Compositional Verification in Linear-Time Temporal Logic

Extended Abstract
  • Yih-Kuen Tsay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1784)

Abstract

In the compositional verification of a concurrent system, one seeks to deduce properties of the system from properties of its constituent modules. This paper supplements our previous work on the same subject to provide a comprehensive compositional framework in linear-time temporal logic. It has been shown by many that specifying properties of a module in the assumption-guarantee style is effective in achieving compositionality. We consider two forms of temporal formulas that correspond to two interpretations of an assumption-guarantee specification and investigate how they can be applied in compositional verification. We argue by examples that the two forms complement each other and both are needed to facilitate the compositional approach. We also show how to handle assumption-guarantee specifications where the assumption contains a liveness property.

References

  1. [1]
    M. Abadi and L. Lamport. Composing specifications. ACM Transactions on Programming Languages and Systems, 15(1):73–132, January 1993.CrossRefGoogle Scholar
  2. [2]
    M. Abadi and L. Lamport. Conjoining specifications. ACM Transactions on Programming Languages and Systems, 17(3):507–534, May 1995.CrossRefGoogle Scholar
  3. [3]
    M. Abadi and G.D. Plotkin. A logical view of composition. Theoretical Computer Science, 114(1):3–30, June 1993.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    R. Alur and T.A. Henzinger. Local liveness for compositional modeling of fair reactive systems. In Computer Aided Verification, Proceedings of the 7th International Conference, LNCS 939, pages 166–179, 1995.Google Scholar
  5. [5]
    A. Aziz, T.R. Shiple, V. Singhal, and A.L. Sangiovanni-Vincentelli. Formula-dependent equivalence for compositional CTL model checking. In Computer Aided Verification, LNCS 818, pages 324–337, June 1994.Google Scholar
  6. [6]
    H. Barringer and R. Kuiper. Hierarchical development of concurrent systems in a temporal logic framework. In S.D. Brookes, A.W. Roscoe, and G. Winskel, editors, Seminar on Concurrency, LNCS 197, pages 35–61. Springer-Verlag, 1984.Google Scholar
  7. [7]
    K.M. Chandy and J. Misra. Parallel Program Design: A Foundation. Addison-Wesley, 1988.Google Scholar
  8. [8]
    E.M. Clarke, D.E. Long, and K.L. McMillan. Compositional model checking. In Proceedings of the 4th IEEE Symposium on Logic in Computer Science, pages 353–362, 1989.Google Scholar
  9. [9]
    P. Collette. Application of the composition principle to Unity-like specifications. In TAPSOFT’ 93: Theory and Practice of Software Development, LNCS 668, pages 230–242. Springer-Verlag, 1993.Google Scholar
  10. [10]
    P. Collette. Design of Compositional Proof Systems Based on Assumption-Guarantee Specifications — Application to UNITY. PhD thesis, Université Catholique de Louvain, June 1994.Google Scholar
  11. [11]
    W.-P. de Roever, H. Langmåck, and A. Pnueli. Compositionality: The Significant Difference. Springer-Verlag, 1998. Lecture Notes in Computer Science 1536.Google Scholar
  12. [12]
    P. Grønning, T.Q. Nielsen, and H.H. Løvengreen. Refinement and composition of transition-based rely-guarantee specifications with auxiliary variables. In K.V. Nori and C.E. Veni Madhavan, editors, Foundations of Software Technology and Theoretical Computer Science, LNCS 472, pages 332–348. Springer-Verlag, 1991.Google Scholar
  13. [13]
    O. Grumberg and D.E. Long. Model checking and modular verification. ACM Transactions on Programming Languages and Systems, 16(3):843–871, May 1994.CrossRefGoogle Scholar
  14. [14]
    C.A.R. Hoare. An axiomatic basis for computer programs. Communications of the ACM, 12(8):576–580, 1969.MATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    C.B. Jones. Tentative steps towards a development method for interfering programs. ACM Transactions on Programming Languages and Systems, 5(4):596–619, October 1983.MATHCrossRefGoogle Scholar
  16. [16]
    B. Jonsson and Y.-K. Tsay. Assumption/guarantee specifications in linear-time temporal logic. Theoretical Computer Science, 167:47–72, October 1996. An extended abstract appeared earlier in TAPSOFT’ 95, LNCS 915.Google Scholar
  17. [17]
    O. Kupferman and M.Y. Vardi. Module checking. In O. Grumberg, editor, Computer-Aided Verification, CAV’ 96, LNCS 1102, pages 75–86. Springer-Verlag, August 1996.Google Scholar
  18. [18]
    O. Kupferman and M.Y. Vardi. Module checking revisited. In Computer-Aided Verification, CAV’ 97, LNCS 1254. Springer-Verlag, June 1997.Google Scholar
  19. [19]
    L. Lamport. Specifying concurrent program modules. ACM Transactions on Programming Languages and Systems, 5(2):190–222, 1983.MATHCrossRefGoogle Scholar
  20. [20]
    L. Lamport. The temporal logic of actions. ACM Transactions on Programming Languages and Systems, 16(3):872–923, May 1994.CrossRefGoogle Scholar
  21. [21]
    Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer-Verlag, 1992.Google Scholar
  22. [22]
    Z. Manna and A. Pnueli. Temporal Verification of Reactive Systems: Safety. Springer-Verlag, 1995.Google Scholar
  23. [23]
    J. Misra and K.M. Chandy. Proofs of networks of processes. IEEE Transactions on Software Engineering, 7(4):417–426, July 1981.CrossRefMathSciNetGoogle Scholar
  24. [24]
    A. Pnueli. The temporal semantics of concurrent programs. Theoretical Computer Science, 13:45–60, 1982.CrossRefMathSciNetGoogle Scholar
  25. [25]
    Y.-K. Tsay. Compositional verification in linear-time temporal logic (the full version). Send requests to tsay@im.ntu.edu.tw.Google Scholar
  26. [26]
    M.Y. Vardi. On the complexity of modular model checking. In Proceedings of the 10th IEEE Symposium on Logic in Computer Science, pages 101–111, June 1995.Google Scholar
  27. [27]
    Q. Xu, A. Cau, and P. Collette. On unifying assumption-commitment style proof rules for concurrency. In B. Jonsson and J. Parrow, editors, CONCUR’ 94: Concurrency Theory, LNCS 836, pages 267–282. Springer-Verlag, 1994.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Yih-Kuen Tsay
    • 1
  1. 1.Department of Information ManagementNational Taiwan UniversityTaiwan

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