Abstract
We survey results on determinacy of games and on the existence of positional winning strategies for parity games and Rabin games. We will then discuss some new developments concerning positional determinacy for path games and for Muller games with infinitely many priorities.
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This research has been partially supported by the European Community Research Training Network “Games and Automata for Synthesis and Validation” (games)
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References
Berwanger, D., Grädel, E., Kreutzer, S.: Once upon a time in the west, Determinacy, complexity and definability of path games. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 226–240. Springer, Heidelberg (2003)
Bouquet, A., Serre, O., Walukiewicz, I.: Pushdown games with unboundedness and regular conditions (submitted for publication)
Cachat, T., Duparc, J., Thomas, W.: Solving pushdown games with a σ 3 winning cndition. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, pp. 322–336. Springer, Heidelberg (2002)
Dziembowski, S., Jurdziński, M., Walukiewicz, I.: How much memory is needed to win infinite games? In: Proceedings of 12th Annual IEEE Symposium on Logic in Computer Science (LICS 1997), pp. 99–110 (1997)
Emerson, A., Jutla, C.: Tree automata, mu-calculus and determinacy. In: Proc. 32nd IEEE Symp. on Foundations of Computer Science, pp. 368–377 (1991)
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 (submitted for publication)
Gurevich, Y., Harrington, L.: Trees, automata and games. In: Proceedings of the 14th Annual ACM Symposium on Theory of Computing, STOC 1982, pp. 60–65 (1982)
Kanamori, A.: The Higher Infinite. Springer, Heidelberg (1991)
Kechris, A.: Classical Descriptive Set Theory. Springer, Heidelberg (1995)
Klarlund, N.: Progress measures, immediate determinacy, and a subset construction for tree automata. Annals of Pure and Applied Logic 69, 243–268 (1994)
Leone, S.: The Good, the Bad and the Ugly, with Clint Eastwood, Eli Wallach, Lee Van Cleef et al. (1966)
Leone, S.: Once Upon a Time in the West, with Charles Bronson, Claudia Cardinale, Henry Fonda et al. (1969)
Martin, D.: Borel determinacy. Annals of Mathematics 102, 336–371 (1975)
Mauldin, R. (ed.): The Scottish Book. Mathematics from the Scottish Café. Birkhäuser, Basel (1981)
Mostowski, A.: Games with forbidden positions, Tech. Rep. Tech. Report 78, University of Gdansk (1991)
Pistore, M., Vardi, M.: The planning spectrum — one, two, three, infinity. In: Proc. 18th IEEE Symp. on Logic in Computer Science (2003)
Swift, J.: Gulliver’s Travels. George Routledge & Sons, London (1906) (first published in 1726)
Thomas, W.: On the synthesis of strategies in infinite games. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 1–13. Springer, Heidelberg (1995)
Thomas, W.: Languages, automata, and logic. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 389–455. Springer, Heidelberg (1997)
Zermelo, E.: Über eine Anwendung der Mengenlehre auf die Theorie des Schachpiels. In: Proc. 5th Internat. Congr. Mathematics, Cambridge, vol. 2, pp. 501–504 (1913)
Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theoretical Computer Science 200, 135–183 (1998)
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Grädel, E. (2004). Positional Determinacy of Infinite Games. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_2
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DOI: https://doi.org/10.1007/978-3-540-24749-4_2
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