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Model Checking Fixed Point Logic with Chop

Part of the Lecture Notes in Computer Science book series (LNCS,volume 2303)

Abstract

This paper examines FLC, which is the modal μ-calculus enriched with a sequential composition operator. Bisimulation invariance and the tree model property are proved. Its succinctness is compared to the modal μ-calculus. The main focus lies on FLC’s model checking problem over finite transition systems. It is proved to be Pspace-hard. A tableau model checker is given and an upper Exptime bound is derived from it. For a fixed alternation depth FLC’s model checking problem turns out to be Pspace-complete.

References

  1. A. K. Chandra, D. C. Kozen, and L. J. Stockmeyer. Alternation. Journal of the ACM, 28(1):114–133, January 1981.

    MATH  CrossRef  MathSciNet  Google Scholar 

  2. E. A. Emerson. Temporaland modal logic. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B: Formal Models and Semantics, chapter 14, pages 996–1072. Elsevier Science Publishers B.V.: Amsterdam, The Netherlands, New York, N.Y., 1990.

    Google Scholar 

  3. E. Allen Emerson. Uniform inevitability is tree automaton inefiable. Information Processing Letters, 24(2):77–79, January 1987.

    MATH  CrossRef  MathSciNet  Google Scholar 

  4. R. Goré. Tableau methods for modaland temporal logics. In M. D’Agostino, D. Gabbay, R. Hähnle, and J. Posegga, editors, Handbook of Tableau Methods. Kluwer, Dordrecht, 1999.

    Google Scholar 

  5. J. F. Groote and H. Hüttel. Undecidable equivalences for basic process algebra. Information and Computation, 115(2):354–371, December 1994.

    MATH  CrossRef  MathSciNet  Google Scholar 

  6. D. Janin and I. Walukiewicz. On the expressive completeness of the propositional μ-calculus with respect to monadic second order logic. In U. Montanari and V. Sassone, editors, CONCUR’ 96: Concurrency Theory, 7th Int. Conf., volume 1119 of LNCS, pages 263–277, Pisa, Italy, 26–29 August 1996. Springer.

    Google Scholar 

  7. D. Kozen. Results on the propositional mu-calculus. TCS, 27:333–354, December 1983.

    Google Scholar 

  8. A. R. Meyer and L. J. Stockmeyer. Word problems requiring exponential time. In ACM Symp. on Theory of Computing (STOC’ 73), pages 1–9, New York, April 1973. ACM Press.

    Google Scholar 

  9. M. Müller-Olm. A modal fixpoint logic with chop. In C. Meinel and S. Tison, editors, Proc. 16th Annual Symp. on Theoretical Aspects of Computer Science, STACS’99, volume 1563 of LNCS, pages 510–520, Trier, Germany, 1999. Springer.

    Google Scholar 

  10. C. Stirling. Modaland temporal logics. In Handbook of Logic in Computer Science, volume 2 (Background: Computational Structures), pages 477–563. Clarendon Press, Oxford, 1992.

    Google Scholar 

  11. A. Tarski. A lattice-theoretical fixpoint theorem and its application. Pacific J.Math., 5:285–309, 1955.

    MATH  MathSciNet  Google Scholar 

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© 2002 Springer-Verlag Berlin Heidelberg

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Lange, M., Stirling, C. (2002). Model Checking Fixed Point Logic with Chop. In: Nielsen, M., Engberg, U. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2002. Lecture Notes in Computer Science, vol 2303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45931-6_18

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  • DOI: https://doi.org/10.1007/3-540-45931-6_18

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  • Print ISBN: 978-3-540-43366-8

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