On Timed Automata with Discrete Time – Structural and Language Theoretical Characterization

  • Hermann Gruber
  • Markus Holzer
  • Astrid Kiehn
  • Barbara König
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3572)


We develop a structural and language theoretical characterization of timed languages over discrete time in terms of a variant of Büchi automata and languages. The so-called tick automaton is a standard Büchi automaton with a special “clock-tick”-input symbol modeling the discrete flow of time. Based on these characterizations we give an alternative proof for the fact that the class of regular timed languages is closed under complementation and formulate a time-warp lemma which, similar to a pumping lemma, can be used to show that a timed language is not regular. The characterizations hold alike for timed automata with and without periodic clock constraints.


Regular Language Acceptance State Time Automaton Silent Transition Clock Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Alur, R., Henzinger, T.: Logics and models of real time: a survey. In: Huizing, C., de Bakker, J.W., Rozenberg, G., de Roever, W.-P. (eds.) REX 1991. LNCS, vol. 600, Springer, Heidelberg (1992)Google Scholar
  3. 3.
    Asarin, E.: Challenges in timed languages: From applied theory to basic theory? EATCS Bulletin 83, 106–120 (2004); Appeared in The Concurrency ColumnzbMATHMathSciNetGoogle Scholar
  4. 4.
    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. 5.
    Berard, B., Petit, A., Diekert, V., Gastin, P.: Characterization of the expressive power of silent transitions in timed automata. Fundamenta Informaticae 36(2- 3), 145–182 (1998)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Choffrut, C., Goldwurm, M.: Timed automata with periodic clock constraints. Journal of Automata, Languages and Combinatorics 5(4), 371–404 (2000)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Henzinger, T.A., Kopke, P.W., Wong-Toi, H.: The expressive power of clocks. In: Fülöp, Z., Gecseg, F. (eds.) ICALP 1995. LNCS, vol. 944, pp. 417–428. Springer, Heidelberg (1995)Google Scholar
  8. 8.
    Pnueli, A., Vardi, M.: Automata-theoretic approach to automated verification – lecture notes (1999),
  9. 9.
    Wilke, T.: Specifying time state sequences in powerful logics and timed automata. In: Langmaack, H., de Roever, W.-P., Vytopil, J. (eds.) FTRTFT 1994 and ProCoS 1994. LNCS, vol. 863, pp. 694–715. Springer, Heidelberg (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hermann Gruber
    • 1
  • Markus Holzer
    • 1
  • Astrid Kiehn
    • 2
  • Barbara König
    • 3
  1. 1.Institut für InformatikTechnische Universität MünchenGarching bei MünchenGermany
  2. 2.Department of Computer Science and EngineeringIndian Institute of Technology DelhiHauz Khas, New DelhiIndia
  3. 3.Institut für Formale Methoden der InformatikUniversität StuttgartStuttgartGermany

Personalised recommendations