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Up-to Techniques for Branching Bisimilarity

  • Rick Erkens
  • Jurriaan Rot
  • Bas LuttikEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12011)

Abstract

Ever since the introduction of behavioral equivalences on processes one has been searching for efficient proof techniques that accompany those equivalences. Both strong bisimilarity and weak bisimilarity are accompanied by an arsenal of up-to techniques: enhancements of their proof methods. For branching bisimilarity, these results have not been established yet. We show that a powerful proof technique is sound for branching bisimilarity by combining the three techniques of up to union, up to expansion and up to context for Bloom’s BB cool format. We then make an initial proposal for casting the correctness proof of the up to context technique in an abstract coalgebraic setting, covering branching but also \(\eta \), delay and weak bisimilarity.

Notes

Acknowledgements

We thank Filippo Bonchi for the idea how to encode branching bisimilarity coalgebraically, and the reviewers for their useful comments.

References

  1. 1.
    Arun-Kumar, S., Hennessy, M.: An efficiency preorder for processes. Acta Inf. 29(8), 737–760 (1992)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bloom, B.: Structural operational semantics for weak bisimulations. TCS 146(1&2), 25–68 (1995)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. In: POPL, pp. 229–239. ACM (1988)Google Scholar
  4. 4.
    Bonchi, F., Petrisan, D., Pous, D., Rot, J.: A general account of coinduction up-to. Acta Inf. 54(2), 127–190 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bonchi, F., Pous, D.: Hacking nondeterminism with induction and coinduction. Commun. ACM 58(2), 87–95 (2015)CrossRefGoogle Scholar
  6. 6.
    Brengos, T.: Weak bisimulation for coalgebras over order enriched monads. Log. Methods Comput. Sci. 11(2), 1–44 (2015) MathSciNetCrossRefGoogle Scholar
  7. 7.
    Fokkink, W., van Glabbeek, R.: Divide and congruence II: from decomposition of modal formulas to preservation of delay and weak bisimilarity. Inf. Comput. 257, 79–113 (2017)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Fokkink, W., van Glabbeek, R., Luttik, B.: Divide and congruence III: from decomposition of modal formulas to preservation of stability and divergence. Inf. Comput. 268, 104435 (2019).  https://doi.org/10.1016/j.ic.2019.104435. Article no. 31 pagesMathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    van Glabbeek, R.: On cool congruence formats for weak bisimulations. TCS 412(28), 3283–3302 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    van Glabbeek, R.J.: A complete axiomatization for branching bisimulation congruence of finite-state behaviours. In: Borzyszkowski, A.M., Sokołowski, S. (eds.) MFCS 1993. LNCS, vol. 711, pp. 473–484. Springer, Heidelberg (1993).  https://doi.org/10.1007/3-540-57182-5_39CrossRefGoogle Scholar
  11. 11.
    Jacobs, B.: Introduction to Coalgebra: Towards Mathematics of States and Observation. Cambridge Tracts in Theoretical Computer Science, vol. 59. Cambridge University Press, Cambridge (2016)Google Scholar
  12. 12.
    Jacobs, B., Hughes, J.: Simulations in coalgebra. ENTCS 82(1), 128–149 (2003)zbMATHGoogle Scholar
  13. 13.
    Milner, R.: Communication and Concurrency. PHI Series in Computer Science. Prentice Hall, Upper Saddle River (1989)Google Scholar
  14. 14.
    Milner, R.: A complete axiomatisation for observational congruence of finite-state behaviors. Inf. Comput. 81(2), 227–247 (1989)CrossRefGoogle Scholar
  15. 15.
    Pous, D.: New up-to techniques for weak bisimulation. TCS 380(1–2), 164–180 (2007)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Pous, D.: Coinduction all the way up. In: LICS, pp. 307–316. ACM (2016)Google Scholar
  17. 17.
    Pous, D., Sangiorgi, D.: Enhancements of the bisimulation proof method (2012)Google Scholar
  18. 18.
    Rutten, J.: Universal coalgebra: a theory of systems. TCS 249(1), 3–80 (2000)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Sangiorgi, D.: On the proof method for bisimulation. In: Wiedermann, J., Hájek, P. (eds.) MFCS 1995. LNCS, vol. 969, pp. 479–488. Springer, Heidelberg (1995).  https://doi.org/10.1007/3-540-60246-1_153CrossRefGoogle Scholar
  20. 20.
    Sangiorgi, D., Milner, R.: The problem of “weak bisimulation up to”. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 32–46. Springer, Heidelberg (1992).  https://doi.org/10.1007/BFb0084781CrossRefGoogle Scholar
  21. 21.
    Sangiorgi, D., Walker, D.: The Pi-Calculus - A Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)zbMATHGoogle Scholar
  22. 22.
    Turi, D., Plotkin, G.: Towards a mathematical operational semantics. In: LICS, pp. 280–291. IEEE (1997)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Eindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.University College LondonLondonUK
  3. 3.Radboud University NijmegenNijmegenThe Netherlands

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