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Approximated parameterized verification of infinite-state processes with global conditions

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Abstract

We present a simple and effective approximated backward reachability procedure for parameterized systems with existentially and universally quantified global conditions. The individual processes operate on unbounded local variables ranging over the natural numbers. In addition, processes may communicate via broadcast, rendez-vous and shared variables. The procedure operates on an over-approximation of the transition system induced by the parameterized system. We verify mutual exclusion for complex protocols such as atomic, non-atomic and distributed versions of Lamport’s bakery algorithm.

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References

  1. Abdulla PA, Čerāns K, Jonsson B, Tsay YK (2000) Algorithmic analysis of programs with well quasi-ordered domains. Inf Comput 160:109–127

    Article  MATH  Google Scholar 

  2. Abdulla PA, Delzanno G (2006) On the coverability problem for constrained multiset rewriting. In: Proc AVIS’06, 5th int workshop automated verification of infinite-state systems

  3. Abdulla PA, Delzanno G, Rezine A (2007) Parameterized verification of infinite-state processes with global conditions. In: Proc 19th int conf on computer aided verification. Lecture notes in computer science, vol 4590. Springer, Berlin, pp 145–157

    Chapter  Google Scholar 

  4. Abdulla PA, Delzanno G, Rezine A (2008) Monotonic abstraction in action (automatic verification of distributed mutex algorithms). In: Yenigün H (ed) ICTAC. Lecture notes in computer science, vol 5160. Springer, Berlin, pp 50–65

    Google Scholar 

  5. Abdulla PA, Henda NB, Delzanno G, Rezine A (2007) Regular model checking without transducers (on efficient verification of parameterized systems). In: Proc TACAS ’07, 13th int conf on tools and algorithms for the construction and analysis of systems

  6. Abdulla PA, Jonsson B, Nilsson M, d’Orso J (2002) Regular model checking made simple and efficient. In: Proc CONCUR 2002, 13th int conf on concurrency theory. Lecture notes in computer science, vol 2421. Springer, Berlin, pp 116–130

    Chapter  Google Scholar 

  7. Andrews G (2000) Foundations of multithreaded, parallel, and distributed programming. Addison Wesley, Reading

    Google Scholar 

  8. Arons T, Pnueli A, Ruah S, Xu J, Zuck L (2001) Parameterized verification with automatically computed inductive assertions. In: Berry G, Comon H, Finkel A (eds) Proc 13th int conf on computer aided verification. Lecture notes in computer science, vol 2102. Springer, Berlin, pp 221–234

    Google Scholar 

  9. Boigelot B, Legay A, Wolper P (2003) Iterating transducers in the large. In: Proc 15th int conf on computer aided verification. Lecture notes in computer science, vol 2725. Springer, Berlin, pp 223–235

    Google Scholar 

  10. Bouajjani A, Habermehl P, Rogalewicz A, Vojnar T (2006) Abstract tree regular model checking of complex dynamic data structures. In: Proc 13th int symp on static analysis

  11. Bozzano M, Delzanno G (2002) Beyond parameterized verification. In: Proc TACAS ’02, 8th int conf on tools and algorithms for the construction and analysis of systems. Lecture notes in computer science, vol 2280. Springer, Berlin, pp 221–235

    Chapter  Google Scholar 

  12. Bultan T, Gerber R, Pugh W (1999) Model-checking concurrent systems with unbounded integer variables. ACM Trans Program Lang Syst 21(4):747–789

    Article  Google Scholar 

  13. Clarke E, Talupur M, Veith H (2006) Environment abstraction for parameterized verification. In: Proc VMCAI ’06, 7th int conf on verification, model checking, and abstract interpretation. Lecture notes in computer science, vol 3855. Springer, Berlin, pp 126–141

    Chapter  Google Scholar 

  14. Delzanno G (2000) Automatic verification of cache coherence protocols. In: Emerson EA, Sistla AP (eds) Proc. 12th int conf on computer aided verification. Lecture notes in computer science, vol 1855. Springer, Berlin, pp 53–68

    Chapter  Google Scholar 

  15. Emerson E, Namjoshi K (1998) On model checking for non-deterministic infinite-state systems. In: Proc LICS ’98, 13th IEEE int symp on logic in computer science, pp 70–80

  16. Esparza J, Finkel A, Mayr R (1999) On the verification of broadcast protocols. In: Proc LICS ’99, 14th IEEE int symp on logic in computer science

  17. Fribourg L, Richardson J (1997) Symbolic verification with gap-order constraints. In: LOPSTR’96. Lecture notes in computer science, vol 1207. Springer, Berlin

    Google Scholar 

  18. German SM, Sistla AP (1992) Reasoning about systems with many processes. J ACM 39(3):675–735

    Article  MATH  MathSciNet  Google Scholar 

  19. Kesten Y, Maler O, Marcus M, Pnueli A, Shahar E (2001) Symbolic model checking with rich assertional languages. Theor Comput Sci 256:93–112

    Article  MATH  MathSciNet  Google Scholar 

  20. Lahiri SK, Bryant RE (2004) Indexed predicate discovery for unbounded system verification. In: CAV 2004, pp 135–147

  21. Lamport L (1974) A new solution of Dijkstra’s concurrent programming problem. Commun ACM 17(8):453–455

    Article  MATH  MathSciNet  Google Scholar 

  22. Revesz P (1993) A closed form evaluation for datalog queries with integer (gap)-order constraints. Theor Comput Sci 116(1):117–149

    Article  MATH  MathSciNet  Google Scholar 

  23. Rezine A (2008) Parameterized systems: Generalizing and simplifying automatic verification. PhD thesis, Uppsala University

  24. Vardi MY, Wolper P (1986) An automata-theoretic approach to automatic program verification. In: Proc LICS ’86, 1st IEEE int symp on logic in computer science, pp 332–344

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Authors and Affiliations

  1. Division of Computer Systems, Uppsala University, Box 337, 75105, Uppsala, Sweden

    Parosh Aziz Abdulla

  2. Dipartimento di Informatica e Scienze dell’Informazione, Università di Genova, Via Dodecaneso 35, 16146, Genova, Italy

    Giorgio Delzanno

  3. Laboratoire d’Informatique Algorithmique: Fondements et Applications, Université Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Ahmed Rezine

Authors
  1. Parosh Aziz Abdulla
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  2. Giorgio Delzanno
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  3. Ahmed Rezine
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Correspondence to Ahmed Rezine.

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Abdulla, P.A., Delzanno, G. & Rezine, A. Approximated parameterized verification of infinite-state processes with global conditions. Form Methods Syst Des 34, 126–156 (2009). https://doi.org/10.1007/s10703-008-0062-9

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