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Checking Simple Properties of Transition Systems Defined by Thue Specifications

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Abstract

In (possibly infinite) deterministic labeled transition systems defined by Thue congruences, labels are considered as functions of states into states. This paper provides a method for computing domains of such functions for a large class of transition systems. The latter are related to model checking of transition systems defined by Thue congruences.

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References

  1. Arnold, A.: Finite Transition Systems, Prentice-Hall International, 1994.

  2. Arnold, A. and Nivat, M.: Comportements de processus, in Colloque AFCET “Les Mathématiques de l'Informatique”, 1982, pp. 35–68.

  3. Autebert, J.-M., Berstel, J. and Boasson, L.: Context-free languages and push-down automata, in G. Rozenberg and A. Salomaa (eds.), Word, Language, Grammar, Handbook of Formal Languages 1, Springer-Verlag, 1997, pp. 111–174.

  4. Avenhaus, J. and Madlener, K.: Theorem proving in hierarchical clausal specifications, Seki Report SR-95-14, Fachbereich Informatik, Universität Kaiserslautern, 1995.

  5. Büchi, J. R.: Regular canonical systems, Archiv Math. Logik Grundlagen. 6 (1964), 91–111.

    Google Scholar 

  6. Book, R. V. and Otto, F.: String-Rewriting Systems, Texts and Monographs in Comput. Sci., Springer-Verlag, 1993.

  7. Calbrix, H. and Knapik, T.: A string-rewriting characterization of Muller and Shupp's contextfree graphs, in V. Arvind and R. Ramanujam (eds.), 18th International Conference on Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Comput. Sci. 1530, Chennai, 1998, pp. 331–342.

  8. Caucal, D.: On the regular structure of prefix rewriting, Theoret. Comput. Sci. 106 (1992), 61–86.

    Google Scholar 

  9. Hennessy, M. and Milner, R.: Algebraic laws for nondeterminism and concurrency, J. ACM 32 (1985), 137–162.

    Google Scholar 

  10. Hopcroft, J. E. and Ullman, J. D.: Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 1979.

  11. Knapik, T.: A procedure for computing normal forms of certain rational sets, in M. Tchuente (ed.), Proceedings of the 4th African Conference on Research in Computer Science, Dakar, Oct. 1998. INRIA - Press Universitaires de Dakar, 1998, pp. 211–225.

  12. Knapik, T. and Calbrix, H.: The graphs of finite monadic semi-Thue systems have a decidable monadic second-order theory, in C. S. Calude and M. J. Dinneen (eds.), Combinatorics, Computation and Logic '99, Auckland, Jan. 1999, Springer-Verlag, 1999, pp. 273–285.

  13. Knapik, T. and Calbrix, H.: Thue specifications and their monadic second-order properties, Fund. Inform. 39(3) (1999), 305–325.

    Google Scholar 

  14. Knapik, T. and Payet, É.: Synchronized product of linear bounded machines, in G. Ciobanu and G. Paun (eds.), 12th International Symposium on Foundamentals of Computation Theory, Lecture Notes in Comput. Sci. 1684, Ia¸si, Aug. 1999, pp. 362–373.

  15. Kuhn, N. and Madlener, K.: A method for enumerating cosets of a group presented by a canonical system, in G. Gonnet (ed.), Proceedings of ISSAC '89, New York, 1989, pp. 338–350.

  16. Narendran, P. and Otto, F.: Some polynomial-time algorithms for finite monadic Church-Rosser Thue systems, Theoret. Comput. Sci. 68 (1989), 319–332.

    Google Scholar 

  17. Payet, É.: Infinite graphs and synchronized product, Fund. Inform. 44(3) (2000), 265–290.

    Google Scholar 

  18. Perrin, D.: Finite automata, in J. van Leeuwen (ed.), Formal Models and Semantics, Handbook of Theoretical Computer Science, Vol. B, Elsevier, 1990, pp. 3–57.

  19. Shoenfield, J. R.: Mathematical Logic, Addison-Wesley, 1967.

  20. Vardi, M. Y. and Wolper, P.: An automata-theoretic approach to automatic program verification, in Proceedings of the Symposium on Logic in Computer Science, Cambridge, Massachusetts, June 1986, pp. 332–344.

  21. Wos, L., Overbeek, R., Lusk, E., and Boyle, J.: Automated Reasoning: Introduction and Applications, McGraw-Hill, 1992.

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  1. ERMIT, Université de la Réunion, BP 7151, 97715, Saint Denis, Messag, Cedex 9, France. e-mail

    Teodor Knapik

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  1. Teodor Knapik
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Knapik, T. Checking Simple Properties of Transition Systems Defined by Thue Specifications. Journal of Automated Reasoning 28, 337–369 (2002). https://doi.org/10.1023/A:1015850228563

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