Abstract
We define governed stuttering bisimulation for parity games, weakening stuttering bisimulation by taking the ownership of vertices into account only when this might lead to observably different games. We show that governed stuttering bisimilarity is an equivalence for parity games and allows for a natural quotienting operation. Moreover, we prove that all pairs of vertices related by governed stuttering bisimilarity are won by the same player in the parity game. Thus, our equivalence can be used as a preprocessing step when solving parity games. Governed stuttering bisimilarity can be decided in \(\mathcal{O}(n^2m)\) time for parity games with n vertices and m edges. Our experiments indicate that governed stuttering bisimilarity is mostly competitive with stuttering equivalence on parity games encoding typical verification problems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49(5), 672–713 (2002)
Arnold, A., Vincent, A., Walukiewicz, I.: Games for synthesis of controllers with partial observation. TCS 303(1), 7–34 (2003)
Badban, B., Fokkink, W., Groote, J.F., Pang, J., van de Pol, J.: Verification of a sliding window protocol in μCRL and PVS. FAC 17, 342–388 (2005)
Berwanger, D., Dawar, A., Hunter, P., Kreutzer, S.: DAG-Width and Parity Games. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 524–536. Springer, Heidelberg (2006)
Blom, S.C.C., Orzan, S.: Distributed branching bisimulation reduction of state spaces. Electronic Notes in Theoretical Computer Science 89(1), 99–113 (2003)
Blom, S., van de Pol, J.: State Space Reduction by Proving Confluence. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 596–694. Springer, Heidelberg (2002)
Browne, M.C., Clarke, E.M., Grumberg, O.: Characterizing finite Kripke structures in propositional temporal logic. TCS 59, 115–131 (1988)
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)
Cranen, S., Keiren, J.J.A., Willemse, T.A.C.: A cure for stuttering parity games. Technical Report 12-05, Eindhoven University of Technology, Eindhoven (2012), http://alexandria.tue.nl/repository/books/732149.pdf
Cranen, S., Keiren, J.J.A., Willemse, T.A.C.: Stuttering Mostly Speeds Up Solving Parity Games. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 207–221. Springer, Heidelberg (2011)
Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy. In: FOCS 1991, pp. 368–377. IEEE Computer Society, Washington, DC (1991)
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)
Fritz, C.: Simulation-Based Simplification of omega-Automata. PhD thesis, Christian-Albrechts-Universität zu Kiel (2005)
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)
Groote, J.F., Pang, J., Wouters, A.G.: Analysis of a distributed system for lifting trucks. In: JLAP, vol. 55, pp. 21–56. Elsevier (2003)
Groote, J.F., Vaandrager, F.W.: An Efficient Algorithm for Branching Bisimulation and Stuttering Equivalence. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 626–638. Springer, Heidelberg (1990)
Jurdziński, M.: Deciding the winner in parity games is in UP ∩ co-UP. IPL 68(3), 119–124 (1998)
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)
Jurdziński, M., Paterson, M., Zwick, U.: A Deterministic Subexponential Algorithm for Solving Parity Games. In: SODA 2006, pp. 117–123. ACM/SIAM (2006)
Keiren, J.J.A., Willemse, T.A.C.: Bisimulation Minimisations for Boolean Equation Systems. In: Namjoshi, K., Zeller, A., Ziv, A. (eds.) HVC 2009. LNCS, vol. 6405, pp. 102–116. Springer, Heidelberg (2011)
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)
McNaughton, R.: Infinite games played on finite graphs. APAL 65(2), 149–184 (1993)
Obdrzálek, J.: Clique-Width and Parity Games. In: CSL, pp. 54–68 (2007)
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)
Stirling, C.: Bisimulation, Model Checking and Other Games. In: Notes for Mathfit Workshop on Finite Model Theory, University of Wales Swansea (1996)
van Glabbeek, R.J., Weijland, W.P.: Branching time and abstraction in bisimulation semantics. J. ACM 43(3), 555–600 (1996)
Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. TCS 200(1-2), 135–183 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cranen, S., Keiren, J.J.A., Willemse, T.A.C. (2012). A Cure for Stuttering Parity Games. In: Roychoudhury, A., D’Souza, M. (eds) Theoretical Aspects of Computing – ICTAC 2012. ICTAC 2012. Lecture Notes in Computer Science, vol 7521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32943-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-32943-2_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32942-5
Online ISBN: 978-3-642-32943-2
eBook Packages: Computer ScienceComputer Science (R0)