Stuttering Mostly Speeds Up Solving Parity Games

  • Sjoerd Cranen
  • Jeroen J. A. Keiren
  • Tim A. C. Willemse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6617)


We study the process theoretic notion of stuttering equivalence in the setting of parity games. We demonstrate that stuttering equivalent vertices have the same winner in the parity game. This means that solving a parity game can be accelerated by minimising the game graph with respect to stuttering equivalence. While, at the outset, it might not be clear that this strategy should pay off, our experiments using typical verification problems illustrate that stuttering equivalence speeds up solving parity games in many cases.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Badban, B., Fokkink, W., Groote, J.F., Pang, J., van de Pol, J.: Verification of a sliding window protocol in μCRL and PVS. Formal Aspects of Computing 17, 342–388 (2005)CrossRefzbMATHGoogle Scholar
  2. 2.
    Blom, S., Orzan, S.: Distributed branching bisimulation reduction of state spaces. ENTCS 89(1) (2003)Google Scholar
  3. 3.
    Browne, M.C., Clarke, E.M., Grumberg, O.: Characterizing finite Kripke structures in propositional temporal logic. Theor. Comput. Sci. 59, 115–131 (1988)CrossRefzbMATHGoogle Scholar
  4. 4.
    Chen, T., Ploeger, B., van de Pol, J., Willemse, T.A.C.: Equivalence checking for infinite systems using parameterized boolean equation systems. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 120–135. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Cranen, S., Keiren, J.J.A., Willemse, T.A.C.: Stuttering equivalence for parity games, arXiv:1102.2366 [cs.LO] (2011)Google Scholar
  6. 6.
    Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy. In: SFCS 1991, Washington, DC, USA, pp. 368–377. IEEE Computer Society, Los Alamitos (1991)Google Scholar
  7. 7.
    Friedmann, O., Lange, M.: Solving parity games in practice. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 182–196. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Fritz, C.: Simulation-Based Simplification of omega-Automata. PhD thesis, Christian-Albrechts-Universität zu Kiel (2005)Google Scholar
  9. 9.
    Fritz, C., Wilke, T.: Simulation relations for alternating parity automata and parity games. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 59–70. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Groote, J.F., Pang, J., Wouters, A.G.: Analysis of a distributed system for lifting trucks. J. Log. Algebr. Program 55, 21–56 (2003)CrossRefzbMATHGoogle Scholar
  11. 11.
    Jurdziński, M.: Small progress measures for solving parity games. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 290–301. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  12. 12.
    Luttik, S.P.: Description and formal specification of the link layer of P1394. In: Workshop on Applied Formal Methods in System Design, pp. 43–56 (1997)Google Scholar
  13. 13.
    McNaughton, R.: Infinite games played on finite graphs. Annals of Pure and Applied Logic 65(2), 149–184 (1993)CrossRefzbMATHGoogle Scholar
  14. 14.
    De Nicola, R., Vaandrager, F.W.: Three logics for branching bisimulation. J. ACM 42(2), 458–487 (1995)CrossRefzbMATHGoogle Scholar
  15. 15.
    Park, D.: Concurrency and automata on infinite sequences. Theor. Comput. Sci. 104, 167–183 (1981)CrossRefGoogle Scholar
  16. 16.
    Schewe, S.: Solving parity games in big steps. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 449–460. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Sighireanu, M., Mateescu, R.: Verification of the Link Layer Protocol of the IEEE-1394 Serial Bus (FireWire): An Experiment with e-Lotos. STTT 2(1), 68–88 (1998)CrossRefzbMATHGoogle Scholar
  18. 18.
    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
  19. 19.
    van de Pol, J., Weber, M.: A multi-core solver for parity games. ENTCS 220(2), 19–34 (2008)zbMATHGoogle Scholar
  20. 20.
    Vöge, J., Jurdziński, M.: A discrete strategy improvement algorithm for solving parity games. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 202–215. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  21. 21.
    Wimmer, R., Herbstritt, M., Hermanns, H., Strampp, K., Becker, B.: Sigref— a symbolic bisimulation tool box. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 477–492. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  22. 22.
    Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theor. Comp. Sci. 200(1-2), 135–183 (1998)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sjoerd Cranen
    • 1
  • Jeroen J. A. Keiren
    • 1
  • Tim A. C. Willemse
    • 1
  1. 1.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenThe Netherlands

Personalised recommendations