Improving Priority Promotion for Parity Games

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• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：10028
• 期：1
• 页码：117-133
• 全文大小：472 KB
• 参考文献：1.Apt, K., Grädel, E.: Lectures in Game Theory for Computer Scientists. Cambridge University Press, Cambridge (2011)CrossRef MATH
  2.Benerecetti, M., Dell’Erba, D., Mogavero, F.: Solving parity games via priority promotion. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9780, pp. 270–290. Springer, Heidelberg (2016). doi:10.​1007/​978-3-319-41540-6_​15 CrossRef
  3.Chatterjee, K., Doyen, L., Henzinger, T., Raskin, J.-F.: Generalized mean-payoff and energy games. In: FSTTCS 2010. LIPIcs, vol. 8, pp. 505–516. Leibniz-Zentrum fuer Informatik (2010)
  4.Condon, A.: The complexity of stochastic games. IC 96(2), 203–224 (1992)MathSciNet MATH
  5.Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. IJGT 8(2), 109–113 (1979)MathSciNet MATH
  6.Emerson, E., Jutla, C.: The complexity of tree automata and logics of programs (extended abstract). In: FOCS 1988, pp. 328–337. IEEE Computer Society (1988)
  7.Emerson, E., Jutla, C.: Tree automata, muCalculus, and determinacy. In: FOCS 1991, pp. 368–377. IEEE Computer Society (1991)
  8.Emerson, E., Jutla, C., Sistla, A.: On model-checking for fragments of \(\mu \) -calculus. In: Courcoubetis, C. (ed.) CAV ’93. LNCS, vol. 697, pp. 385–396. Springer, Heidelberg (1993). doi:10.​1007/​3-540-56922-7_​32 CrossRef
  9.Friedmann, O., Lange, M.: Solving parity games in practice. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 182–196. Springer, Heidelberg (2009). doi:10.​1007/​978-3-642-04761-9_​15 CrossRef
  10.Grädel, E., Thomas, W., Wilke, T.: Automata Logics, and Infinite Games: A Guide to Current Research. LNCS, vol. 2500. Springer, Heidelberg (2002)CrossRef MATH
  11.Gurevich, V., Karzanov, A., Khachivan, L.: Cyclic games and an algorithm to find minimax cycle means in directed graphs. USSRCMMP 28(5), 85–91 (1990)
  12.Jurdziński, M.: Deciding the winner in parity games is in UP \(\cap \) co-Up. IPL 68(3), 119–124 (1998)MathSciNet CrossRef MATH
  13.Jurdziński, M.: Small progress measures for solving parity games. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 290–301. Springer, Heidelberg (2000). doi:10.​1007/​3-540-46541-3_​24 CrossRef
  14.Jurdziński, M., Paterson, M., Zwick, U.: A deterministic subexponential algorithm for solving parity games. SJM 38(4), 1519–1532 (2008)MathSciNet MATH
  15.Kupferman, O., Vardi, M.: Weak alternating automata and tree automata emptiness. In: STOC 1998, pp. 224–233. Association for Computing Machinery (1998)
  16.Kupferman, O., Vardi, M., Wolper, P.: An automata theoretic approach to branching-time model checking. JACM 47(2), 312–360 (2000)MathSciNet CrossRef MATH
  17.Mostowski, A.W.: Regular expressions for infinite trees and a standard form of automata. In: Skowron, A. (ed.) SCT 1984. LNCS, vol. 208, pp. 157–168. Springer, Heidelberg (1985). doi:10.​1007/​3-540-16066-3_​15 CrossRef
  18.Mostowski, A.: Games with forbidden positions. University of Gdańsk, Gdańsk, Poland, Technical report (1991)
  19.Schewe, S.: Solving parity games in big steps. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 449–460. Springer, Heidelberg (2007). doi:10.​1007/​978-3-540-77050-3_​37 CrossRef
  20.Schewe, S.: An optimal strategy improvement algorithm for solving parity and payoff games. In: Kaminski, M., Martini, S. (eds.) CSL 2008. LNCS, vol. 5213, pp. 369–384. Springer, Heidelberg (2008). doi:10.​1007/​978-3-540-87531-4_​27 CrossRef
  21.Schewe, S., Trivedi, A., Varghese, T.: Symmetric strategy improvement. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 388–400. Springer, Heidelberg (2015). doi:10.​1007/​978-3-662-47666-6_​31
  22.Vöge, J., Jurdziński, M.: A discrete strategy improvement algorithm for solving parity games. In: Allen Emerson, E., Sistla, A.P. (eds.) CAV 2000. Lecture Notes in Computer Science, vol. 1855, pp. 202–215. Springer, Heidelberg (2000). doi:10.​1007/​10722167_​18 CrossRef
  23.Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. TCS 200(1–2), 135–183 (1998)MathSciNet CrossRef MATH
  24.Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. TCS 158(1–2), 343–359 (1996)MathSciNet CrossRef MATH
  
• 作者单位：Massimo Benerecetti (15)
  Daniele Dell’Erba (15)
  Fabio Mogavero (16)
  
  15. Università degli Studi di Napoli Federico II, Naples, Italy
  16. Oxford University, Oxford, UK
  
• 丛书名：Hardware and Software: Verification and Testing
• ISBN：978-3-319-49052-6
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：10028

文摘

Parity games are two-player infinite-duration games on graphs that play a crucial role in various fields of theoretical computer science. Finding efficient algorithms to solve these games in practice is widely acknowledged as a core problem in formal verification, as it leads to efficient solutions of the model-checking and satisfiability problems of expressive temporal logics, e.g., the modal \(\mu \) Calculus. Their solution can be reduced to the problem of identifying sets of positions of the game, called dominions, in each of which a player can force a win by remaining in the set forever. Recently, a novel technique to compute dominions, called priority promotion, has been proposed, which is based on the notions of quasi dominion, a relaxed form of dominion, and dominion space. The underlying framework is general enough to accommodate different instantiations of the solution procedure, whose correctness is ensured by the nature of the space itself. In this paper we propose a new such instantiation, called region recovery, that tries to reduce the possible exponential behaviours exhibited by the original method in the worst case. The resulting procedure not only often outperforms the original priority promotion approach, but so far no exponential worst case is known.