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Language Emptiness of Continuous-Time Parametric Timed Automata

  • Nikola Beneš
  • Peter Bezděk
  • Kim G. Larsen
  • Jiří Srba
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9135)

Abstract

Parametric timed automata extend the standard timed automata with the possibility to use parameters in the clock guards. In general, if the parameters are real-valued, the problem of language emptiness of such automata is undecidable even for various restricted subclasses. We thus focus on the case where parameters are assumed to be integer-valued, while the time still remains continuous. On the one hand, we show that the problem remains undecidable for parametric timed automata with three clocks and one parameter. On the other hand, for the case with arbitrary many clocks where only one of these clocks is compared with (an arbitrary number of) parameters, we show that the parametric language emptiness is decidable. The undecidability result tightens the bounds of a previous result which assumed six parameters, while the decidability result extends the existing approaches that deal with discrete-time semantics only. To the best of our knowledge, this is the first positive result in the case of continuous-time and unbounded integer parameters, except for the rather simple case of single-clock automata.

Keywords

Time Slot Corner Point Time Division Multiple Access Safety Problem Integer Parameter 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Nikola Beneš
    • 1
  • Peter Bezděk
    • 1
  • Kim G. Larsen
    • 2
  • Jiří Srba
    • 2
  1. 1.Faculty of InformaticsMasaryk University BrnoBrnoCzech Republic
  2. 2.Department of Computer ScienceAalborg UniversityAalborgDenmark

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