Hariri P(a) Q(a,b) f(a)→b g(a)→a P(a) Q(a,a) f(a)→a g(a)→b P(a) R(a) Q(a,b) ... P(a) Q(b,c) Borders of Decidability in Verification of DCDSs March, 2013 20 / 34
  79. 79. History Preserving Bisimulation f(a)→a g(a)→a P(a) R(a) Q(a,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→c g(a)→c f(a)→c g(a)→c f(a)→a g(a)→a P(a) R(a) Q(c,c) P(a) Q(a,a) P(a) Q(c,c) P(a) R(a) Q(a,a) f(a)→a g(a)→b f(a)→b g(a)→a P(a) R(a) Q(b,a) P(a) Q(b,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→b g(a)→c f(a)→b g(a)→c P(a) R(a) Q(b,c) Babak Bagheri Hariri P(a) Q(a,b) f(a)→b g(a)→a P(a) Q(a,a) f(a)→a g(a)→b P(a) R(a) Q(a,b) ... P(a) Q(b,c) Borders of Decidability in Verification of DCDSs March, 2013 20 / 34
  80. 80. History Preserving Bisimulation f(a)→a g(a)→a P(a) R(a) Q(a,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→c g(a)→c f(a)→c g(a)→c f(a)→a g(a)→a P(a) R(a) Q(c,c) P(a) Q(a,a) P(a) Q(c,c) P(a) R(a) Q(a,a) f(a)→a g(a)→b f(a)→b g(a)→a P(a) R(a) Q(b,a) P(a) Q(b,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→b g(a)→c f(a)→b g(a)→c P(a) R(a) Q(b,c) Babak Bagheri Hariri P(a) Q(a,b) f(a)→b g(a)→a P(a) Q(a,a) f(a)→a g(a)→b P(a) R(a) Q(a,b) ... P(a) Q(b,c) Borders of Decidability in Verification of DCDSs March, 2013 20 / 34
  81. 81. History Preserving Bisimulation f(a)→a g(a)→a P(a) R(a) Q(a,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→c g(a)→c f(a)→c g(a)→c f(a)→a g(a)→a P(a) R(a) Q(c,c) P(a) Q(a,a) P(a) Q(c,c) P(a) R(a) Q(a,a) f(a)→a g(a)→b P(a) R(a) Q(b,a) P(a) Q(b,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→b g(a)→c P(a) R(a) Q(b,c) Babak Bagheri Hariri f(a)→b g(a)→a f(a)→b g(a)→c Two transition systems are history preserving bisimilar. P(a) Q(a,b) f(a)→b g(a)→a P(a) Q(a,a) f(a)→a g(a)→b P(a) R(a) Q(a,b) ... P(a) Q(b,c) Borders of Decidability in Verification of DCDSs March, 2013 20 / 34
  82. 82. History Preserving Bisimulation f(a)→a g(a)→a P(a) R(a) Q(a,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→c g(a)→c f(a)→c g(a)→c f(a)→a g(a)→a P(a) R(a) Q(c,c) P(a) Q(a,a) P(a) Q(c,c) P(a) R(a) Q(a,a) f(a)→a g(a)→b Babak Bagheri Hariri f(a)→b g(a)→a P(a) R(a) Q(b,a) P(a) Q(b,a) f(a)→b g(a)→b f(a)→b g(a)→b P(a) R(a) Q(b,b) P(a) Q(b,b) f(a)→b g(a)→c f(a)→b g(a)→c P(a) R(a) Q(b,c) Two transition systems are history preserving bisimilar. Consequently, satisfy the same set of µLA properties. P(a) Q(a,b) f(a)→b g(a)→a P(a) Q(a,a) f(a)→a g(a)→b P(a) R(a) Q(a,b) ... P(a) Q(b,c) Borders of Decidability in Verification of DCDSs March, 2013 20 / 34
  83. 83. Undecidability Results for State-bounded Systems Theorem Verification of µLA over state-bounded DCDSs is undecidable. Idea: the logic can arbitrarily quantify over the infinitely many values encountered during a single run, and start comparing them. Technical proof: satisfiability of LTL with freeze quantifiers can be encoded as a model checking problem of µLA formulae over state-bounded DCDSs. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 21 / 34
  84. 84. Decidability Results for State-bounded Systems Theorem Verification of µLP over state-bounded DCDSs is decidable and can be reduced to model checking of propositional µ-calculus over a finite transition system. Steps: 1 . ... . . Prune infinite branching (isomorphic types). . ... . . . . ... . . . ... . . . . Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 22 / 34
