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An Algebraic Characterization of Data and Timed Languages

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CONCUR 2001 — Concurrency Theory (CONCUR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2154))

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Abstract

Algebra offers an elegant and powerful approach to understand regular languages and finite automata. Such framework has been notoriously lacking for timed languages and timed automata. We introduce the notion of monoid recognizability for data languages, which include timed languages as special case, in a way that respects the spirit of the classical situation. We study closure properties and hierarchies in this model, and prove that emptiness is decidable under natural hypotheses. Our class of recognizable languages properly includes many families of deterministic timed languages that have been proposed until now, and the same holds for non-deterministic versions.

Research partly supported by the French project RNRT “Calife”

Research partly supported by the French-India project CEPIPRA nℴ2102 - 1

Research supported by NSERC, FCAR, and the von Humboldt Foundation

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References

  1. Autebert, J.-M., Beauquier, J., and Boasson, L.Langages sur des alphabets infinis. Discrete Applied Mathematics, vol. 2:1–20, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  2. Asarin, E., Caspi, P., and Maler, O., A Kleene Theorem for Timed Automata. In Proc. 12th IEEE Symp. Logic in Computer Science (LICS’97), pp. 160–171. IEEE Computer Society Press, June 1997.

    Google Scholar 

  3. Alur, R. and Dill, D.A Theory of Timed Automata. Theoretical Computer Science, vol. 126(2):183–235, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  4. Alur, R., Fix, L., and Henzinger, T. A.Event-Clock Automata:Determinizable Class of Timed Automata. In Proc. 6th Int. Conf. Computer Aided Verification (CAV’94), vol. 818 of Lecture Notes in Computer Science, pp. 1–13. Springer-Verlag, June 1994.

    Google Scholar 

  5. Asarin, E.Equations on Timed Languages. In Hybrid Systems: Computation and Control, vol. 1386 of Lecture Notes in Computer Science. Springer-Verlag, Apr. 1998.

    Google Scholar 

  6. Bouyer, P. and Petit, A.Decomposition and Composition of Timed Automata. In Proc. 26th Int. Coll. Automata, Languages, and Programming (ICALP’99), vol. 1644 of Lecture Notes in Computer Science, pp. 210–219. Springer-Verlag, July 1999.

    Chapter  Google Scholar 

  7. Bouyer, P. and Petit, A.A Kleene/Büchi-like Theorem for Clock Languages. Journal of Automata, Languages and Combinatorics, 2001. To appear.

    Google Scholar 

  8. Bouyer, P., Petit, A., and Thérien, D.An Algebraic Characterization of Data and Timed Languages. Research report LSV-01-1, Laboratoire Spécification et Vérification, Ecole Normale Supérieure de Cachan, 2001.

    Google Scholar 

  9. Choffrut, C. and Goldwurm, M.Timed Automata with Periodic Clock Constraints. Journal of Automata, Languages and Combinatorics, vol. 5(4):371–404, 2000.

    MATH  MathSciNet  Google Scholar 

  10. Clarke, E., Grumberg, O., and Peled, D.Model Checking. The MIT Press, Cambridge, Massachusetts, 1999.

    Google Scholar 

  11. Demichelis, F. and Zielonka, W.Controlled Timed Automata. In Proc. 9th Int. Conf. Concurrency Theory (CONCUR’98), vol. 1466 of Lecture Notes in Computer Science, pp. 455–469. Springer-Verlag, Sep. 1998.

    Chapter  Google Scholar 

  12. Henzinger, P. W., and Wong-Toi, H.The Expressive Power of Clocks. In Proc. 22nd Int. Coll. Automata, Languages, and Programming (ICALP’95), vol. 944 of Lecture Notes in Computer Science, pp. 335–346. Springer-Verlag, July 1995.

    Google Scholar 

  13. Henzinger, T. A., Raskin, J.-F., and Schobbens, P.-Y.The Regular Real-Time Languages. In Proc. 25th Int. Coll. Automata, Languages, and Programming (ICALP’98), vol. 1443 of Lecture Notes in Computer Science, pp. 580–591. Springer-Verlag, July 1998.

    Chapter  Google Scholar 

  14. Kaminski, M. and Francez, N.Finite-Memory Automata. Theoretical Computer Science, vol. 134:329–363, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  15. Minsky, M.Computation: Finite and Infinite Machines. Prentice Hall Int., 1967.

    Google Scholar 

  16. Pin, J.-E.Varieties of Formal Languages. North Oxford, London et Plenum, New-York, 1986.

    MATH  Google Scholar 

  17. Rozenberg, G. and Salomaa, A., eds. Handbook of Formal Languages. Springer-Verlag, 1997.

    Google Scholar 

  18. Wilke, T.Specifying Timed State Sequences in Powerful Decidable Logics and Timed Automata. In Proc. 3rd Int. Symp. Formal Techniques in Real-Time and Fault-Tolerant Systems (FTRTFT’94), vol. 863 of Lecture Notes in Computer Science, pp. 694–715. Springer-Verlag, Sep. 1994.

    Google Scholar 

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Author information

Authors and Affiliations

  1. LSV, CNRS UMR 8643, ENS de Cachan, 61 Av. du Président Wilson, 94235, Cachan Cedex, France

    Patricia Bouyer & Antoine Petit

  2. School of Computer Science, McGill University, 3480 University, Montréal, QC, Canada, H3A 2A7

    Denis Thérien

Authors
  1. Patricia Bouyer
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  2. Antoine Petit
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  3. Denis Thérien
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Editor information

Editors and Affiliations

  1. Department of Computer Science, BRICS, Aalborg University, Fredrik Bajersvej 7, 9220, Aalborg, Denmark

    Kim G. Larsen

  2. BRICS, Aarhus University, Ny Munkegade, Bldg. 540, 8000, Aarhus C, Denmark

    Mogens Nielsen

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Bouyer, P., Petit, A., Thérien, D. (2001). An Algebraic Characterization of Data and Timed Languages. In: Larsen, K.G., Nielsen, M. (eds) CONCUR 2001 — Concurrency Theory. CONCUR 2001. Lecture Notes in Computer Science, vol 2154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44685-0_17

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  • DOI: https://doi.org/10.1007/3-540-44685-0_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42497-0

  • Online ISBN: 978-3-540-44685-9

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