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Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
Parameterized Model Checking for Timed Systems with Conjunctive Guards
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Parameterized Model Checking for Timed Systems with Conjunctive Guards

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In this work we extend the Emerson and Kahlon’s cutoff theorems for process skeletons with conjunctive guards to Parameterized Networks of Timed Automata, i.e. systems obtained by an unbounded number …

In this work we extend the Emerson and Kahlon’s cutoff theorems for process skeletons with conjunctive guards to Parameterized Networks of Timed Automata, i.e. systems obtained by an unbounded number of Timed Automata instantiated from a finite set U_1 , ..., U_n of Timed Automata templates. In this way we aim at giving a first tool to universally verify software systems where an unknown number of software components (i.e. processes) interact with temporal constraints. It is often the case, indeed, that distributed algorithms show an heterogeneous nature, combining dynamic aspects with real-time aspects. In the paper we will also show how to model check a protocol that uses special variables storing identifiers of the participating processes (i.e. PIDs) in Timed Automata with conjunctive guards. This is non-trivial, since solutions to the parameterized verification problem often relies on the processes to be symmetric, i.e. indistinguishable. On the other side, many popular distributed algorithms make use of PIDs and thus cannot directly apply those solutions.

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  • 1. Parameterized Model-Checking for Timed Systems with Conjunctive Guards Luca Spalazzi, and Francesco Spegni fspalazzi,spegnig@dii.univpm.it DII @ UnivPM, Ancona, Italy Veri
  • 2. ed Software: Theories, Tools and Experiments 18th July 2014 L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 1 / 31
  • 3. Intro You are here... 1 Intro 2 System Model 3 Speci
  • 4. cation 4 Cuto Theorems 5 An example 6 Final discussion L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 2 / 31
  • 5. Intro Parameterized Model-Checking Problem De
  • 6. nition INPUT: process templates P1; : : : ; Pm, speci
  • 7. cation OUTPUT: True: if 8(n1; : : : ; nk ) : P(n1)jj : : : jjP(nk ) j= False: otherwise (+ counterexample) Undecidable in general see. (Apt and Kozen, '86), parameterized reachability Relevance to Software Veri
  • 8. cation (Fault Tolerant) Distributed Algorithms Security Protocols . . . L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 3 / 31
  • 9. Intro Parameterized Model-Checking Problem De
  • 10. nition INPUT: process templates P1; : : : ; Pm, speci
  • 11. cation OUTPUT: True: if 8(n1; : : : ; nk ) : P(n1)jj : : : jjP(nk ) j= False: otherwise (+ counterexample) Undecidable in general see. (Apt and Kozen, '86), parameterized reachability Relevance to Software Veri
  • 12. cation (Fault Tolerant) Distributed Algorithms Security Protocols . . . L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 3 / 31
  • 13. Intro Parameterized Model-Checking Problem De
  • 14. nition INPUT: process templates P1; : : : ; Pm, speci
  • 15. cation OUTPUT: True: if 8(n1; : : : ; nk ) : P(n1)jj : : : jjP(nk ) j= False: otherwise (+ counterexample) Undecidable in general see. (Apt and Kozen, '86), parameterized reachability Relevance to Software Veri
  • 16. cation (Fault Tolerant) Distributed Algorithms Security Protocols . . . L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 3 / 31
  • 17. Intro Cuto upper bound to the number of copies for each process template Cuto Theorem for Untimed Systems with Conjunctive/Disjunctive guards (Emerson and Kahlon, 2003) plus: automatic, modular approach (reuse model checkers) minus: complexity may be high (i.e. non optimal) until now, no work on cuto for timed systems (that we know. . . ) L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 4 / 31
  • 18. Intro Parameterized Veri
  • 19. cation of Timed Systems Several formalisms (Timed Automata, Hybrid Systems, . . . ) Some negative results on parameterized veri
  • 20. cation . . . . . . all these results require synchronous rendezvous Let's try dierent synchronization (e.g. conjunctive guards . . . ) L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 5 / 31
  • 21. System Model You are here... 1 Intro 2 System Model 3 Speci
  • 22. cation 4 Cuto Theorems 5 An example 6 Final discussion L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 6 / 31
  • 23. System Model Parameterized Networks of Timed Automata - 1 Timed Automaton: P = (S; ^s; C;

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