Applying Petri Net Unfoldings for Verification of Mobile Systems

1. Applying Petri Net Unfoldings for Verification of Mobile Systems Apostolos Niaouris Joint work with V. Khomenko, M. Koutny MOCA ‘06

2. Outline • Mobility and π-calculus • Model checking π-calculus • p-nets • Translation from π-calculus to p-nets • Implementation issues • Examples and experimental results • Next steps

3. Mobility and π-calculus • Mobility – one of the main features of many crucial modern distributed computing systems of ever growing complexity • Formal analysis and verification using process algebras like π-calculus • π-calculus can express dynamic changes in a process ability to communicate with the external environment, by passing references (channels) through interactions on previously known channels

4. π-calculus • Syntax of π-calculus • countably infinite set of channels • Free channels of P:fn(P) • Agent obtained from P by replacing all free occurrences of c by b: {b/c}P • Well-formed π-calculus expression

5. Representing π-calculus • Context-based expressions • set of restricted channels • set of channel holders • partial mapping

6. Representing π-calculus • Context-based expressions • set of restricted channels • set of channel holders • partial mapping type-K type-R type-I

7. Model checking π-calculus Pi-calculus expression At the moment, only finite pi-calculus is supported

8. Model checking π-calculus Pi-calculus expression Safe High-level PN (p-nets) Automatic translation

9. p-nets • Transitions • Places

10. p-nets • Transitions • Places

11. p-nets • Transitions • Places

12. p-nets • Transitions • Places

13. p-nets • Transitions • Places • Tag-place

14. Operators for p-nets Operators for choice, parallel composition and restriction

15. From π-calculus to p-nets • Translation of base process 0 and the three prefixes

16. From π-calculus to p-nets • For compound sub-expressions • Restriction operator • Tokens

17. Model checking π-calculus Pi-calculus expression Safe High-level PN (p-nets) PUNF MPSat Property Checking PN unfolding

18. Implementation issues • Infinity of new channels • Read arcs • Non-safeness • Partial-transition expansion • Reducing the number of holder places

19. Example • Classroom example • Scalable specification • 1 teacher process • 3,4 student processes • Check for proper termination

20. Example NESS a?ness a T ness h1 h4 h3 h2

21. Example h1!ness | h2!ness | h3!ness | h4!ness NESS a T ness h1 h4 ness ness ness h3 h2 ness

22. Example h1?addr1 | h2?addr2 | h3?addr3 | h4?addr4 NESS a T ness ness ness ness ness h1 h4 ness ness h3 h2 ness ness

23. Example NESS a T ness h1 h4 h2 h3 ness ness ness ness

24. h!h1. h1!done. STOP + h?another1.addr1!h1.addr1!another1. h1!done.STOP Example NESS a T ness ness ness h1 h4 h3 h2 ness h ness h ness ness

25. Experiments

26. Experiments

27. Experiments

28. Next steps • We need efficient extensions of the unfolding approach for read arcs • Introduce a restricted form of recursion still allowing one to use model-checking • Deal with the state space explosion caused by aspects other than high level of concurrency • Further performance comparisons of this model with other approaches