A Nonarchimedian Discretization for Timed Languages

  • Cătălin Dima
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2791)

Abstract

We give a new discretization of behaviors of timed automata. In this discretization, timed languages are represented as sets of words containing action symbols, a clock tick symbol 1, and two delay symbols δ (negative delay) and δ +  (positive delay). Unlike the region construction, our discretization commutes with intersection. We show that discretizations of timed automata are, in general, context-sensitive languages over Σ ∪ {1,δ + ,δ, and give a class of automata that equals the class of languages that are discretizations of timed automata, and show that their emptiness problem is decidable.

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References

  1. [ACM02]
    Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. Journal of ACM 49, 172–206 (2002)CrossRefMathSciNetGoogle Scholar
  2. [AD94]
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)MATHCrossRefMathSciNetGoogle Scholar
  3. [AD03]
    Asarin, E., Dima, C.: Balanced timed regular expressions. ENTCS, vol. 68(5) (2003)Google Scholar
  4. [Bea98]
    Beauquier, D.: Pumping lemmas for timed automata. In: Nivat, M. (ed.) FOSSACS 1998. LNCS, vol. 1378, pp. 81–94. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. [Bel57]
    Bellmann, R.: Dynamic Programming. Princeton University Press, Princeton (1957)Google Scholar
  6. [BP99]
    Bouyer, P., Petit, A.: Decomposition and composition of timed automata. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 210–219. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. [BP02]
    Bouyer, P., Petit, A.: A Kleene/Büchi-like theorem for clock languages. Journal of Automata, Languages and Combinatorics (2002) (to appear)Google Scholar
  8. [BPT01]
    Bouyer, P., Petit, A., Thrien, D.: An algebraic characterization of data and timed languages. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 248–261. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. [Dim01]
    Dima, C.: An algebraic theory of real-time formal languages. PhD thesis, Université Joseph Fourier Grenoble, France (2001)Google Scholar
  10. [Dim02]
    Dima, C.: Computing reachability relations in timed automata. In: Proceedings of LICS 2002, pp. 177–186 (2002)Google Scholar
  11. [DT99]
    D’Souza, D., Thiagarajan, P.S.: Product interval automata: A subclass of timed automata. In: Pandu Rangan, C., Raman, V., Sarukkai, S. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 60–71. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. [Her98]
    Herrmann, P.: Timed automata and recognizability. Information Processing Letters 65, 313–318 (1998)MATHCrossRefMathSciNetGoogle Scholar
  13. [HU92]
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley/Narosa Publishing House (1992)Google Scholar
  14. [LPY97]
    Larsen, K.G., Petterson, P., Yi, W.: Uppaal: Status & developments. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 456–459. Springer, Heidelberg (1997)Google Scholar
  15. [Yov98]
    Yovine, S.: Model-checking timed automata. In: Rozenberg, G. (ed.) EEF School 1996. LNCS, vol. 1494, pp. 114–152. Springer, Heidelberg (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Cătălin Dima
    • 1
  1. 1.ENSEIRBTalence CedexFrance

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