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Structures in Concurrency Theory pp 326–340Cite as

Failure-based Equivalences Are Faster Than Many Believe

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Part of the book series: Workshops in Computing ((WORKSHOPS COMP.))

Abstract

It has been known at least since 1983 that the checking of failure equivalence of two labelled transition systems is a PSPACE-complete problem, while the same problem for observation equivalence can be solved in roughly cubic time. Correspondingly, a widespread belief has arisen that failure-based equivalences are slower for the verification of concurrent systems than observation equivalence. In this article it is shown that this belief is based on a misinterpretation of the theoretical complexity result. Both theoretical and experimental evidence is given to the claim that failure-based equivalences are often faster in practice than observation equivalence. It is argued that the weakest congruence preserving given properties is in a certain sense optimal for the verification of those properties. Results giving weakest congruences for several verification tasks are surveyed.

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References

  1. Kanellakis, P. C. & Smolka, S. A.: CCS Expressions, Finite State Processes, and Three Problems of Equivalence. Proceedings of the 2nd Annual ACM Symposium on Principles of Distributed Computing, Montreal, Canada, August 1983, pp. 228–240.

    Google Scholar 

  2. Kanellakis, P. C. & Smolka, S. A.: CCS Expressions, Finite State Processes, and Three Problems of Equivalence. Information and Computation 86 (1990) pp. 43–68.

    Article  MATH  MathSciNet  Google Scholar 

  3. Milner, R.: Communication and Concurrency. Prentice-Hall 1989, 260 p.

    MATH  Google Scholar 

  4. Brookes, S. D., Hoare, C. A. R. & Roscoe, A. W.: A Theory of Communicating Sequential Processes. Journal of the ACM, 31 (3) 1984, pp. 560–599.

    Article  MATH  MathSciNet  Google Scholar 

  5. Brookes, S. D. & Rounds, W. C.: Behavioural Equivalence Relationships Induced by Programming Logics. Proceedings of 10th International Conference on Automata, Languages, and Programming, Barcelona, Spain, Lecture Notes in Computer Science 154, Springer-Verlag 1983, pp. 97–108.

    Google Scholar 

  6. Fernandez, J.-C.: An Implementation of an Efficient Algorithm for Bisimulation Equivalence. Science of Computer Programming 13 (1989/90) 219–236.

    Google Scholar 

  7. Eloranta, J.: Minimizing the Number of Transitions with Respect to Observation Equivalence. BIT 31 (1991), 576–590.

    Article  MATH  MathSciNet  Google Scholar 

  8. Inverardi, P. & Priami, C.: Evaluation of Tools for the Analysis of Communicating Systems. EATCS Bulletin 45, October 1991, pp. 158–185.

    MATH  Google Scholar 

  9. Bouajjani, A., Fernandez, J.-C. & Halbwachs, N.: Minimal Model Generation. Computer-Aided Verification ’90 (Proceedings of a Workshop), AMS-ACM DIM ACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 3, American Mathematical Society 1991, pp. 85–91.

    Google Scholar 

  10. Valmari, A.: Alleviating State Explosion during Verification of Behavioural Equivalence. Department of Computer Science, University of Helsinki, Report A- 1992-4, Helsinki, Finland 1992, 57 p.

    Google Scholar 

  11. Brinksma, E.: A Theory for the Derivation of Tests. Protocol Specification, Test-ing and Verification VIII (Proceedings of International IFIP WG 6.1 Symposium, 1988), North-Holland 1988, pp. 63–74.

    Google Scholar 

  12. Courcoubetis, C., Vardi, M., Wolper, P. & Yannakakis, M.: Memory Efficient Algorithms for the Verification of Temporal Properties. Formal Methods in Sys-tem Design, 1: 275–288 (1992).

    Article  Google Scholar 

  13. Valmari, A.: On-the-fly Verification with Stubborn Sets. Proceedings of CAV’93, 5th International Conference on Computer-Aided Verification, Elounda, Greece, Lecture Notes in Computer Science 697, Springer-Verlag 1993, pp. 397–408.

    Google Scholar 

  14. Madelaine, E. & Vergamini, D.: AUTO: A Verification Tool for Distributed Systems Using Reduction of Finite Automata Networks. Formal Description Techniques II (Proceedings of FORTE ’89), North-Holland 1990, pp. 61–66.

    Google Scholar 

  15. Graf, S. & Steffen, B.: Compositional Minimization of Finite State Processes. Computer-Aided Verification ’90 (Proceedings of a workshop), AMS-ACM DIM ACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 3, American Mathematical Society 1991, pp. 57–73.

    Google Scholar 

  16. Valmari, A.: Compositional State Space Generation. Advances in Petri Nets 1993, Lecture Notes in Computer Science 674, Springer-Verlag 1993, pp. 427–457.