  85. 85. Decidability Results for State-bounded Systems Theorem Verification of µLP over state-bounded DCDSs is decidable and can be reduced to model checking of propositional µ-calculus over a finite transition system. non p-bisimilar Steps: 1 2 . ... . . Prune infinite branching (isomorphic types). Finite abstraction along the runs: µLP looses track of previous values that do not exist anymore. New values can be replaced with old, non-persisting ones. This eventually leads to recycle the old values without generating new ones. . ... . . . . ... . p-bisimilar . . ... . . . . Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 22 / 34
  86. 86. Decidability Results for State-bounded Systems Theorem Verification of µLP over state-bounded DCDSs is decidable and can be reduced to model checking of propositional µ-calculus over a finite transition system. Steps: 1 2 . ... . . Prune infinite branching (isomorphic types). Finite abstraction along the runs: . ... . . µLP looses track of previous values that do not exist anymore. New values can be replaced with old, non-persisting ones. This eventually leads to recycle the old values without generating new ones. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs . . ... . March, 2013 22 / 34
  87. 87. Decidability Results for State-bounded Systems Theorem Verification of µLP over state-bounded DCDSs is decidable and can be reduced to model checking of propositional µ-calculus over a finite transition system. Steps: 1 2 . . . Prune infinite branching (isomorphic types). Finite abstraction along the runs: . . . µLP looses track of previous values that do not exist anymore. New values can be replaced with old, non-persisting ones. This eventually leads to recycle the old values without generating new ones. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs . . . March, 2013 22 / 34
  88. 88. Weak-acyclicity I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 23 / 34
  89. 89. Weak-acyclicity P(a) I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 23 / 34
  90. 90. Weak-acyclicity P(a) I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) Babak Bagheri Hariri R(a) Borders of Decidability in Verification of DCDSs March, 2013 23 / 34
  91. 91. Weak-acyclicity f (a) → b P(a) I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) Babak Bagheri Hariri P(b) R(a) Borders of Decidability in Verification of DCDSs March, 2013 23 / 34
  92. 92. Weak-acyclicity f (a) → b P(a) I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) P(b) f (a) → b R(a) R(b) Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 23 / 34
  93. 93. Weak-acyclicity f (a) → b f (a) → b f (b) → c P(b) P(c) P(a) I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) f (a) → b R(a) R(b) Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 23 / 34
  94. 94. Weak-acyclicity f (a) → b f (a) → b f (b) → c P(b) P(c) f (a) → b f (a) → b f (b) → c R(b) R(c) P(a) I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) Babak Bagheri Hariri R(a) Borders of Decidability in Verification of DCDSs ... March, 2013 23 / 34
  95. 95. Weak-acyclicity f (a) → b f (a) → b f (b) → c P(b) P(c) f (a) → b f (a) → b f (b) → c R(b) R(c) P(a) I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) R(a) ... I0 = {P(a)}   P(x) P(x),  P(x) R(f (x)) α:   R(x) S(f (x)) Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 23 / 34
  96. 96. Weak-acyclicity f (a) → b f (a) → b f (b) → c P(b) P(c) f (a) → b f (a) → b f (b) → c R(b) R(c) P(a) I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) I0 = {P(a)}   P(x) P(x),  P(x) R(f (x)) α:   R(x) S(f (x)) Babak Bagheri Hariri R(a) ... P(a) Borders of Decidability in Verification of DCDSs March, 2013 23 / 34
  97. 97. Weak-acyclicity f (a) → b f (a) → b f (b) → c P(b) P(c) f (a) → b f (a) → b f (b) → c R(b) R(c) P(a) I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) I0 = {P(a)}   P(x) P(x),  P(x) R(f (x)) α:   R(x) S(f (x)) Babak Bagheri Hariri R(a) ... P(a) f (a) → b P(a), R(b) Borders of Decidability in Verification of DCDSs March, 2013 23 / 34
