Abstract
We consider two-player zero-sum games on graphs. On the basis of the information available to the players these games can be classified as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided partial-observation (one player has partial-observation and the other player has complete-observation); and (c) complete-observation (both players have complete view of the game). We survey the complexity results for the problem of deciding the winner in various classes of partial-observation games with ω-regular winning conditions specified as parity objectives. We present a reduction from the class of parity objectives that depend on sequence of states of the game to the sub-class of parity objectives that only depend on the sequence of observations. We also establish that partial-observation acyclic games are PSPACE-complete.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49, 672–713 (2002)
Baier, C., Bertrand, N., Größer, M.: On decision problems for probabilistic Büchi automata. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 287–301. Springer, Heidelberg (2008)
Bertrand, N., Genest, B., Gimbert, H.: Qualitative determinacy and decidability of stochastic games with signals. In: LICS, pp. 319–328. IEEE Computer Society, Los Alamitos (2009)
Berwanger, D., Doyen, L.: On the power of imperfect information. In: FSTTCS, Dagstuhl Seminar Proceedings 08004. Internationales Begegnungs- und Forschungszentrum fuer Informatik, IBFI (2008)
Büchi, J.R., Landweber, L.H.: Solving sequential conditions by finite-state strategies. Transactions of the AMS 138, 295–311 (1969)
Chatterjee, K., Doyen, L., Gimbert, H., Henzinger, T.A.: Randomness for free. In: Hlineny, P. (ed.) MFCS 2010. LNCS, vol. 6281, pp. 246–257. Springer, Heidelberg (2010)
Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Algorithms for omega-regular games of incomplete information. Logical Methods in Computer Science 3(3:4) (2007)
Chatterjee, K., Henzinger, T.A.: Probabilistic automata on infinite words: Decidability and undecidability results. In: ATVA. Springer, Heidelberg (2010)
de Alfaro, L., Henzinger, T.A.: Interface theories for component-based design. In: Henzinger, T.A., Kirsch, C.M. (eds.) EMSOFT 2001. LNCS, vol. 2211, pp. 148–165. Springer, Heidelberg (2001)
Emerson, E.A., Jutla, C.: Tree automata, mu-calculus and determinacy. In: FOCS, pp. 368–377. IEEE, Los Alamitos (1991)
Gimbert, H., Oualhadj, Y.: Probabilistic automata on finite words: Decidable and undecidable problems. In: Gavoille, C. (ed.) ICALP 2010, Part II. LNCS, vol. 6199, pp. 527–538. Springer, Heidelberg (2010)
Gripon, V., Serre, O.: Qualitative concurrent stochastic games with imperfect information. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 200–211. Springer, Heidelberg (2009)
Henzinger, T.A., Kupferman, O., Rajamani, S.: Fair simulation. Information and Computation 173, 64–81 (2002)
Immerman, N.: Number of quantifiers is better than number of tape cells. Journal of Computer and System Sciences 22, 384–406 (1981)
Kechris, A.: Classical Descriptive Set Theory. Springer, Heidelberg (1995)
Martin, D.A.: Borel determinacy. Annals of Mathematics 102(2), 363–371 (1975)
Martin, D.A.: The determinacy of Blackwell games. The Journal of Symbolic Logic 63(4), 1565–1581 (1998)
McNaughton, R.: Infinite games played on finite graphs. Annals of Pure and Applied Logic 65, 149–184 (1993)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1993)
Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL, pp. 179–190. ACM Press, New York (1989)
Ramadge, P.J., Wonham, W.M.: Supervisory control of a class of discrete-event processes. SIAM Journal of Control and Optimization 25(1), 206–230 (1987)
Reif, J.H.: Universal games of incomplete information. In: STOC, pp. 288–308. ACM Press, New York (1979)
Reif, J.H.: The complexity of two-player games of incomplete information. Journal of Computer and System Sciences 29(2), 274–301 (1984)
Safra, S.: On the complexity of ω-automata. In: FOCS, pp. 319–327. IEEE Computer Society Press, Los Alamitos (1988)
Thomas, W.: Languages, automata, and logic. In: Handbook of Formal Languages, ch. 7, vol. 3, Beyond Words, pp. 389–455. Springer, Heidelberg (1997)
Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state systems. In: FOCS, pp. 327–338. IEEE Computer Society Press, Los Alamitos (1985)
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
Chatterjee, K., Doyen, L. (2010). The Complexity of Partial-Observation Parity Games. In: Fermüller, C.G., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2010. Lecture Notes in Computer Science, vol 6397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16242-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-16242-8_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16241-1
Online ISBN: 978-3-642-16242-8
eBook Packages: Computer ScienceComputer Science (R0)