Intersection of Regular Signal-Event (Timed) Languages

  • Béatrice Bérard
  • Paul Gastin
  • Antoine Petit
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4202)


We propose in this paper a construction for a “well known” result: regular signal-event languages are closed by intersection. In fact, while this result is indeed trivial for languages defined by Alur and Dill’s timed automata (the proof is an immediate extension of the one in the untimed case), it turns out that the construction is much more tricky when considering the most involved model of signal-event automata. While several constructions have been proposed in particular cases, it is the first time, up to our knowledge, that a construction working on finite and infinite signal-event words and taking into account signal stuttering, unobservability of zero-duration τ-signals and Zeno runs is proposed.


Normal Form Repeated State Instantaneous Event Silent Transition Clock Constraint 
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  1. 1.
    Alur, R., Dill, D.L.: Automata for modeling real-time systems. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  2. 2.
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Asarin, E., Caspi, P., Maler, O.: A Kleene theorem for timed automata. In: Proceedings of LICS 1997, pp. 160–171. IEEE Comp. Soc. Press, Los Alamitos (1997)Google Scholar
  4. 4.
    Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. Journal of the ACM 49(2), 172–206 (2002)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Bérard, B., Diekert, V., Gastin, P., Petit, A.: Characterization of the expressive power of silent transitions in timed automata. Fundamenta Informaticae 36, 145–182 (1998)MATHMathSciNetGoogle Scholar
  6. 6.
    Bérard, B., Gastin, P., Petit, A.: Refinements and abstractions of signal-event (timed) languages. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 67–81. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Bérard, B., Gastin, P., Petit, A.: Timed substitutions for regular signal-event languages. Research Report LSV-06-04, Laboratoire Spécification et Vérification, ENS Cachan, France (February 2006)Google Scholar
  8. 8.
    Bouyer, P.: Forward analysis of updatable timed automata. Formal Methods in System Design 24(3), 281–320 (2004)MATHCrossRefGoogle Scholar
  9. 9.
    Cuijpers, P.J.L., Reniers, M.A., Engels, A.G.: Beyond zeno-behaviour. Technical Report CSR 01-04, Department of Computing Science, University of Technology, Eindhoven (2001)Google Scholar
  10. 10.
    Dima, C.: Real-Time Automata and the Kleene Algebra of Sets of Real Numbers. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 279–289. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  11. 11.
    Durand-Lose, J.: A Kleene theorem for splitable signals. Information Processing Letters 89, 237–245 (2004)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Hansen, M.R., Pandya, P.K., Zhou, C.: Finite divergence. Theoretical Computer Science 138, 113–139 (1995)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Perrin, D., Pin, J.-E.: Infinite words. Elsevier, Amsterdam (2004)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Béatrice Bérard
    • 1
  • Paul Gastin
    • 2
  • Antoine Petit
    • 2
  1. 1.LAMSADEUniversité Paris Dauphine & CNRSParisFrance
  2. 2.LSV, ENS de Cachan & CNRSCachanFrance

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