Positional determinacy of games with infinitely many priorities

Logical Methods in Computer Science

Volumn 2, Issue 4, 2006, Pages

  Grädel, Erich ^a   Walukiewicz, Igor ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

Games; Logic; Muller games; Parity games; Positional determinacy

Indexed keywords

COMPUTER SCIENCE; COMPUTERS;

GAMES; LOGIC; MULLER GAMES; PARITY GAMES; POSITIONAL DETERMINACY;

GAME THEORY;

EID: 38049008836     PISSN: None     EISSN: 18605974     Source Type: Journal    
DOI: 10.2168/LMCS-2(4:6)2006     Document Type: Article

References (29)

1. A. Arnold, A. Vincent, and I. Walukiewicz, Games for synthesis of controllers with partial observation, Theoretical Computer Science, 303 (2003), pp. 7-34.
2. D. Berwanger, A. Dawar, P. Hunter, and S. Kreutzer, Dag-width and parity games, in Proceedings of 23rd Annual Symposium on Theoretical Aspects of Computer Science, STACS 2006, Lecture Notes in Computer Science Nr. 3848, 2006, pp. 524-536.
3. D. Berwanger and E. Grädel, Fixed-point logics and solitaire games, Theory of Computing Systems, 37 (2004), pp. 675-694.
4. D. Berwanger and E. Grädel, Entanglement-A measure for the complexity of directed graphs with applications to logic and games, in Proceedings of LPAR 2004, Lecture Notes in Computer Science Nr. 3452, Springer-Verlag, 2005, pp. 209-223.
5. A. Blumensath and E. Grädel, Finite presentations of infinite structures: Automata and interpretations, Theory of Computing Systems, 37 (2004), pp. 641-674.
6. A. Bouquet, O. Serre, and I. Walukiewicz, Pushdown games with unboundedness and regular conditions, in Proceedings of FSTTCS’03, Lecture Notes in Computer Science Nr. 2914, 2003, pp. 88-99.
7. T. Cachat, J. Duparc, and W. Thomas, Solving pushdown games with a ∑3 winning cndition, in Computer Science Logic, CSL 2002, Lecture Notes in Computer Science Nr. 2471, Springer-Verlag, 2002, pp. 322-336.
8. T. Colcombet and D. Niwiński, On the positional determinacy of edge-labeled games, Theoretical Computer Science, (2006).
9. S. Dziembowski, M. Jurdziński, and I. Walukiewicz, How much memory is needed to win infinite games?, in Proceedings of 12th Annual IEEE Symposium on Logic in Computer Science (LICS 97), 1997, pp. 99-110.
10. A. Emerson and C. Jutla, Tree automata, mu-calculus and determinacy, in Proc. 32nd IEEE Symp. on Foundations of Computer Science, 1991, pp. 368-377.
11. A. Emerson, C. Jutla, and P. Sistla, On model checking for the μ-calculus and its fragments, Theoretical Computer Science, 258 (2001), pp. 491-522.
12. H. Gimbert, Parity and exploration games on infinite graphs, in Proceedings of CSL 2004, Lecture Notes in Computer Science Nr. 3210, Springer, 2004, pp. 56-70.
13. H. Gimbert and W. Zielonka, Games where you can play optimally without any memory, in CONCUR 2005-Concurrency Theory, 16th International Conference, Lecture Notes in Computer Science Nr. 3653, Springer, 2005, pp. 428-442.
14. E. Grädel, Finite Model Theory and Descriptive Complexity, in Finite Model Theory and Its Applications, Springer-Verlag, 2006. To appear.
15. E. Grädel, W. Thomas, and T. Wilke, eds., Automata, Logics, and Infinite Games, Lecture Notes in Computer Science Nr. 2500, Springer, 2002.
16. Y. Gurevich and L. Harrington, Trees, automata and games, in Proceedings of the 14th Annual ACM Symposium on Theory of Computing, STOC ’82, 1982, pp. 60-65.
17. M. Jurdziński, Deciding the winner in parity games is in UP ∩ Co-UP, Information Processing Letters, 68 (1998), pp. 119-124.
18. M. Jurdziński, Small progress measures for solving parity games, in Proceedings of 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Lecture Notes in Computer Science Nr. 1770, Springer, 2000, pp. 290-301.
19. M. Jurdziński, M. Paterson, and U. Zwick, A deterministic subexponential algorithm for solving parity games, in Proceedings of ACM-SIAM Proceedings on Discrete Algorithms, SODA 2006, 2006, pp. 117-123.
20. E. Kopczynski, Half-positional determinacy of infinite games, in Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Lecture Notes in Computer Science Nr. 4052, 2006, pp. 336-347.
21. O. Kupferman and M. Vardi, An automata-theoretic approach to reasoning about infinite-state systems, in Proceedings of 12th International Conference on Computer-Aided Verification CAV 2000, Lecture Notes in Computer Science Nr. 1855, Springer, 2000, pp. 36-52.
22. D. Martin, Borel determinacy, Annals of Mathematics, 102 (1975), pp. 336-371.
23. R. McNaughton, Infinite games played on finite graphs, Annals of Pure and Applied Logic, 65 (1993), pp. 149-184.
24. A. Mostowski, Games with forbidden positions, Tech. Rep. Tech. Report 78, University of Gdansk, 1991.
25. J. Obdrzalek, Fast mu-calculus model checking when tree-width is bounded, in Proceedings of CAV 2003, vol. 2752 of LNCS, Springer, 2003, pp. 80-92.
26. J. Obdrzalek, DAG-width-connectivity measure for directed graphs, in Proceedings of ACM-SIAM Proceedings on Discrete Algorithms, SODA 2006, 2006, pp. 814-821.
27. O. Serre, Games with winning conditions of high Borel complexity, in Proceedings of ICALP 2004, vol. 3142 of Lecture Notes in Computer Science, 2004, pp. 1150-1162.
28. I. Walukiewicz, Pushdown processes: Games and model checking, Information and Computation, 164 (2001), pp. 234-263.
29. W. Zielonka, Infinite games on finitely coloured graphs with applications to automata on infinite trees, Theoretical Computer Science, 200 (1998), pp. 135-183