Reducing Model Checking of the Many to the Few

  • E. Allen Emerson
  • Vineet Kahlon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1831)


The Parameterized Model Checking Problem (PMCP) is to determine whether a temporal property is true for every size instance of a system comprised of many homogenous processes. Unfortunately, it is undecidable in general. We are able to establish, nonetheless, decidability of the PMCP in quite a broad framework. We consider asynchronous systems comprised of an arbitrary number of homogeneous copies of a generic process template. The process template is represented as a synchronization skeleton while correctness properties are expressed using Indexed CTL*∖ X. We reduce model checking for systems of arbitrary size n to model checking for systems of size up to (of) a small cutoff size c. This establishes decidability of PMCP as it is only necessary to model check a finite number of relatively small systems. Efficient decidability can be obtained in some cases. The results generalize to systems comprised of multiple heterogeneous classes of processes, where each class is instantiated by many homogenous copies of the class template (e.g., m readers and n writers).


Model Check Global State Local Computation Mutual Exclusion Transition Graph 
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  1. 1.
    Apt, K., Kozen, D.: Limits for automatic verification of finite-state concurrent systems. Information Processing Letters 15, 307–309 (1986)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Attie, P.C., Emerson, E.A.: Synthesis of Concurrent Systems with Many Similar Processes. ACM Transactions on Programming Languages and Systems 20(1), 51–115 (1998)CrossRefGoogle Scholar
  3. 3.
    Browne, M.C., Clarke, E.M., Grumberg, O.: Reasoning about Networks with Many Identical Finite State Processes. Information and Control 81(1), 13–31 (1989)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Clarke, E.M., Grumberg, O.: Avoiding the State Explosion Problem in Temporal Logic Model Checking Algorithms. In: Proceedings of the Sixth Annual ACM Symposium on Principles of Distributed Computing, pp. 294–303 (1987)Google Scholar
  5. 5.
    Clarke, E.M., Grumberg, O., Jha, S.: Verifying Parameterized Networks using Abstracion and Regular Languages. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 395–407. Springer, Heidelberg (1995)Google Scholar
  6. 6.
    Emerson, E.A., Namjoshi, K.S.: Reasoning about Rings. In: Conference Record of POPL 1995: 22nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 85–94 (1995)Google Scholar
  7. 7.
    Emerson, E.A., Namjoshi, K.S.: Automatic Verification of Parameterized Synchronous Systems. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102. Springer, Heidelberg (1996)Google Scholar
  8. 8.
    Emerson, E.A., Sistla, A.P.: Symmetry and Model Checking. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697. Springer, Heidelberg (1993)Google Scholar
  9. 9.
    Emerson, E., Trefler, R.: Parametric Quantitative Temporal Reasoning.In: LICS(1999),pp. 336–343 (1999)Google Scholar
  10. 10.
    German, S.M., Sistla, A.P.: Reasoning about Systems with Many Processes.J. ACM 39(3) (July 1992)Google Scholar
  11. 11.
    Ip, C., Dill, D.: Better verification through symmetry. In: Proceedings of the 11th International Symposium on Computer Hardware Description Languages and their Applications (1993)Google Scholar
  12. 12.
    Ip, C., Dill, D.: Verifying Systems with Replicated Components in Murphi. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 147–158. Springer, Heidelberg (1996)Google Scholar
  13. 13.
    Kurshan, R.P., McMillan, L.: A Structural Induction Theorem for Processes. In: Proceedings of the Eight Annual ACM Symposium on Principles of Distributed Computing, pp. 239–247 (1989)Google Scholar
  14. 14.
    Lichtenstein, O., Pnueli, A.: Checking that finite state concurrent programs satisfy their linear specifications. In: Conference Record of POPL 1985: 12nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 97–107 (1985)Google Scholar
  15. 15.
    Lubachevsky, B.: An Approach to Automating the Verification of Compact Parallel Coordination Programs I. Acta Informatica 21 (1984)Google Scholar
  16. 16.
    McMillan, K.: Verification of Infinite State Systems by Compositional Model Checking. In: Pierre, L., Kropf, T. (eds.) CHARME 1999. LNCS, vol. 1703, pp. 219–237. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  17. 17.
    Pnueli, A.: The Temporal Logic of Programs. In: Proceedings of the eighteenth Symposium on Foundations of Computer Science (1977)Google Scholar
  18. 18.
    Pong, F., Dubois, M.: A New Approach for the Verification of Cache Coherence Protocols. IEEE Transactions on Parallel and Distributed Systems (August 1995)Google Scholar
  19. 19.
    Sistla, A.P.: Parameterized Verification of Linear Networks Using Automata as Invariants. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 412–423. Springer, Heidelberg (1997)Google Scholar
  20. 20.
    Vardi, M., Wolper, P.: An Automata-theoretic Approach to Automatic Program Verification. In: Proceedings, Symposium on Logic in Computer Science, pp. 332–344 (1986)Google Scholar
  21. 21.
    Vernier, I.: Specification and Verification of Parameterized Parallel Programs. In: Proceedings of the 8th International Symposium on Computer and Information Sciences, Istanbul, Turkey, pp. 622–625 (1993)Google Scholar
  22. 22.
    Wolper, P., Lovinfosse, V.: Verifying Properties of Large Sets of Processes with Network Invariants. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407. Springer, Heidelberg (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • E. Allen Emerson
    • 1
  • Vineet Kahlon
    • 1
  1. 1.Department of Computer SciencesThe University of Texas at AustinAustinUSA

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