Network Invariants in Action*

  • Yonit Kesten
  • Amir Pnueli
  • Elad Shahar
  • Lenore Zuck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2421)


The paper presents the method of network invariants for verifying a wide spectrum of LTL properties, including liveness, of parameterized systems. This method can be applied to establish the validity of the property over a system S(n) for every value of the parameter n. The application of the method requires checking abstraction relations between two finite-state systems. We present a proof rule, based on the method of Abstraction Mapping by Abadi and Lamport, which has been implemented on the tlv modelc hecker and incorporates both history and prophecy variables. The effectiveness of the network invariant method is illustrated on several examples, including a deterministic and probabilistic versions of the dining-philosophers problem.


Model Check Network Invariant Concrete State Liveness Property Proof Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Abadi and L. Lamport. The existence of refinement mappings. Theoretical Computer Science, 82(2):253–284, May 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    K. R. Apt and D. Kozen. Limits for automatic program verification of finite-state concurrent systems. Information Processing Letters, 22(6), 1986.Google Scholar
  3. 3.
    M. Browne, E. Clarke, and O. Grumberg. Reasoning about networks with many finite state processes. PODC’86, pages 240–248.Google Scholar
  4. 4.
    E. Clarke, O. Grumberg, and S. Jha. Verifying parametrized networks using abstraction and regular languages. CONCUR’95, pages 395–407.Google Scholar
  5. 5.
    E. Dijkstra, W. Feijen, and A. van Gasteren. Derivation of a termination detection algorithm for disrtibued computations. Info. Proc. Lett., 16:217–219, 1983.Google Scholar
  6. 6.
    E. Emerson and V. Kahlon. Reducing model checking of the many to the few. In CADE-17, pages 236–255, 2000.Google Scholar
  7. 7.
    E. Emerson and K. Namjoshi. Automatic verification of parameterized synchronous systems. CAV’96, LNCS 1102.Google Scholar
  8. 8.
    N. Halbwachs, F. Lagnier, and C. Ratel. An experience in proving regular networks of processes by modular model checking. Acta Informatica, 29(6/7):523–543, 1992.zbMATHCrossRefGoogle Scholar
  9. 9.
    C. Ip and D. Dill. Verifying systems with replicated components in Murφ. CAV’96, LNCS 1102.Google Scholar
  10. 10.
    Y. Kesten and A. Pnueli. Control and data abstractions: The cornerstones of formal verification. Software Tools for Technology Transfer, 2(4):328–342, 2000.zbMATHCrossRefGoogle Scholar
  11. 11.
    Y. Kesten and A. Pnueli. Verification by augmented finitary abstraction. Information and Computation, a special issue on Compositionality, 163:203–243, 2000.zbMATHMathSciNetGoogle Scholar
  12. 12.
    Y. Kesten, A. Pnueli, E. Shahar, and L. D. Zuck. Network invariant in action. Technical report, The weizmann Institute of Science, 2002.Google Scholar
  13. 13.
    R. P. Kurshan and K. L. McMillan. A structural induction theorem for processes. Information and Computation, 117:1–11, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    D. Lehmann and M. O. Rabin. On the advantages of free choice: A symmetric and fully distributed solution to the dining philosophers problem. POPL’81, pages 133–138.Google Scholar
  15. 15.
    D. Lesens, N. Halbwachs, and P. Raymond. Automatic verification of parameterized linear networks of processes. POPL’97.Google Scholar
  16. 16.
    Z. Manna, A. Anuchitanukul, N. Bjørner, A. Browne, E. Chang, M. Colón, L. D. Alfaro, H. Devarajan, H. Sipma, and T. Uribe. STeP: The Stanford Temporal Prover. Stanford, California, 1994.Google Scholar
  17. 17.
    Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer Verlag, New York, 1991.zbMATHGoogle Scholar
  18. 18.
    Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, New York, 1995.Google Scholar
  19. 19.
    A. Pnueli, S. Ruah, and L. Zuck. Automatic deductive verification with invisible invariants. TACAS’01, LNCS 2031, pages 82–97.Google Scholar
  20. 20.
    A. Pnueli and E. Shahar. A platform for combining deductive with algorithmic verification. CAV’96, LNCS 1102, pages 184–195.Google Scholar
  21. 21.
    A. Pnueli, J. Xu, and L. Zuck. Liveness with (0, 1,∞)-counter abstraction. To appear in CAV’02.Google Scholar
  22. 22.
    A. Roychoudhury and I. Ramakrishnan. Automated inductive verification of parameterized protocols. CAV’01, LNCS 2102.Google Scholar
  23. 23.
    Z. Shtadler and O. Grumberg. Network grammars, communication behaviors and automatic verification. CAV’89, LNCS 407, pages 151–165.Google Scholar
  24. 24.
    A. Sistla and S. German. Reasoning about systems with many processes. J. ACM, 39:675–735, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    P. Wolper and V. Lovinfosse. Verifying properties of large sets of processes with network invariants. CAV’89, LNCS 407, pages 68–80.Google Scholar
  26. 26.
    L. Zuck, A. Pnueli, and Y. Kesten. Automatic verification of free choice. In Proc. of the 3rd workshop on Verification, Model Checking, and Abstract Interpretation, LNCS 2294, 2002.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Yonit Kesten
    • 1
  • Amir Pnueli
    • 2
  • Elad Shahar
    • 2
  • Lenore Zuck
    • 3
  1. 1.Ben Gurion UniversityGermany
  2. 2.Weizmann Institute of ScienceWeizmann
  3. 3.New York UniversityNew York

Personalised recommendations