Timed Games and Deterministic Separability

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


We thank S. Krishna for fruitful discussions. We kindly thank the anonymous reviewers for their helpful comments.

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Lorenzo Clemente, Sławomir Lasota, and Radosław Piórkowski. Timed Games and Deterministic Separability. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 121:1-121:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We study a generalisation of Büchi-Landweber games to the timed setting. The winning condition is specified by a non-deterministic timed automaton with epsilon transitions and only Player I can elapse time. We show that for fixed number of clocks and maximal numerical constant available to Player II, it is decidable whether she has a winning timed controller using these resources. More interestingly, we also show that the problem remains decidable even when the maximal numerical constant is not specified in advance, which is an important technical novelty not present in previous literature on timed games. We complement these two decidability result by showing undecidability when the number of clocks available to Player II is not fixed. As an application of timed games, and our main motivation to study them, we show that they can be used to solve the deterministic separability problem for nondeterministic timed automata with epsilon transitions. This is a novel decision problem about timed automata which has not been studied before. We show that separability is decidable when the number of clocks of the separating automaton is fixed and the maximal constant is not. The problem whether separability is decidable without bounding the number of clocks of the separator remains an interesting open problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Quantitative automata
  • Theory of computation → Timed and hybrid models
  • Timed automata
  • separability problems
  • timed games


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