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Determinisability of One-Clock Timed Automata

Authors Lorenzo Clemente , Sławomir Lasota , Radosław Piórkowski

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Author Details

Lorenzo Clemente
  • University of Warsaw, Poland
Sławomir Lasota
  • University of Warsaw, Poland
Radosław Piórkowski
  • University of Warsaw, Poland

Funding

  • Clemente, Lorenzo: Partially supported by the Polish NCN grant 2017/26/D/ST6/00201.
  • Lasota, Sławomir: Partially supported by the Polish NCN grant 2019/35/B/ST6/02322 and by the ERC grant LIPA, agreement no. 683080.
  • Piórkowski, Radosław: Partially supported by the Polish NCN grant 2017/27/B/ST6/02093.

Acknowledgements

We thank S. Krishna for fruitful discussions and the anonymous reviewers for their constructive comments.

Cite As Get BibTex

Lorenzo Clemente, Sławomir Lasota, and Radosław Piórkowski. Determinisability of One-Clock Timed Automata. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 42:1-42:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.CONCUR.2020.42

Abstract

The deterministic membership problem for timed automata asks whether the timed language recognised by a nondeterministic timed automaton can be recognised by a deterministic timed automaton. We show that the problem is decidable when the input automaton is a one-clock nondeterministic timed automaton without epsilon transitions and the number of clocks of the deterministic timed automaton is fixed. We show that the problem in all the other cases is undecidable, i.e., when either 1) the input nondeterministic timed automaton has two clocks or more, or 2) it uses epsilon transitions, or 3) the number of clocks of the output deterministic automaton is not fixed.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Timed and hybrid models
Keywords
  • Timed automata
  • determinisation
  • deterministic membership problem

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