Verification of Data-Centric Dynamic Systems Babak Bagheri Hariri - PowerPoint PPT Presentation

Verification of Data-Centric Dynamic Systems Babak Bagheri Hariri Supervisor: Diego Calvanese KRDB Research Centre for Knowledge and Data Free University of Bozen-Bolzano September, 2012 Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 1 / 11

Modeling both structural and behavioral aspects Data Process Data+Process Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 2 / 11

Modeling both structural and behavioral aspects Data Process Data+Process In our research we study the boundaries of decidability : Design • formalisms for modeling knowledge and behavior , • languages for expressing dynamic properties , such that: Verification of dynamic properties over the given formalism is decidable . Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 2 / 11

Data-Centric Dynamic Systems (DCDS) We introduce DCDS, to • explore different variants of modeling data and process • abstract away from irrelevant factors of different scenario. Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 3 / 11

Data-Centric Dynamic Systems (DCDS) Data layer Process layer DCDS 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 Euro/USD ⋆ Nondeterministic services: e.g., current exchange rate of Euro/USD Allow one also to take into account user-input. Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 3 / 11

DCDS, example Data Layer peer Schema Instance Customer Cust ( ann ) In Debt Customer peer ( mark , john ) closed Gold ( john ) owes Gold Customer Loan Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 4 / 11

DCDS, example Data Layer peer Schema Instance Customer Cust ( ann ) In Debt Customer peer ( mark , john ) closed Gold ( john ) owes Gold Customer Loan Process Layer Actions GetLoan ( x ) : Conditions peer ( x , y ) ∧ Gold ( y ) �− → GetLoan ( x ) ∃ y . peer ( x , y ) � { owes ( x , UInput ( x )) } , Cust ( z ) � { Cust ( z ) } , Service Calls Loan ( z ) � { Loan ( z ) } , UInput ( x ) InDebt ( z ) � { InDebt ( z ) } , Gold ( z ) � { Gold ( z ) } Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 4 / 11

DCDS, example Data Layer peer Schema Instance Customer Cust ( ann ) peer ( mark , john ) In Debt Customer Gold ( john ) closed owes ( mark , owes Gold Customer Loan UInput ( mark )) Process Layer Actions GetLoan ( x ) : Conditions peer ( x , y ) ∧ Gold ( y ) �− → GetLoan ( x ) ∃ y . peer ( x , y ) � { owes ( x , UInput ( x )) } , Cust ( z ) � { Cust ( z ) } , Service Calls Loan ( z ) � { Loan ( z ) } , UInput ( x ) InDebt ( z ) � { InDebt ( z ) } , Gold ( z ) � { Gold ( z ) } Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 4 / 11

Deterministic services 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 Data-Centric Dynamic Systems VTSA 2012 5 / 11

Deterministic services 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 Data-Centric Dynamic Systems VTSA 2012 5 / 11

Deterministic services semantics - via transition systems f(a) �→ g(a) �→ � P ( x ) � P ( x ) ∧ Q ( f ( x ) , g ( x )) P(a) R(a) Q( , ) Q ( a , a ) ∧ P ( x ) � R ( x ) , I = { P ( a ) , Q ( a , a ) } P(a) Q(a,a) Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 5 / 11

Deterministic services semantics - via transition systems f(a) �→ a g(a) �→ � P ( x ) � P ( x ) ∧ Q ( f ( x ) , g ( x )) P(a) R(a) Q(a, ) Q ( a , a ) ∧ P ( x ) � R ( x ) , I = { P ( a ) , Q ( a , a ) } P(a) Q(a,a) Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 5 / 11

Deterministic services semantics - via transition systems f(a) �→ a g(a) �→ a � P ( x ) � P ( x ) ∧ Q ( f ( x ) , g ( x )) P(a) R(a) Q(a,a) Q ( a , a ) ∧ P ( x ) � R ( x ) , I = { P ( a ) , Q ( a , a ) } P(a) Q(a,a) Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 5 / 11

