A Nonarchimedian Discretization for Timed Languages

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


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.


Regular Expression Action Symbol Region Construction Clock Constraint Clock Tick 
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  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)zbMATHCrossRefMathSciNetGoogle 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)zbMATHCrossRefMathSciNetGoogle 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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