Abstract
We study infinite games where one of the players always has a positional (memory-less) winning strategy, while the other player may use a history-dependent strategy. We investigate winning conditions which guarantee such a property for all arenas, or all finite arenas. Our main result is that this property is decidable in single exponential time for a given prefix independent ω-regular winning condition. We also exhibit a big class of winning conditions (XPS) which has this property.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Colcombet, T., Niwiński, D.: On the positional determinacy of edge-labeled games. Theor. Comput. Sci. 352, 190–196 (2006)
Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy. In: Proceedings 32th Annual IEEE Symp. on Foundations of Comput. Sci., pp. 368–377. IEEE Computer Society Press, Los Alamitos (1991)
Grädel, E.: Positional Determinacy of Infinite Games. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 4–18. Springer, Heidelberg (2004)
Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)
Grädel, E., Walukiewicz, I.: Positional determinacy of games with infinitely many priorities. Logical Methods in Computer Science 2(4:6), 1–22 (2006)
Gimbert, H., Zielonka, W.: When can you play positionally? In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 686–697. Springer, Heidelberg (2004)
Gimbert, H., Zielonka, W.: Games Where You Can Play Optimally Without Any Memory. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 428–442. Springer, Heidelberg (2005)
Klarlund, N.: Progress measures, immediate determinacy, and a subset construction for tree automata. In: Proc. 7th IEEE Symp. on Logic in Computer Science (1992)
Kopczyński, E.: Half-Positional Determinacy of Infinite Games. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 336–347. Springer, Heidelberg (2006)
Kopczyński, E.: Half-positional determinacy of infinite games. Draft. http://www.mimuw.edu.pl/~erykk/papers/hpwc.ps
Martin, D.A.: Borel determinacy. Ann. Math. 102, 363–371 (1975)
McNaughton, R.: Infinite games played on finite graphs. Annals of Pure and Applied Logic 65, 149–184 (1993)
Mostowski, A.W.: Games with forbidden positions. Technical Report 78, Uniwersytet Gdański, Instytut Matematyki (1991)
Zielonka, W.: Infinite Games on Finitely Coloured Graphs with Applications to Automata on Infinite Trees. Theor. Comp. Sci. 200(1-2), 135–183 (1998)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kopczyński, E. (2007). Omega-Regular Half-Positional Winning Conditions. In: Duparc, J., Henzinger, T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74915-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-74915-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74914-1
Online ISBN: 978-3-540-74915-8
eBook Packages: Computer ScienceComputer Science (R0)