Parameterized Verification of Infinite-State Processes with Global Conditions

  • Parosh Aziz Abdulla
  • Giorgio Delzanno
  • Ahmed Rezine
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4590)


We present a simple and effective approximated backward reachability algorithm 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. We apply the algorithm to verify mutual exclusion for complex protocols such as Lamport’s bakery algorithm both with and without atomicity conditions, a distributed version of the bakery algorithm, and Ricart-Agrawala’s distributed mutual exclusion algorithm.


Parameterized System Transition System Global Condition Transition Rule Mutual Exclusion 
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  1. 1.
    Abdulla, P.A., Čerāns, K., Jonsson, B., Yih-Kuen, T.: Algorithmic analysis of programs with well quasi-ordered domains. Information and Computation 160, 109–127 (2000)zbMATHCrossRefGoogle Scholar
  2. 2.
    Abdulla, P.A., Delzanno, G.: On the coverability problem for constrained multiset rewriting. In: Proc. AVIS 2006Google Scholar
  3. 3.
    Abdulla, P.A., Delzanno, G., Rezine, A.: Parameterized Verification of Infinite-state Processes with Global Conditions, Technical Report 2007-014, Uppsala University (April 2007)Google Scholar
  4. 4.
    Abdulla, P.A., Henda, N.B., Delzanno, G., Rezine, A.: Regular model checking without transducers. In: Proc. TACAS 2007 (to appear, 2007)Google Scholar
  5. 5.
    Abdulla, P.A., Jonsson, B., Nilsson, M., d’Orso, J.: Regular model checking made simple and efficient. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, Springer, Heidelberg (2002)Google Scholar
  6. 6.
    Andrews, G.: Foundations of Multithreaded, Parallel, and Distributed Programming. Addison-Wesley, Reading (2000)Google Scholar
  7. 7.
    Arons, T., Pnueli, A., Ruah, S., Xu, J., Zuck, L.: Parameterized verification with automatically computed inductive assertions. In: Agha, G.A., De Cindio, F., Rozenberg, G. (eds.) Concurrent Object-Oriented Programming and Petri Nets. LNCS, vol. 2102, Springer, Heidelberg (2001)Google Scholar
  8. 8.
    Boigelot, B., Legay, A., Wolper, P.: Iterating transducers in the large. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, Springer, Heidelberg (2003)Google Scholar
  9. 9.
    Bozzano, M., Delzanno, G.: Beyond parameterized verification. In: Katoen, J.-P., Stevens, P. (eds.) ETAPS 2002 and TACAS 2002. LNCS, vol. 2280, Springer, Heidelberg (2002)Google Scholar
  10. 10.
    Bultan, T., Gerber, R., Pugh, W.: Model-checking concurrent systems with unbounded integer variables. ACM TOPLAS 21(4), 747–789 (1999)CrossRefGoogle Scholar
  11. 11.
    Clarke, E., Talupur, M., Veith, H.: Environment abstraction for parameterized verification. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 126–141. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Delzanno, G.: Automatic verification of cache coherence protocols. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Emerson, E., Namjoshi, K.: On model checking for non-deterministic infinite-state systems. In: Proc. LICS 1998 (1998)Google Scholar
  14. 14.
    Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: Proc. LICS’ 99, 14th IEEE Int. Symp., IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  15. 15.
    Fribourg, L., Richardson, J.: Symbolic verification with gap-order constraints. In: Gallagher, J.P. (ed.) LOPSTR 1996. LNCS, vol. 1207, Springer, Heidelberg (1997)Google Scholar
  16. 16.
    German, S.M., Sistla, A.P.: Reasoning about systems with many identical processes. Journal of the ACM 39(3), 675–735 (1992)zbMATHCrossRefGoogle Scholar
  17. 17.
    Kesten, Y., Maler, O., Marcus, M., Pnueli, A., Shahar, E.: Symbolic model checking with rich assertional languages. TCS 256, 93–112 (2001)zbMATHCrossRefGoogle Scholar
  18. 18.
    Lahiri, S.K., Bryant, R.E.: Indexed predicate discovery for unbounded system verification. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 135–147. Springer, Heidelberg (2004)Google Scholar
  19. 19.
    Lamport, L.: A new solution of dijkstra’s concurrent programming problem. Commun. ACM 17(8), 453–455 (1974)zbMATHCrossRefGoogle Scholar
  20. 20.
    Revesz, P.: A closed form evaluation for datalog queries with integer (gap)-order constraints. Theoretical Computer Science 116(1), 117–149 (1993)zbMATHCrossRefGoogle Scholar
  21. 21.
    Ricart, G., Agrawal, A.K.: An optimal algorithm for mutual exclusion in computer networks. Communications of the ACM 24(1), 9–17 (1981)CrossRefGoogle Scholar
  22. 22.
    Sedletsky, E., Pnueli, A., Ben-Ari, M.: Formal verification of the ricart-agrawala algorithm. In: Proc. FSTTCS 2000 (2000)Google Scholar
  23. 23.
    Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Proc. LICS 1986 (June 1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Parosh Aziz Abdulla
    • 1
  • Giorgio Delzanno
    • 2
  • Ahmed Rezine
    • 1
  1. 1.Uppsala UniversitySweden
  2. 2.Università di GenovaItaly

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