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Compositional verification of probabilistic processes

  • Kim G. Larsen
  • Arne Skou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 630)

Abstract

We introduce a simple calculus of probabilistic processes and we apply it as basis for an initial investigation of compositional verification for probabilistic processes. In particular we study the problem of decomposing logical specifications with respect to operators of the calculus. This study identifies a new probabilistic logic, which is needed in order to support decomposition. Complete axiomatizations are offered for both the calculus and the logic.

Keywords

Label Transition System Process Algebra Probabilistic Process Disjunctive Normal Form Propositional Dynamic Logic 
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.

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References

  1. [AW91]
    H Andersen and G Winskel. Compositional Checking of Satisfaction. In Proceedings of CAV '91, 1991.Google Scholar
  2. [BK84]
    J. Bergstra and J. Klop. Process algebra for synchronous communication. Information and Control, 60:109–137, 1984.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [BM89]
    B. Bloom and A. Meyer. A remark on bisimulation between probabilistic processes. In A. Meyer and M. Taitslin, editors, Logic at Botik '89, volume 363 of Lecture Notes in Computer Science, pages 26–40, 1989.Google Scholar
  4. [Chr90]
    I. Christoff. Tesing Equivalences for Probabilistic Processes. PhD thesis, Uppsala University, 1990.Google Scholar
  5. [CSZ91]
    R. Cleaveland, S. A. Smolka, and A. Zwarico. Testing Preorders for Probabilistic Processes. To appear in Proceedings of ICALP '92, 1991.Google Scholar
  6. [FHM88]
    R. Fagin, J. Y. Halpern, and N. Megiddo. A Logic for Reasoning about Probabilities. In Proceedings of LICS '88, pages 410–421, 1988.Google Scholar
  7. [GJS90]
    A. Giacalone, C. Jou, and S. Smolka. Algebraic Reasoning for Probabilistic Concurrent Systems. In Proceedings of Working Conference on Programming Concetps and Methods. IFIP TC2, 1990.Google Scholar
  8. [Hen88]
    M. Hennessy. Algebraic Theory of Processes. MIT Press, 1988.Google Scholar
  9. [HJ90]
    H. Hansson and B. Jonsson. A Calculus for Communicating Systems with Time and Probabilities. In Proc. 11th IEEE Real-Time Systems Symposium, Orlando, Florida, 1990.Google Scholar
  10. [HM85]
    M. Hennessy and R. Milner. Algebraic laws for nondeterminism and concurrency. Journal of the Association for Computing Machinery, pages 137–161, 1985.Google Scholar
  11. [Hoa85]
    C. Hoare. Communicating Sequential Processes. Prentice-Hall, 1985.Google Scholar
  12. [JL91]
    B. Jonsson and K. G. Larsen. Specification and Refinement of Probabilistic Processes. In Proceedings of LICS '91, 1991.Google Scholar
  13. [JP89]
    C. Jones and G. Plotkin. A Probabilistic Powerdomain of Evaluations. In Proceedings of 4th LICS, 1989.Google Scholar
  14. [Koz81]
    D. Kozen. Semantics of Probabilistic Programs. JCSS, 22, 1981.Google Scholar
  15. [Koz83]
    D. Kozen. A Probabilistic PDL. In Proceedings 10th ACM POPL, 1983.Google Scholar
  16. [Lar90]
    K.G. Larsen. Ideal specification formalism = expressivity + compositionality + decidability + testability + ... Lecture Notes in Computer Science, 458, 1990. Invited paper at CONCUR'90.Google Scholar
  17. [Lar91]
    K. G. Larsen. The Expressive Power of Implicit Specifications. In Proceedings of ICALP '91, 1991.Google Scholar
  18. [LS89]
    K.G. Larsen and A. Skou. Bisimulation through probabilistic testing: Preliminary report. In Proceedings 16'th ACM POPL, 1989. Full version in Information and Computation vol 94 no 1, 1991.Google Scholar
  19. [LX90]
    K. G. Larsen and L. Xinxin. Compositionality through an Operarional Semantics of Contexts. In Proceedings of ICALP '90,1990. Full version in Journal of Logic Computation, vol. 1 no. 6, pp 761–795, 1991.Google Scholar
  20. [Mil83]
    R. Milner. Calculi for synchrony and asynchrony. Theoretical Computer Science, 25:267–310, 1983.zbMATHMathSciNetCrossRefGoogle Scholar
  21. [Mil89]
    R. Milner. Communication and Concurrency. Prentice-Hall, 1989.Google Scholar
  22. [Pnu85]
    A. Pnueli. Linear and branching structures in the semantics and logics of reactive systems. In W. Braur, editor, ICALP '85, volume 194 of Lecture Notes in Computer Science, pages 15–32, 1985.Google Scholar
  23. [PZ86]
    A. Pnueli and L. Zuck. Verification of Multiprocess Probabilistic Protocols. Distributed Computing, 1, 1986.Google Scholar
  24. [Sko89]
    A. Skou. Validation of Concurrent Processes, with emphasis of testing. PhD thesis, Aalborg University Centre, 1989.Google Scholar
  25. [Var85]
    M. Y. Vardi. Automatic Verification of Probabilistic Concurrent Finite-State Programs. In Proceedings 26th IEEE FOCS, 1985.Google Scholar
  26. [vGSST90]
    R. van Glabbeek, B. Steffen, S.A. Smolka, and C.M.N. Tofts. Reactive, Generative, and Stratified Models of Probabilistic Processes. In Proceedings of LICS '90, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Kim G. Larsen
    • 1
  • Arne Skou
    • 1
  1. 1.Dep. of Math. and Comp. Sc.Aalborg UniversityAalborgDenmark

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