Using Canonical Representations of Solutions to Speed Up Infinite-State Model Checking

  • Tatiana Rybina
  • Andrei Voronkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2404)

Abstract

In this paper we discuss reachability analysis for infinite-state systems in which states can be represented by a vector of integers. We propose a new algorithm for verifying reachability properties based on canonical representations of solutions to systems of linear inequations over integers instead of decision procedures for integer or real arithmetic. Experimental results demonstrate that problems in protocol verification which are beyond the reach of other existing systems can be solved completely automatically.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. A. Abdulla, K. Cerans, B. Jonsson, and Y.-K. Tsay. Algorithmic analysis of programs with well quasi-ordered domains. Information and Computation, 160(1–2): 109–127, January 2000.Google Scholar
  2. 2.
    F. Ajili and E. Contejean. Avoiding slack variables in the solving of linear Diophantine equations and inequations. Theoretical Computer Science, 173(1):183–208, 1997.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    B. Bérard and L. Fribourg. Reachability analysis of (timed) Petri nets using real arithmetic. In J. C. M. Baeten and S. Mauw, editors, CONCUR’99: Concurrency Theory, 10th International Conference, volume 1664 of Lecture Notes in Computer Science, pages 178–193. Springer Verlag, 1999.CrossRefGoogle Scholar
  4. 4.
    T. Bultan. Action Language: a specification language for model checking reactive systems. In ICSE 2000, Proceedings of the 22nd International Conference on Software Engineering, pages 335–344, Limerick, Ireland, 2000. ACM.Google Scholar
  5. 5.
    T. Bultan, R. Gerber, and W. Pugh. Model-checking concurrent systems with unbounded integer variables: symbolic representations, approximations, and experimental results. ACM Transactions on Programming Languages and Systems, 21(4):747–789, 1999.CrossRefGoogle Scholar
  6. 6.
    E. Contejean and H. Devie. An efficient incremental algorithm for solving of systems of linear diophantine equations. Information and Computation, 113(1):143–172, 1994.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    G. Delzanno. Automatic verification of parametrized cache coherence protocols. In A. E. Emerson and A. P. Sistla, editors, Computer Aided Verification, 12th International Conference, CAV 2000, volume 1855 of Lecture Notes in Computer Science, pages 53–68. Springer Verlag, 2000.Google Scholar
  8. 8.
    G. Delzanno and A. Podelski. Constraint-based deductive model checking. International Journal on Software Tools for Technology Transfer, 3(3):250–270, 2001.MATHGoogle Scholar
  9. 9.
    J. Esparza, A. Finkel, and R. Mayr. On the verification of broadcast protocols. In 14th Annual IEEE Symposium on Logic in Computer Science (LICS’99), pages352–359, Trento, Italy, 1999. IEEE Computer Society.Google Scholar
  10. 10.
    N. Halbwachs, Y.-E. Proy, and P. Roumanoff. Verification of real-time systems using linear relation analysis. Formal Methods in System Design, 11(2):157–185, 1997.CrossRefGoogle Scholar
  11. 11.
    T. A. Henzinger, P.-H. Ho, and H. Wong-Toi. Hy-tech: a model checker for hybrid systems. International Journal on Software Tools for Technology Transfer, 1(1–2): 110–122, 1997.MATHGoogle Scholar
  12. 12.
    D. Hilbert. Über die Theorie der algebraischen Formen. Mathematische Annalen, 36:473–534, 1890.CrossRefMathSciNetGoogle Scholar
  13. 13.
    O. Kupferman and M. Vardi. Model checking of safety properties. Formal Methods in System Design, 19(3):291–314, 2001.MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    W. Pugh. Counting solutions to Presburger formulas: how and why. ACM SIGPLAN Notices, 29(6):121–134, June 1994. Proceedings of the ACM SIGPLAN’94 Conference on Programming Languages Design and Implementation (PLDI).Google Scholar
  15. 15.
    T. Rybina and A. Voronkov. A logical reconstruction of reachability. submitted, 2002.Google Scholar
  16. 16.
    A. Schrijver. Theory of Linear and Integer Programming. John Wiley and Sons, 1998.Google Scholar
  17. 17.
    A. P. Tomás and M. Filgueiras. An algorithm for solving systems of linear diophantine equations in naturals. In E. Costa and A. Cardoso, editors, Progress in Artificial Intelligence, 8th Portugese Conference on Artificial Intelligence, EPIA’ 97, volume 1323 of Lecture Notes in Artificial Intelligence, pages 73–84, Coimbra, Portugal, 1997. Springer Verlag.Google Scholar
  18. 18.
    A. Voronkov. An incremental algorithm for finding the basis of solutions to systems of linear Diophantine equations and inequations. unpublished, January 2002.Google Scholar
  19. 19.
    T. Yavuz-Kahveci, M. Tuncer, and T. Bultan. A library for composite symbolic representations. In T. Margaria, editor, Tools and Algorithms for Construction and Analysis of Systems, 7th International Conference, TACAS 2001, volume 1384 of Lecture Notes in Computer Science, pages 52–66, Genova, Italy, 2001. Springer Verlag.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Tatiana Rybina
    • 1
  • Andrei Voronkov
    • 1
  1. 1.University of ManchesterUK

Personalised recommendations