CONCUR 2002: CONCUR 2002 — Concurrency Theory pp 255-272 | Cite as
A Decidable Fixpoint Logic for Time-Outs*
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Abstract
We show decidability of the satisfiability problem for an extension of the modal μ-calculus with event-recording clocks. Based on techniques for deciding the untimed μ-calculus, we present a complete set of reduction rules for constructing tableaux for formulas of this eventrecording logic. To keep track of the actual value of the clocks, the premises and conclusions of our tableau rules are augmented with timing contexts, which are sets of timing constraints satisfied by the actual value of the clocks. The decidability problem is shown to be EXPTIME complete. In addition, we address the problem of model synthesis, that is, given a formula φ, we construct an event-recording automaton that satisfies φ.
Keywords
Model Check Temporal Logic Label Transition System Reduction Rule Linear Time Temporal Logic
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References
- 1.R. Alur. Techniques for Automatic Verification of Real-Time Systems. PhD thesis, Stanford University, 1991.Google Scholar
- 2.R. Alur, C. Courcoubetis, and D. Dill. Model checking in dense real-time. Information and Computation, 104(1):2–34, 1993.MATHCrossRefMathSciNetGoogle Scholar
- 3.R. Alur, L. Fix, and T. A. Henzinger. Event-clock automata: A determinizable class of timed automata. Theoretical Computer Science, 211(1–2):253–273, 1999.MATHCrossRefMathSciNetGoogle Scholar
- 4.Rajeev Alur and David L. Dill. A theory of timed automata. Theoretical Computer Science, 126(2):183–235, 25 April 1994.MATHCrossRefMathSciNetGoogle Scholar
- 5.Rajeev Alur, Tomás Feder, and Thomas A. Henzinger. The benefits of relaxing punctuality. Journal of the ACM, 43(1):116–146, January 1996.MATHCrossRefMathSciNetGoogle Scholar
- 6.Rajeev Alur and Thomas Henzinger. Real-time logics: Complexity and expressiveness. Information and Computation, 104(1):35–77, May 1993.MATHCrossRefMathSciNetGoogle Scholar
- 7.Rajeev Alur and Thomas A. Henzinger. A really temporal logic. Journal of the ACM, 41(1):181–204, 1994.MATHCrossRefMathSciNetGoogle Scholar
- 8.Conrado Daws and Stavros Tripakis. Model checking of real-time reachability properties using abstractions. Lecture Notes in Computer Science, 1384:313–329, 1998.Google Scholar
- 9.Deepak D’souza. A logical characterization of event recording automata. In Proceedings of FTRTFT, volume 1926 of LNCS, 2000.Google Scholar
- 10.E. Allen Emerson and Charanjit S. Jutla. The complexity of tree automata and logics of programs. In 29th Annual Symposium on Foundations of Computer Science, pages 328–337. IEEE, 1988.Google Scholar
- 11.E. Allen Emerson and Charanjit S. Jutla. On simultaneously determinizing and complementing ω-automata (extended abstract). In Proceedings, Fourth Annual Symposium on Logic in Computer Science, pages 333–342, 1989.Google Scholar
- 12.E. Allen Emerson, A. K. Mok, A. Prasad Sistla, and Jai Srinivasan. Quantitative temporal reasoning. LNCS, 531:136–145, 1991.Google Scholar
- 13.S. Graf and J. Sifakis. A modal characterization of observational congruence on finite terms of CCS. Information and Control, 68(1–3):125–145, 1986.MATHCrossRefMathSciNetGoogle Scholar
- 14.T. A. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine. Symbolic model checking for real-time systems. Information and Computation, 111(2):193–244, June 1994.MATHCrossRefMathSciNetGoogle Scholar
- 15.R. Koymans. Specifying real-time properties with metric temporal logic. Real-Time Systems, 2(4):255–299, November 1990.CrossRefGoogle Scholar
- 16.D. Kozen. Results on the propositional mu-calculus. Theoretical Computer Science, 27(3):333–354, December 1983.MATHCrossRefMathSciNetGoogle Scholar
- 17.F. Laroussinie, K. G. Larsen, and C. Weise. From timed automata to logic— and back. Lecture Notes in Computer Science, 969:529–539, 1995.Google Scholar
- 18.K. G. Larsen, P. Pettersson, and W. Yi. Model-checking for real-time systems. Lecture Notes in Computer Science, 965:62–88, 1995.Google Scholar
- 19.Damian Niwiński and Igor Walukiewicz. Games for the μ-calculus. Theoretical Computer Science, 163(1–2):99–116, 1996.CrossRefMathSciNetMATHGoogle Scholar
- 20.P. Pettersson. Modelling and Verification of Real-Time Systems Using Timed Automata: Theory and Practice. PhD thesis, Uppsala University, 1999.Google Scholar
- 21.Jean-FranÇois Raskin and Pierre-Yves Schobbens. The logic of event clocks: Decidability, complexity and expressiveness. Journal of Automata, Languages and Combinatorics, 4(3):247–282, 1999.MATHMathSciNetGoogle Scholar
- 22.Maria Sorea. Results on event-recording logic. Technical Report SRI-CSL-01-06, Computer Science Laboratory, SRI International, 2001. http://www.csl.sri.com/papers/csl-01-06/.
- 23.Maria Sorea. Tempo: A model-checker for event-recording automata. Technical Report SRI-CSL-01-04, Computer Science Laboratory, SRI International, 2001. A short version appeared at the Workshop on Real-Time Tools 2001, Aalborg, Denmark. http://www.csl.sri.com/papers/csl-01-04/.
- 24.B. Steffen and A. Ingólfsdóttir. Characteristic formulae for processes with divergence. Information and Computation, 110(1):149–163, April 1994.MATHCrossRefMathSciNetGoogle Scholar
- 25.C. Stirling and D. Walker. Local model checking in the modal mu-calculus. Theoretical Computer Science, 89(1):161–177, 1991.MATHCrossRefMathSciNetGoogle Scholar
- 26.R. S. Streett and E. A. Emerson. An automata theoretic decision procedure for the propositional mu-calculus. Information and Computation, 81(3):249–264, 1989.MATHCrossRefMathSciNetGoogle Scholar
- 27.Howard Wong-Toi. Symbolic Approximations for Verifying Real-Time Systems. PhD thesis, Stanford University, November 1994.Google Scholar
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