  98. 98. Weak-acyclicity f (a) → b f (a) → b f (b) → c P(b) P(c) f (a) → b f (a) → b f (b) → c R(b) R(c) P(a) I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) I0 = {P(a)}   P(x) P(x),  P(x) R(f (x)) α:   R(x) S(f (x)) Babak Bagheri Hariri R(a) ... f (a) → b f (b) → c P(a) P(a), R(b), S (c) f (a) → b P(a), R(b) Borders of Decidability in Verification of DCDSs March, 2013 23 / 34
  99. 99. Weak-acyclicity f (a) → b f (a) → b f (b) → c P(b) P(c) f (a) → b f (a) → b f (b) → c R(b) R(c) P(a) I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) I0 = {P(a)}   P(x) P(x),  P(x) R(f (x)) α:   R(x) S(f (x)) Babak Bagheri Hariri R(a) ... f (a) → b f (b) → c P(a) P(a), R(b), S (c) f (a) → b P(a), R(b) Borders of Decidability in Verification of DCDSs March, 2013 23 / 34
  100. 100. Weak-acyclicity I0 = {P(a)} P(x) R(x), α: R(x) P(f (x)) I0 = {P(a)}   P(x) P(x),  P(x) R(f (x)) α:   R(x) S(f (x)) Babak Bagheri Hariri P R * * R P Borders of Decidability in Verification of DCDSs * S March, 2013 23 / 34
  101. 101. Model checking of DCDSs System Specification Design/Develop FO Temporal Properties Data-Centric System Construct faithful finite-state abstraction Construct faithful propositional temporal properties Finite-state abstraction Propositional Properties (Classic) Finite-state model checker rejected Babak Bagheri Hariri accepted Model Checking Borders of Decidability in Verification of DCDSs Verified March, 2013 24 / 34
  102. 102. Knowledge and Action Bases (KAB) Ontology Process KAB T T A A • To better capture the semantics of the domain of interest at conceptual level • To take into account the incomplete information Data Layer: Description logic KB • Data schema: (DL-Lite-A)TBox • Data instance: (DL-Lite-A) ABox unrestricted weak-acyclicity Babak Bagheri Hariri µLFO µLA µLP µL U ← U ← U ←U ? D → D →D D: decidable U: undecidable Borders of Decidability in Verification of DCDSs March, 2013 25 / 34
  103. 103. Separation Principle and Semantic Layer The evolution of the artifact system occurs at the artifact layer. • Processes are defined over the database schemas of the artifacts. The semantic layer can be added on top of the artifact layer to: • Understand the artifact system in terms of concepts and relationships relevant for the domain of interest. Unified view of the whole system. Interconnection of different artifacts that share information, though with different representation. Specification of queries as well as static and dynamic constraint at the conceptual level. • Verify and monitor whether the artifact system satisfies dynamic constraints specified over the semantic layer. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 26 / 34
  104. 104. Semantically-governed Artifact-Centric Models Semantic layer: I-HUB’s conceptual schema (TBox) composed of semantic constraints that define the “data boundaries” of the artifact system. TBox Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 27 / 34
  105. 105. Semantically-governed Artifact-Centric Models Real data are concretely maintained at the artifact layer. Snapshot: database instances of artifacts. TBox Db Dc Da Artifact System Snapshot Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 28 / 34
  106. 106. Semantically-governed Artifact-Centric Models Each snapshot is conceptualized in the ontology, in terms of an ABox. Mappings define how to obtain the virtual ABox from the data sources. TBox Semantic Layer Snapshot ABox1 Mappings Db Dc Da Artifact System Snapshot Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 29 / 34
