Quantitative verification and control via the mu-calculus

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2761, Issue , 2003, Pages 103-127

  De Alfaro, Luca ^a  

^a University of California Santa Cruz   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CALCULATIONS; SPECIFICATIONS;

CONTROL PROBLEMS; LINEAR-TIME PROPERTIES; MU-CALCULUS; PROBABILISTIC EXTENSION; QUANTITATIVE VERIFICATION; SYMBOLIC ALGORITHMS; SYSTEM SPECIFICATION;

TEMPORAL LOGIC;

EID: 35248832952     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-45187-7_7     Document Type: Article

References (39)

1. R. Alur, T.A. Henzinger, and O. Kupferman. Alternating time temporal logic. J. ACM, 49:672-713, 2002.
2. R. Alur, T.A. Henzinger, O. Kupferman, and M.Y. Vardi. Alternating refinement relations. In CONCUR 97: Concurrency Theory. 8th Int. Conf., volume 1466 of Lect. Notes in Camp. Sci., pages 163-178. Springer-Verlag, 1998.
3. G. Bhat and R. Cleaveland. Efficient model checking via the equational μ-calculus. In Proc. 11th IEEE Symp. Logic in Comp. Sci., pages 304-312, 1996.
4. D.P. Bertsekas. Dynamic Programming and Optimal Control. Athena Scientific, 1995. Volumes I and II.
5. J.R. Büchi and L.H. Landweber. Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc., 138:295-311, 1969.
6. R.E. Bryant. Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers, C-35(8):677-691, 1986.
7. A. Condon. The complexity of stochastic games. Information and Computation, 96:203-224, 1992.
8. L. de Alfaro and T.A. Henzinger. Concurrent omega-regular games. In Proc. 15th IEEE Symp. Logic in Comp. Sci., pages 141-154, 2000.
9. L. de Alfaro, T.A. Henzinger, and O. Kupferman. Concurrent reachability games. In Proc. 39th IEEE Symp. Found. of Comp. Sci., pages 564-575. IEEE Computer Society Press, 1998.
10. L. de Alfaro, T.A. Henzinger, and R. Majumdar. From verification to control: Dynamic programs for omega-regular objectives. In Proc. 16th IEEE Symp. Logic in Comp. Sci., pages 279-290. IEEE Press, 2001.
11. L. de Alfaro, T.A. Henzinger, and R. Majumdar. Symbolic algorithms for infinite-state games. In CONCUR 01: Concurrency Theory. 12th Int. Conf., volume 2154 of Lect. Notes in Comp. Sci., pages 536-550. Springer-Verlag, 2001.
12. L. de Alfaro, T.A. Henzinger, and R. Majumdar. Discounting the future in systems theory. In Proc. 30th Int. Colloq. Aut. Lang. Prog., Lect. Notes in Comp. Sci. Springer-Verlag, 2003.
13. L. de Alfaro and R. Majumdar. Quantitative solution of omega-regular games. In Proc. 33rd ACM Symp. Theory of Comp., pages 675-683. ACM Press, 2001.
14. J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled markov processes. Information and Computation, 179(2):163-193, 2002.
15. C. Derman. Finite State Markovian Decision Processes. Academic Press, 1970.
16. J. Desharnais, V. Gupta, R. Jagadeesan, and P. Panangaden. Metrics for labelled markov systems. In CONCUR'99: Concurrency Theory. 10th Int. Conf., volume 1664 of Lect. Notes in Comp. Sci., pages 258-273. Springer, 1999.
17. J. Desharnais, V. Gupta, R. Jagadeesan, and P. Panangaden. The metric analogue of weak bisimulation for probabilistic processes. In Proc. 17th IEEE Symp. Logic in Comp. Sci., pages 413-422, 2002.
18. E.A. Emerson and C.S. Jutla. Tree automata, mu-calculus and determinacy (extended abstract). In Proc. 32nd IEEE Symp. Found. of Comp. Sci., pages 368-377. IEEE Computer Society Press, 1991.
19. E.A. Emerson and C.L. Lei. Efficient model checking in fragments of the prepositional μ-calculus. In Proc. First IEEE Symp. Logic in Comp. Sci., pages 267-278, 1986.
20. H. Everett. Recursive games. In Contributions to the Theory of Games III, volume 39 of Annals of Mathematical Studies, pages 47-78, 1957.
21. Y.A. Feldman. A decidable prepositional probabilistic dynamic logic. In Proc. 15th ACM Symp. Theory of Comp., pages 298-309, 1983.
22. Y.A. Feldman and D. Harel. A probabilistic dynamic logic. In Proc. 14th ACM Symp. Theory of Comp., pages 181-195, 1982.
23. J. Filar and K. Vrieze. Competitive Markov Decision Processes. Springer-Verlag, 1997.
24. M. Huth and M. Kwiatkowska. Quantitative analysis and model checking. In Proc. 12th IEEE Symp. Logic in Comp. Sci., pages 111-122, 1997.
25. T.A. Henzinger and R. Majumdar. A classification of symbolic transition systems. In Proc. of 17th Annual Symp. on Theor. Asp. of Comp. Sci., volume 1770 of Lect. Notes in Comp. Sci., pages 13-34. Springer-Verlag, 2000.
26. D. Kozen. A probabilistic PDL. In Proc. 15th ACM Symp. Theory of Comp., pages 291-297, 1983.
27. D. Kozen. Results on the propositional μ-calculus. Theoretical Computer Science, 27(3):333-354, 1983.
28. J.G. Kemeny, J.L. Snell, and A.W. Knapp. Denumerable Markov Chains. D. Van Nostrand Company, 1966.
29. D.A. Martin. The determinacy of Blackwell games. The Journal of Symbolic Logic, 63(4):1565-1581, 1998.
30. R. Milner. Operational and algebraic semantics of concurrent processes. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, pages 1202-1242. Elsevier Science Publishers (North-Holland), Amsterdam, 1990.
31. Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer-Verlag, New York, 1991.
32. J.H. Reif. Logic for probabilistic programming. In Proc. 12th ACM Symp. Theory of Comp., pages 8-13, 1980.
33. K.I. Rosenthal. Quantales and Their Applications, volume 234 of Pitman Research Notes in Mathematics Series. Longman Scientific & Technical, Harlow, 1990.
34. L.S. Shapley. Stochastic games. Proc. Nat. Acad. Sci. USA, 39:1095-1100, 1953.
35. W. Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, chapter 4, pages 135-191. Elsevier Science Publishers (North-Holland), Amsterdam, 1990.
36. W. Thomas. On the synthesis of strategies in infinite games. In Proc. of 12th Annual Symp. on Theor. Asp. of Comp. Sci., volume 900 of Lect. Notes in Comp. Sci., pages 1-13. Springer-Verlag, 1995.
37. F. van Breugel and J. Worrel. An algorithm for quantitative verification of probabilistic transition systems. In CONCUR 01: Concurrency Theory. 12th Int. Conf., volume 2154 of Lect. Notes in Comp. Sci., pages 336-350, 2001.
38. F. van Breugel and J. Worrel. Towards quantitative verification of probabilistic systems. In Proc. 28th Int. Colloq. Aut. Lang. Prog., volume 2076 of Lect. Notes in Comp. Sci., pages 421-432. Springer-Verlag, 2001.
39. J. von Neumann. Zur Theorie der Gesellschaftsspiele. Math. Annal, 100:295-320, 1928.