Deterministic services semantics - via transition systems f(a) �→ a g(a) �→ a � P ( x ) � P ( x ) ∧ Q ( f ( x ) , g ( x )) P(a) R(a) Q(a,a) Q ( a , a ) ∧ P ( x ) � R ( x ) , 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 Data-Centric Dynamic Systems VTSA 2012 5 / 11

Deterministic services semantics - via transition systems f(a) �→ a g(a) �→ a � P ( x ) � P ( x ) ∧ Q ( f ( x ) , g ( x )) P(a) R(a) Q(a,a) Q ( a , a ) ∧ P ( x ) � R ( x ) , 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) Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 5 / 11

Deterministic services semantics - via transition systems f(a) �→ a g(a) �→ a � P ( x ) � P ( x ) ∧ Q ( f ( x ) , g ( x )) P(a) R(a) Q(a,a) Q ( a , a ) ∧ P ( x ) � R ( x ) , 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 Data-Centric Dynamic Systems VTSA 2012 5 / 11

Deterministic services semantics - via transition systems f(a) �→ a g(a) �→ a � P ( x ) � P ( x ) ∧ Q ( f ( x ) , g ( x )) P(a) R(a) Q(a,a) Q ( a , a ) ∧ P ( x ) � R ( x ) , 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 Data-Centric Dynamic Systems VTSA 2012 5 / 11

Deterministic services semantics - via transition systems f(a) �→ a g(a) �→ a � P ( x ) � P ( x ) ∧ Q ( f ( x ) , g ( x )) P(a) R(a) Q(a,a) Q ( a , a ) ∧ P ( x ) � R ( x ) , f(a) �→ a g(a) �→ b f(a) �→ a g(a) �→ b I = { P ( a ) , Q ( a , a ) } P(a) R(a) Q(a,b) P(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 Data-Centric Dynamic Systems VTSA 2012 5 / 11

Deterministic services semantics - via transition systems f(a) �→ a g(a) �→ a � P ( x ) � P ( x ) ∧ Q ( f ( x ) , g ( x )) P(a) R(a) Q(a,a) Q ( a , a ) ∧ P ( x ) � R ( x ) , f(a) �→ a g(a) �→ b f(a) �→ a g(a) �→ b I = { P ( a ) , Q ( a , a ) } P(a) R(a) Q(a,b) P(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 Data-Centric Dynamic Systems VTSA 2012 5 / 11

Deterministic services semantics - via transition systems f(a) �→ a g(a) �→ a � P ( x ) � P ( x ) ∧ Q ( f ( x ) , g ( x )) P(a) R(a) Q(a,a) Q ( a , a ) ∧ P ( x ) � R ( x ) , f(a) �→ a g(a) �→ b f(a) �→ a g(a) �→ b I = { P ( a ) , Q ( a , a ) } 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) Q(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) . . . Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 5 / 11

Verification formalisms • We propose different FO variants of µ -calculus. • µ L is not expressive enough to compare µ L FO over time objects created by the process. • Verification of µ L FO is undecidable, even for very restricted DCDSs! µ L LTL PDL CTL HML Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 6 / 11

Verification formalisms • We propose different FO variants of µ -calculus. • µ L is not expressive enough to compare µ L FO over time objects created by the process. • Verification of µ L FO is undecidable, even for very restricted DCDSs! µ L A µ L P We introduce: µ L P and µ L A as extensions of µ L with µ L (restricted) first order quantification. LTL PDL CTL HML Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 6 / 11

Verification formalisms • We propose different FO variants of µ -calculus. • µ L is not expressive enough to compare µ L FO over time objects created by the process. • Verification of µ L FO is undecidable, even for very restricted DCDSs! µ L A µ L P We introduce: µ L P and µ L A as extensions of µ L with µ L (restricted) first order quantification. Example in µ L : A Liveness property: LTL PDL CTL µ Z . ([ ∃ x . Gold ( x ) ∧ InDebt ( x )] ∨ �−� Z ) HML ≡ F [ ∃ x . Gold ( x ) ∧ InDebt ( x )] Babak Bagheri Hariri Data-Centric Dynamic Systems VTSA 2012 6 / 11