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)

Abstract

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.

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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

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