CONCUR 1999: CONCUR’99 Concurrency Theory pp 525-540 | Cite as

Proof-Checking Protocols Using Bisimulations

  • Christine Röckl
  • Javier Esparza
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1664)

Abstract

We report on our experience in using the Isabelle/HOL theorem prover to mechanize proofs of observation equivalence for systems with infinitely many states, and for parameterized systems. We follow the direct approach: An infinite relation containing the pair of systems to be shown equivalent is defined, and then proved to be a weak bisimulation. The weak bisimilarity proof is split into many cases, corresponding to the derivatives of the pairs in the relation. Isabelle/HOL automatically proves simple cases, and guarantees that no case is forgotten. The strengths and weaknesses of the approach are discussed.

Keywords

Theorem Prover Transition Rule Proof System Parallel Composition Proof Obligation 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Baeten and W. Weijland. Process Algebra. Cambridge University Press, 1990.Google Scholar
  2. 2.
    K. A. Bartlett, R. A. Scantlebury, and P. T. Wilkinson. A note on reliable fullduplex transmission over half-duplex links. Comm. of the ACM, 12(5):260–261, May 1969.CrossRefGoogle Scholar
  3. 3.
    J. A. Bergstra and J. W. Klop. Verification of an alternating bit protocol by means of process algebra. In Mathematical Methods of Specification and Synthesis of Software Systems’ 85, volume 215 of LNCS. Springer, 1985.Google Scholar
  4. 4.
    M. Bezem and J. F. Groote. A formal verification of the alternating bit protocol in the calculus of constructions. Logic Group Preprint Series 88, Dept. of Philosophy, Utrecht University, 1993.Google Scholar
  5. 5.
    E. Gimenez. An application of co-inductive types in Coq: Verification of the alternating bit protocol. In Proc. TYPES’95, volume 1158 of LNCS, pages 135–152. Springer, 1996.Google Scholar
  6. 6.
    J. F. Groote and J. G. Springintveld. Focus points and convergent process operators. Logic Group Preprint Series 142, Dept. of Philosophy, Utrecht University, 1995.Google Scholar
  7. 7.
    J. F. Groote and J. G. Springintveld. Algebraic verification of a distributed summation algorithm. Technical Report CS-R9640, CWI, Amsterdam, 1996.Google Scholar
  8. 8.
    T. Hardin and B. Mammass. Proving the bounded retransmission protocol in the pi-calculus. In Proc. INFINITY’98, 1998.Google Scholar
  9. 9.
    R. Milner. Communication and Concurrency. Prentice-Hall, 1989.Google Scholar
  10. 10.
    R. Milner and D. Sangiorgi. The problem of weak bisimulation up-to. In Proc. CONCUR’92, volume 630 of LNCS. Springer, 1992.Google Scholar
  11. 11.
    K. Namjoshi. A simple characterization of stuttering bisimulation. In Proc. FSTTCS’97, volume 1346 of LNCS, pages 284–296. Springer, 1997.Google Scholar
  12. 12.
    V. Natarajan and R. Cleaveland. Divergence and fair testing. In Proc. ICALP’95, volume 944 of LNCS, pages 648–659. Springer, 1995.Google Scholar
  13. 13.
    T. Nipkow and K. Slind. I/O automata in Isabelle/HOL. In Proc. TYPES’94, volume 996 of LNCS, pages 101–119. Springer, 1994.Google Scholar
  14. 14.
    K. Paliwoda and J. Sanders. The sliding-window protocol. Technical Report PRG66, Programming Research Group, Oxford University, March 1988.Google Scholar
  15. 15.
    L. C. Paulson. Isabelle’s object-logics. Technical Report 286, University of Cambridge, Computer Laboratory, 1993.Google Scholar
  16. 16.
    L. C. Paulson. Isabelle: a generic theorem prover, volume 828 of LNCS. Springer, 1994.MATHGoogle Scholar
  17. 17.
    G. Plotkin. Structural operational semantics. Technical report, DAIMI, Aarhus University, 1981.Google Scholar
  18. 18.
    D. Sangiorgi. On the proof method for bisimulation. In Proc. MFCS’95, volume 969 of LNCS, pages 479–488. Springer, 1995.Google Scholar
  19. 19.
    J. L. A. Snepscheut. The sliding-window protocol revisited. Formal Aspects of Computing, 7:3–17, 1995.MATHCrossRefGoogle Scholar
  20. 20.
    D. Walker. Bisimulation and divergence. Information and Computation, 85(2):202241, 1990.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Christine Röckl
    • 1
  • Javier Esparza
    • 1
  1. 1.Technische Universität MünchenFakultät für InformatikMünchen

Personalised recommendations