Abstract
Two-player games are used to model open systems. One player models the system, trying to respect some specification, while the other player models the environment. In classical model checking, the objective is to verify that the system can respect its specification, whatever the environment does.
In this article, we consider a more realistic scenario when the environment is supposed to be fair. We define a notion of fair player in two-player games. Our solution is inspired by Banach-Mazur games, and leads to a definition of a novel class of 3-player games called ABM-games. For ω-regular specifications on finite arenas, we explore the properties of ABM-games and devise an algorithm for solving them. As the main result, we show that winning in an ABM-game (i.e. winning against a fair player) is equivalent to winning with probability one against the randomized adversary.
Chapter PDF
Similar content being viewed by others
References
Baier, C., Bertrand, N., Bouyer, P., Brihaye, T., Größer, M.: Almost-sure model checking of infinite paths in one-clock timed automata. In: LICS 2008, pp. 217–226. IEEE Computer Society, Los Alamitos (2008)
Baier, C., Kwiatkowska, M.: Model checking for a probabilistic branching time logic with fairness. Distributed Computing 11(3), 125–155 (1998)
Bertrand, N., Genest, B., Gimbert, H.: Qualitative determinacy and decidability of stochastic games with signals. In: LICS 2009, pp. 319–328. IEEE Computer Society, Los Alamitos (2009)
Berwanger, D., Grädel, E., Kreutzer, S.: Once upon a time in the West. Determinacy, complexity and definability of path games. In: Vardi, M.Y., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 226–240. Springer, Heidelberg (2003)
Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Algorithms for omega-regular games with imperfect information. Logical Methods in Computer Science 3(3) (2007)
Chatterjee, K., Jurdziński, M., Henzinger, T.A.: Quantitative stochastic parity games. In: SODA 2004, pp. 114–123. ACM/SIAM (2004)
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)
Emerson, E.A., Jutla, C.: Tree automata, mu-calculus and determinacy (extended abstract). In: FOCS 1991, pp. 368–377. IEEE Computer Society, Los Alamitos (1991)
Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)
Lichtenstein, O., Pnueli, A., Zuck, L.D.: The glory of the past. In: Parikh, R. (ed.) Logic of Programs 1985. LNCS, vol. 193, pp. 196–218. Springer, Heidelberg (1985)
Mauldin, D. (ed.): The Scottish Book. Birkhäuser, Basel (1981)
Schmalz, M., Varacca, D., Völzer, H.: Counterexamples in probabilistic LTL model checking for Markov chains. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009 - Concurrency Theory. LNCS, vol. 5710, pp. 587–602. Springer, Heidelberg (2009)
Schmalz, M., Völzer, H., Varacca, D.: Model checking almost all paths can be less expensive than checking all paths. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 532–543. Springer, Heidelberg (2007)
Varacca, D., Völzer, H.: Temporal logics and model checking for fairly correct systems. In: LICS 2006, pp. 389–398. IEEE Computer Society, Los Alamitos (2006)
Völzer, H., Varacca, D., Kindler, E.: Defining fairness. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 458–472. Springer, Heidelberg (2005)
Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theor. Computer Science 200, 135–183 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Asarin, E., Chane-Yack-Fa, R., Varacca, D. (2010). Fair Adversaries and Randomization in Two-Player Games. In: Ong, L. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2010. Lecture Notes in Computer Science, vol 6014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12032-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-12032-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12031-2
Online ISBN: 978-3-642-12032-9
eBook Packages: Computer ScienceComputer Science (R0)