Computing Maximal Bisimulations

  • Alexandre Boulgakov
  • Thomas Gibson-Robinson
  • A. W. Roscoe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8829)

Abstract

We present and compare several algorithms for computing the maximal strong bisimulation, the maximal divergence-respecting delay bisimulation, and the maximal divergence-respecting weak bisimulation of a generalised labelled transition system. These bisimulation relations preserve CSP semantics, as well as the operational semantics of programs in other languages with operational semantics described by such GLTSs and relying only on observational equivalence. They can therefore be used to combat the space explosion problem faced in explicit model checking for such languages

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References

  1. 1.
    Park, D.: Concurrency and automata on infinite sequences. Springer, Heidelberg (1981)Google Scholar
  2. 2.
    Milner, R.: A modal characterisation of observable machine-behaviour. In: Astesiano, E., Böhm, C. (eds.) CAAP 1981. LNCS, vol. 112, pp. 25–34. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  3. 3.
    van Glabbeek, R.J., Weijland, W.P.: Branching time and abstraction in bisimulation semantics. J. ACM 43, 555–600 (1996)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Phillips, I., Ulidowski, I.: Ordered SOS rules and weak bisimulation. In: Theory and Formal Methods (1996)Google Scholar
  5. 5.
    Sangiorgi, D.: A theory of bisimulation for the π-calculus. Acta informatica 33(1), 69–97 (1996)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Inc., Upper Saddle River (1985)Google Scholar
  7. 7.
    Roscoe, A.W.: The Theory and Practice of Concurrency (1998)Google Scholar
  8. 8.
    Roscoe, A.W.: Understanding Concurrent Systems. Springer, Heidelberg (2010)CrossRefMATHGoogle Scholar
  9. 9.
    Roscoe, A.W.: Model-Checking CSP. In: A Classical Mind: Essays in Honour of CAR Hoare (1994)Google Scholar
  10. 10.
    Gibson-Robinson, T., Armstrong, P., Boulgakov, A., Roscoe, A.: FDR3—A Modern Refinement Checker for CSP (2014)Google Scholar
  11. 11.
    Roscoe, A.W., Gardiner, P., Goldsmith, M., Hulance, J., Jackson, D.M., Scattergood, J.: Hierarchical compression for model-checking CSP, or How to check 1020 dining philosophers for deadlock. In: Brinksma, E., Steffen, B., Cleaveland, W.R., Larsen, K.G., Margaria, T. (eds.) TACAS 1995. LNCS, vol. 1019, pp. 133–152. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  12. 12.
    Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM Journal on Computing 16(6), 973–989 (1987)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Fernandez, J.-C.: An implementation of an efficient algorithm for bisimulation equivalence. Science of Computer Programming 13(2), 219–236 (1990)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Van Glabbeek, R., Weijland, W.: Branching time and abstraction in bisimulation semantics: extended abstract. Rep./Centrum voor wiskunde en informatica. Computer science; CS-R8911 (1989)Google Scholar
  15. 15.
    Groote, J., Vaandrager, F.: An efficient algorithm for branching bisimulation and stuttering equivalence. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 626–638. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  16. 16.
    Armstrong, P., Goldsmith, M., Lowe, G., Ouaknine, J., Palikareva, H., Roscoe, A.W., Worrell, J.: Recent developments in FDR. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 699–704. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  17. 17.
    Floyd, R.W.: Algorithm 97: Shortest path. Commun. ACM 5, 345 (1962)CrossRefGoogle Scholar
  18. 18.
    Tarjan, R.E.: Depth-first search and linear graph algorithms. SIAM Journal on Computing 1(2), 146–160 (1972)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Tarjan, R.E.: Edge-disjoint spanning trees and depth-first search. Acta Informatica 6(2), 171–185 (1976)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Alexandre Boulgakov
    • 1
  • Thomas Gibson-Robinson
    • 1
  • A. W. Roscoe
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordOxfordUK

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