    Google Scholar 

  17. Räuchle, T. & Toueg, S.: Exposure to Deadlock for Communicating Processes is Hard to Detect. Information Processing Letters 21 (1985) pp. 63–68.

    Article  MATH  MathSciNet  Google Scholar 

  18. Jones, N. D., Landweber, L. H. & Lien, Y. E.: Complexity of Some Problems in Petri Nets. Theoretical Computer Science 4 (1977) pp. 277–299.

    Article  MATH  MathSciNet  Google Scholar 

  19. Valmari, A.: Some Polynomial Space Complete Concurrency Problems. Tampere University of Technology, Software Systems Laboratory, Report 4, 1988, 34 p.

    Google Scholar 

  20. Hopcroft, J. E. & Ullman, J. D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley 1979, 418 p.

    MATH  Google Scholar 

  21. Valmari, A. & Tienari, M.: An Improved Failures Equivalence for Finite-State Systems with a Reduction Algorithm. Protocol Specification, Testing and Verification XI, North-Holland 1991, pp. 3–18.

    Google Scholar 

  22. Eloranta, J.: Minimal Transition Systems with Respect to Divergence Preserving Behavioural Equivalences. Doctoral thesis, University of Helsinki, Department of Computer Science, Report A-1994-1, Helsinki, Finland 1994, 162 p.

    Google Scholar 

  23. Rabinovich, A.: Checking Equivalences Between Concurrent Systems of Finite Agents (Extended Abstract). Proceedings of ICALP 92, Lecture Notes in Computer Science 623, Springer-Verlag 1992, pp. 696–707.

    Google Scholar 

  24. Cleaveland, R., Parrow, J. & Steffen, B.: The Concurrency Workbench. Proceedings of the Workshop on Automatic Verification Methods for Finite-State Systems, Lecture Notes in Computer Science 407, Springer-Verlag 1990, pp. 24–37.

    Google Scholar 

  25. Valmari, A., Kemppainen, J., Clegg, M. & Levanto, M.: Putting Advanced Reachability Analysis Techniques Together: the “ARA” Tool. Proceedings of Formal Methods Europe ’93, Lecture Notes in Computer Science 670, Springer-Verlag 1993, pp. 597–616.

    Google Scholar 

  26. Bolognesi, T. & Brinksma, E.: Introduction to the ISO Specification Language LOTOS. Computer Networks and ISDN Systems 14, 1987, pp. 25–59. Also in: The Formal Description Technique LOTOS, North-Holland 1989, pp. 23–73.

    Google Scholar 

  27. Valmari, A. & Tienari, M.: Compositional Failure-Based Semantic Models for Basic LOTOS. To appear in Formal Aspects of Computing, 29 p.

    Google Scholar 

  28. Valmari, A.: The Weakest Deadlock-Preserving Congruence. To appear in Infor-mation Processing Letters.

    Google Scholar 

  29. Hoare, C. A. R.: Communicating Sequential Processes. Prentice-Hall 1985, 256 p.

    MATH  Google Scholar 

  30. Bergstra, J. A., Klop, J. W. & Olderog, E.-R.: Failures without Chaos: A New Process Semantics for Fair Abstraction. Formal Description of Programming Concepts III, North-Holland, 1987, pp. 77–103.

    Google Scholar 

  31. Manna, Z. & Pnueli, A.: The Temporal Logic of Reactive and Concurrent Sys-tems: Specification. Springer-Verlag 1992, 427 p.

    Book  Google Scholar 

  32. Kaivola, R. & Valmari, A.: The Weakest Compositional Semantic Equivalence Preserving Nexttime-less Linear Temporal Logic. Proceedings of CONCUR ’92, Lecture Notes in Computer Science 630, Springer-Verlag 1992, pp. 207–221.

    Google Scholar 

  33. Setälä, M. & Valmari, A.: Validation and Verification with Weak Process Semantics. Proceedings of Nordic Seminar on Dependable Computing Systems 1994, Lyngby, Denmark, August 1994, pp. 15–26.

    Google Scholar 

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Authors and Affiliations

  1. Software Systems Laboratory, Tampere University of Technology, PO Box 553, FIN-33101, Tampere, Finland

    Antti Valmari

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  1. Antti Valmari
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Editors and Affiliations

  1. Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099, Berlin, Germany

    Jörg Desel Dr. rer. nat.

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© 1995 British Computer Society

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Valmari, A. (1995). Failure-based Equivalences Are Faster Than Many Believe. In: Desel, J. (eds) Structures in Concurrency Theory. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3078-9_22

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  • DOI: https://doi.org/10.1007/978-1-4471-3078-9_22

  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-19982-3

  • Online ISBN: 978-1-4471-3078-9

  • eBook Packages: Springer Book Archive

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