Kleene theorems for event-clock automata

  • Cătălin Dima
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1684)


We define some class of regular expressions equivalent to event-clock automata. It is shown that regular expressions cannot be given a compositional semantics in terms of timed state sequences. We introduce a modified version of timed state sequences supporting a partial operation of concatenation on which we may build the semantics of regular expressions. A forgetting map then induces a semantics in terms of the classic version of timed state sequences. We also define several types of languages of automata in terms of classic or modified timed state sequences. Two Kleene theorems, one for each type of timed state sequences, relating expressions and event-clock automata are proved.


Regular Expression Expressive Power Empty Word Observable Action Limited Observation 
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. [AD94]
    R. Alur and D.L. Dill. A theory of timed automata, Theoretical Computer Science, 126, 183–235, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [AFH94]
    R. Alur, L. Fix and T.A. Henzinger. A determinizable class of timed automata, Theoretical Computer Science, 211, 253–273, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [ACM97]
    E. Asarin, P. Caspi and O. Maler, A Kleene Theorem for Timed Automata, in G. Winskel (Ed.) Proc. LICS’97, 160–171, 1997.Google Scholar
  4. [BP99]
    P. Bouyer and A. Petit, Decomposition and composition of timed automata, to appear in Proc. of ICALP’ 99, LNCS series, 1999.Google Scholar
  5. [Di1]
    C. Dima. Real-time automata and their class of accepted languages, draft of a UNU/IIST report, available at
  6. [Di2]
    C. Dima. Complementation of real-time automata, submitted to FCT&TCS’99, available at
  7. [Di3]
    C. Dima. Automata and Regular Expressions for Real-Time Languages, submitted to AFL’99, abstract available at
  8. [Di4]
    C. Dima. Removing transitions from event-clock automata, in preparation, available at
  9. [HRS98]
    T.A. Henzinger, J.-F. Raskin and P.-Y. Schobbens. The regular real-time languages, in Proceedings of the 25-th International Colloquium on Automata, Languages and Programming LNCS series, Springer Verlag, 1998.Google Scholar
  10. [HU]
    John E. Hopcroft and Jeffrey D. Ullman, Introduction to Automata Theory, Languages and Computation, Addison-Wesley/Narosa Publishing House, eighth edition, New Delhi, 1992.Google Scholar
  11. [RS97]
    J.-F. Raskin and P.-Y. Schobbens. State-clock logic: a decidable real-time logic, in Hybrid and Real-Time Systems, LNCS 1201, 33–47, Springer Verlag, 1997.CrossRefGoogle Scholar
  12. [Tho90]
    W. Thomas. Automata on infinite objects, in J. van Leeuwen (Ed.), Handbook of Theoretical Computer Science, vol B, 133–191, Elsevier, Amsterdam, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Cătălin Dima
    • 1
  1. 1.Department of Foundations of Computer ScienceBucharest UniversityBucharest

Personalised recommendations