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.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-540-74915-8_7
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