  107. 107. Semantically-governed A3 M The system evolves using actions executed over the artifact layer. Semantic layer used to understand the evolution at the conceptual level. TBox TBox Semantic Layer Snapshot Semantic Layer Snapshot ABox1 ABox2 Mappings Mappings D'b Db Dc D'c Da Artifact System Snapshot D'a Artifact System Snapshot Action execution Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 30 / 34
  108. 108. Semantically-governed A3 M Semantic governance: semantic layer used to regulate the actions’ execution at the artifact layer. TBox TBox Semantic Layer Snapshot Semantic Layer Snapshot ABox1 ABox2 Mappings Mappings D'b Db Dc D'c Da Artifact System Snapshot D'a Artifact System Snapshot Action execution Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 31 / 34
  109. 109. Next steps • Relaxation of syntactic restrictions for state-boundedness. • Investigating the connection to other infinite-state formalisms. Petri nets; LTL with freeze quantifier; Well-structured transition systems. • Investigate the connection to more classic notations in BPM. BPMNs; Petri Nets. • Investigating the fragments with lower complexities. • Develop a fully-fledged model checker for DCDSs. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 32 / 34
  110. 110. Publications Journal Articles • Babak Bagheri Hariri, Diego Calvanese, Marco Montali, Giuseppe De Giacomo, Riccardo De Masellis, and Paolo Felli. “Description logic Knowledge and Action Bases”. Journal of Artificial Intelligence Research (JAIR), 2012. To appear. Conference Papers • • • Babak Bagheri Hariri, Diego Calvanese, Marco Montali, Giuseppe De Giacomo, and Alin Deutsch. “Verification of relational data-centric dynamic systems with external services”. In Proc. of the 32nd ACM SIGACT SIGMOD SIGART Symp. on Principles of Database Systems (PODS 2013), 2013. To appear Babak Bagheri Hariri, Diego Calvanese, Marco Montali, Giuseppe De Giacomo, Riccardo De Masellis, and Paolo Felli. “Verification of description logic Knowledge and Action Bases”. In Proc. of the 20th European Conf. on Artificial Intelligence (ECAI 2012), volume 242 of Frontiers in Artificial Intelligence and Applications, pages 103-108, 2012. Babak Bagheri Hariri, Diego Calvanese, Giuseppe De Giacomo, Riccardo De Masellis, and Paolo Felli. “Foundations of relational artifacts verification”. In Proc. of the 9th Int. Conference on Business Process Management (BPM 2011), volume 6896 of Lecture Notes in Computer Science, pages 379-395. Springer, 2011. Workshop Papers • Babak Bagheri Hariri, Diego Calvanese, Giuseppe De Giacomo, and Riccardo De Masellis. ‘’Verification of conjunctive-query based semantic artifacts”. In Proc. of the 24th Int. Workshop on Description Logics (DL 2011), volume 745 of CEUR Electronic Workshop Proceedings, pages 48-58, 2011. Technical Reports • • D. Calvanese, G. De Giacomo, B. Bagheri Hariri, R. De Masellis, D. Lembo, M. Montali,. “Techniques and Tools for KAB to Manage Action Linkage with Artifact Layer”. ACSI Project Deliverable D2.4.1, 2012. Babak Bagheri Hariri, Diego Calvanese, Giuseppe De Giacomo, Alin Deutsch, and Marco Montali. “Verification of relational data-centric dynamic systems with external services”. CoRR Technical Report, March 2012. Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 33 / 34
  111. 111. Thanks! Questions, Comments, Suggestions ? aC   Si   Babak Bagheri Hariri Borders of Decidability in Verification of DCDSs March, 2013 34 / 34

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