• DOI:10.1007/978-3-662-47666-6_6
• Corpus ID: 3898378

Language Emptiness of Continuous-Time Parametric Timed Automata

@inproceedings{Benes2015LanguageEO,
  title={Language Emptiness of Continuous-Time Parametric Timed Automata},
  author={Nikola Benes and Peter Bezdek and Kim Guldstrand Larsen and Jir{\'i} Srba},
  booktitle={International Colloquium on Automata, Languages and Programming},
  year={2015}
}

• Nikola Benes, Peter Bezdek, +1 author J. Srba
• Published in
  International Colloquium on…
  29 April 2015
• Computer Science, Mathematics

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.