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Testing equivalence as a bisimulation equivalence

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Formal Aspects of Computing

Abstract

In this paper we show how the testing equivalences and preorders on transition systems may be interpreted as instances of generalized bisimulation equivalences and prebisimulation preorders. The characterization relies on defining transformations on the transition systems in such a way that the testing relations on the original systems correspond to (pre)bisimulation relations on the altered systems. On the basis of these results, it is possible to use algorithms for determining the (pre)bisimulation relations in the case of finite-state transition systems to compute the testing relations.

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References

  1. Bloom, B., Istrail, S., and Meyer, A. “Bisimulation Can't Be Traced.”Proceedings of the ACM Symposium on Principles of Programming Languages, 1988.

  2. Cleaveland, R., Parrow, J., and Steffen, B. “The Concurrency Workbench.” InProceedings of the Workshop on Automatic Verification Methods for Finite-State Systems, pp. 24–37.Lecture Notes in Computer Science 407. Springer-Verlag, Berlin, 1989.

    Google Scholar 

  3. Cleaveland, R., Parrow, J., and Steffen, B. “A Semantics-Based Verification Tool for Finite-State Systems.” InProceedings of the Ninth Annual Workshop on Protocol Specification, Testing and Verification, pp. 287–302. North-Holland, Amsterdam, 1990.

    Google Scholar 

  4. Cleaveland, R., Parrow, J., and Steffen, B. “The Concurrency Workbench: A Semantics-Based Verification Tool for Finite-State Systems.” To appear inACM Transactions on Programming Languages and Systems.

  5. DeNicola, R. and Hennessy, M. “Testing Equivalences for Processes.”Theoretical Computer Science 24, 1984, pp. 83–113.

    Google Scholar 

  6. Hennessy, M. “A Term Model for Synchronous Processes.”Information and Control, v. 51, n. 1, October 1981, pp. 58–75.

    Google Scholar 

  7. Hennessy, M. “Acceptance Trees.”Journal of the ACM, v. 32, n. 4, October 1985, pp. 896–928.

    Google Scholar 

  8. Hennessy, M.Algebraic Theory of Processes. MIT Press, Cambridge, 1988.

    Google Scholar 

  9. Hennessy, M. and Milner, R. “Algebraic Laws for Nondeterminism and Concurrency.”Journal of the ACM, v. 32, n. 1, January 1985, pp. 137–161.

    Google Scholar 

  10. Hoare, C.A.R.Communicating Sequential Processes. Prentice-Hall International, London, 1985.

    Google Scholar 

  11. Hopcroft, J. and Ullman, J.Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading, 1979.

    Google Scholar 

  12. Kanellakis, P.C. and Smolka, S.A. “CCS Expressions, Finite State Processes, and Three Problems of Equivalence.”Information and Computation, v. 86, n. 1, May 1990, pp. 43–68.

    Google Scholar 

  13. Larsen, K. and Skou, A. “Bisimulation through Probabilistic Testing.”Proceedings of the ACM Symposium on Principles of Programming Languages, 1989.

  14. Milner, R.A Calculus of Communicating Systems. Lecture Notes in Computer Science 92. Springer-Verlag, Berlin, 1980.

    Google Scholar 

  15. Milner, R. “Calculi for Synchrony and Asynchrony.”Theoretical Computer Science, v. 25, n. 3, July 1983, pp. 267–310.

    Google Scholar 

  16. Milner, R.Communication and Concurrency. Prentice-Hall, 1989.

  17. Paige, R. and Tarjan, R.E. “Three Partition Refinement Algorithms.”SIAM Journal of Computing, v. 16, n. 6, December 1987, pp. 973–989.

    Google Scholar 

  18. Park, D. “Concurrency and Automata in Infinite Strings.”Lecture Notes in Computer Science 104, pp. 167–183. Springer-Verlag, Berlin, 1981.

    Google Scholar 

  19. Walker, D. “Bisimulations and Divergence in CCS.”Information and Computation 85, n. 2, pp. 202–241, 1990.

    Google Scholar 

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Cleaveland, R., Hennessy, M. Testing equivalence as a bisimulation equivalence. Formal Aspects of Computing 5, 1–20 (1993). https://doi.org/10.1007/BF01211314

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  • DOI: https://doi.org/10.1007/BF01211314

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