Quantitative solution of omega-regular games

Journal of Computer and System Sciences

Volumn 68, Issue 2, 2004, Pages 374-397

  De Alfaro, Luca ^a   Majumdar, Rupak ^b  

^a University of California Santa Cruz   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Automata; Games; Probabilities algorithm; Temporal logic; Calculus

Indexed keywords

ALGORITHMS; AUTOMATA THEORY; OPTIMIZATION; PROBABILISTIC LOGICS; PROBABILITY DISTRIBUTIONS; STATE SPACE METHODS;

OMEGA-REGULAR GAMES; PROBABILISTIC ALGORITHM; TEMPORAL LOGIC;

GAME THEORY;

EID: 1842614975     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcss.2003.07.009     Document Type: Article

References (37)

1. A. Aziz, V. Singhal, F. Balarin, R. Brayton, A. Sangiovanni-Vincentelli, It usually works: the temporal logic of stochastic systems, in: Computer Aided Verification, Lecture Notes in Computer Science, Vol. 939, Springer, New York, 1995.
2. A. Bianco, L. de Alfaro, Model checking of probabilistic and nondeterministic systems, in: Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science, Vol. 1026, Springer, New York, 1995, pp. 499-513.
3. J. Büchi, L. Landweber, Solving sequential conditions by finite-state strategies, Trans. Amer. Math. Soc. 138 (1969) 295-311.
4. J. Burch, K. McMillan, E. Clarke, D. Dill, Sequential circuit verification using symbolic model checking, in: Proceedings of the 27th ACM/IEEE Design Automation Conference, Orlando, FL, USA, June 1990, pp. 46-51.
5. C. Chang, H. Keisler, Model Theory, 3rd Edition, North Holland, Amsterdam, 1990.
6. C. Courcoubetis, M. Yannakakis, Markov decision processes and regular events, in: Proc. 17th Int. Colloq. Aut. Lang. Prog., Lecture Notes in Computer Science, Vol. 443, Springer-Verlag, New York, 1990, pp. 336-349.
7. L. de Alfaro, T. Henzinger, Concurrent omega-regular games, in: Proceedings of the 15th IEEE Symposium on Logic in Computer Science, 2000, pp. 141-154.
8. L. de Alfaro, T. Henzinger, O. Kupferman, Concurrent reachability games, in: Proceedings of the 39th IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Silver Spring, MD, 1998, pp. 564-575.
9. L. de Alfaro, M. Kwiatkowska, G. Norman, D. Parker, R. Segala, Symbolic model checking of concurrent probabilistic processes using MTBDDs and the Kronecker representation, in: TACAS: Tools and Algorithms for the Construction and Analysis of Systems, Lecture Notes in Computer Science, Vol. 1785, Springer, New York, 2000, pp. 395-410.
10. E. Emerson, C. Jutla, Tree automata, mu-calculus and determinacy (extended abstract), in: Proceedings of the 32nd IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Silver Spring, MD, 1991, pp. 368-377.
11. H. Everett, Recursive games, in: Contributions to the Theory of Games III, Annals of Mathematical Studies, Vol. 39, 1957, pp. 47-78.
12. J. Filar, K. Vrieze, Competitive Markov Decision Processes, Springer, New York, 1997.
13. Y. Gurevich, L. Harrington, Trees, automata and games, in: Proceedings of the 14th ACM Symposium on Theory of Computing, ACM Press, New York, 1982, pp. 60-65.
14. M. Huth, M. Kwiatkowska, Quantitative analysis and model checking, in: Proceedings of the 12th IEEE Symposium on Logic in Computer Science, 1997, pp. 111-122.
15. D. Kozen, A probabilistic PDL, in: Proceedings of the 15th ACM Symposium on Theory of Computing, 1983, pp. 291-297.
16. D. Kozen, Results on the propositional μ-calculus, Theoret. Comput. Sci. 27 (3) (1983) 333-354.
17. P. Kumar, T. Shiau, Existence of value and randomized strategies in zero-sum discrete-time stochastic dynamic games, SIAM J. Control Optim. 19 (5) (1981) 617-634.
18. Z. Manna, A. Pnueli, The Temporal Logic of Reactive and Concurrent Systems: Specification, Springer, New York, 1991.
19. D. Martin, The determinacy of Blackwell games, J. Symbolic Logic 63 (4) (1998) 1565-1581.
20. A. McIver, Reasoning about efficiency within a probabilitic μ-calculus, in: Proceedings of the PROBMIV, Technical Report CSR-98-4, University of Birmingham, School of Computer Science, 1998, pp. 45-58.
21. A. McIver, C. Morgan, Demonic, angelic and unbounded probabilistic choices in sequential programs, Acta Inform. 37 (4/5) (2001) 329-354.
22. R. McNaughton, Infinite games played on finite graphs, Ann. Pure Appl. Logic 65 (1993) 149-184.
23. C. Morgan, A. McIver, K. Seidel, Probabilistic predicate transformers, ACM Trans. Prog. Lang Systems 18 (3) (1996) 325-353.
24. A. Mostowski, Regular expressions for infinite trees and a standard form of automata, in: Computation Theory, Lecture Notes in the Computer Science, Vol. 208, Springer, New York, 1984, pp. 157-168.
25. G. Owen, Game Theory, Academic Press, New York, 1995.
26. T. Raghavan, J. Filar, Algorithms for stochastic games - a survey, ZOR - Methods Models of Oper. Res. 35 (1991) 437-472.
27. S. Safra, On the complexity of ω-automata, in: Proceedings of the 29th IEEE Symposium on Foundation of Computer Science, IEEE Computer Society Press, Silver Spring, MD, 1988, pp. 319-327.
28. S. Safra, Exponential determinization for ω-automatawith strong-fairness acceptance condition, in: Proceedings of the ACM Symposium on Theory of Computing, 1992, pp. 275-282.
29. L. Shapley, Stochastic games, Proc. Natl. Acad. Sci. USA 39 (1953) 1095-1100.
30. A. Tarski, A Decision Method for Elementary Algebra and Geometry, University of California Press, Berkeley, Los Angeles, 1951.
31. W. Thomas, On the synthesis of strategies in infinite games, in: Proceedings of 12th Annual Symposium on Theoretical Aspects of Computer, Science, Lecture Notes in Computer Science, Vol. 900, Springer, New York, 1995, pp. 1-13.
32. F. Thuijsman, O. Vrieze, The bad match, a total reward stochastic game, Oper. Res. Spektrum 9 (1987) 93-99.
33. M. Vardi, Automatic verification of probabilistic concurrent finite-state systems, in: Proceedings of the 26th IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Silver Spring, MD, 1985, pp. 327-338.
34. M. Vardi, P. Wolper, Reasoning about infinite computations, Inform. and Comput. 115 (1) (1994) 1-37.
35. J. von Neumann, O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, NJ, 1947.
36. H. Weyl, Elementary proof of a minmax theorem due to von Neumann, in: Contributions to the Theory of Games, I, Annals of Mathematical Studies, Vol. 24, Princeton University Press, Princeton, NJ, 1950, pp. 19-25.
37. D. Williams, Probability With Martingales, Cambridge University Press, Cambridge, 1991.