Branching Bisimulation Games

  • David de Frutos Escrig
  • Jeroen J. A. Keiren
  • Tim A. C. WillemseEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9688)


Branching bisimilarity and branching bisimilarity with explicit divergences are typically used in process algebras with silent steps when relating implementations to specifications. When an implementation fails to conform to its specification, i.e., when both are not related by branching bisimilarity [with explicit divergence], pinpointing the root causes can be challenging. In this paper, we provide characterisations of branching bisimilarity [with explicit divergence] as games between \(\textsc {Spoiler}\) and \(\textsc {Duplicator}\), offering an operational understanding of both relations. Moreover, we show how such games can be used to assist in diagnosing non-conformance between implementation and specification.


Transition System Winning Strategy Label Transition System Process Algebra 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.


  1. 1.
    Basten, T.: Branching bisimilarity is an equivalence indeed!. Inform. Process. Lett. 58(3), 141–147 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Blom, S., Fokkink, W.J., Groote, J.F., van Langevelde, I., Lisser, B., van de Pol, J.: mgrCRL: a toolset for analysing algebraic specifications. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 250–254. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Bulychev, P.E., Konnov, I.V., Zakharov, V.A.: Computing (bi)simulation relations preserving CTL*-X for ordinary and fair Kripke structures. Inst. Syst. Program. Russ. Acad. Sci. Math. Meth. Algorithm 12, 59–76 (2007)Google Scholar
  4. 4.
    Cranen, S., Groote, J.F., Keiren, J.J.A., Stappers, F.P.M., de Vink, E.P., Wesselink, W., Willemse, T.A.C.: An overview of the mCRL2 toolset and its recent advances. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013 (ETAPS 2013). LNCS, vol. 7795, pp. 199–213. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  5. 5.
    Garavel, H., Lang, F., Mateescu, R., Serwe, W.: CADP 2011: a toolbox for the construction and analysis of distributed processes. Int. J. Softw. Tools Technol. Transf. 15(2), 89–107 (2013)CrossRefzbMATHGoogle Scholar
  6. 6.
    Gerth, R., Kuiper, R., Peled, D., Penczek, W.: A partial order approach to branching time logic model checking. Inform. Comput. 150(2), 132–152 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Grädel, E., Thomas, W., Wilke, T. (eds.): Automata Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  8. 8.
    Groote, J.F., Vaandrager, F.W.: An efficient algorithm for branching and stuttering equivalence. In: Paterson, M.S. (ed.) Automata, Languages and Programming. LNCS, vol. 443, pp. 626–638. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  9. 9.
    Groote, J.F., Wijs, A.: An O(m log n) algorithm for stuttering equivalence and branching bisimulation. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 607–624. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49674-9_40 CrossRefGoogle Scholar
  10. 10.
    Hennessy, M., Milner, R.: On observing nondeterminism and concurrency. In: de Bakker, J., van Leeuwen, J. (eds.) Automata, Languages and Programming. LNCS, vol. 85, pp. 299–309. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  11. 11.
    Korver, H.: Computing distinguishing formulas for branching bisimulation. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575, pp. 13–23. Springer, Heidelberg (1992)Google Scholar
  12. 12.
    Namjoshi, K.S.: A simple characterization of stuttering bisimulation. In: Ramesh, S., Sivakumar, G. (eds.) FST TCS 1997. LNCS, vol. 1346, pp. 284–296. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  13. 13.
    Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) Theoretical Computer Science. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  14. 14.
    Reniers, M.A., Schoren, R., Willemse, T.A.C.: Results on embeddings between state-based and event-based systems. Comput. J. 57(1), 73–92 (2014)CrossRefGoogle Scholar
  15. 15.
    Stevens, P., Stirling, C.: Practical model-checking using games. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 85–101. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  16. 16.
    Stirling, C.: Modal and temporal logics for processes. In: Moller, F., Birtwistle, G. (eds.) Structure versus Automata. LNCS, vol. 1043, pp. 149–237. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  17. 17.
    Thomas, W.: On the Ehrenfeucht-Fraïssé game in theoretical computer science. In: Gaudel, M.-C., Jouannaud, J.-P. (eds.) TAPSOFT’93: Theory and Practice of Software Development. LNCS, vol. 668, pp. 559–568. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  18. 18.
    van Glabbeek, R.J., Luttik, S.P., Trçka, N.: Branching bisimilarity with explicit divergence. Fundam. Inform. 93(4), 371–392 (2009)MathSciNetzbMATHGoogle Scholar
  19. 19.
    van Glabbeek, R.J., Weijland, W.P.: Branching time and abstraction in bisimulation semantics. J. ACM 43(3), 555–600 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Yin, Q., Fu, Y., He, C., Huang, M., Tao, X.: Branching bisimilarity checking for PRS. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014, Part II. LNCS, vol. 8573, pp. 363–374. Springer, Heidelberg (2014)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  • David de Frutos Escrig
    • 1
  • Jeroen J. A. Keiren
    • 2
    • 3
  • Tim A. C. Willemse
    • 4
    Email author
  1. 1.Dpto. Sistemas Informáticos y Computación - Facultad CC. MatemáticasUniversidad Complutense de MadridMadridSpain
  2. 2.Open University in the NetherlandsHeerlenThe Netherlands
  3. 3.Radboud UniversityNijmegenThe Netherlands
  4. 4.Eindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations