Deterministic and Game Separability for Regular Languages of Infinite Trees

Authors Lorenzo Clemente , Michał Skrzypczak

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Lorenzo Clemente
  • University of Warsaw, Poland
Michał Skrzypczak
  • University of Warsaw, Poland

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Lorenzo Clemente and Michał Skrzypczak. Deterministic and Game Separability for Regular Languages of Infinite Trees. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 126:1-126:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We show that it is decidable whether two regular languages of infinite trees are separable by a deterministic language, resp., a game language. We consider two variants of separability, depending on whether the set of priorities of the separator is fixed, or not. In each case, we show that separability can be decided in EXPTIME, and that separating automata of exponential size suffice. We obtain our results by reducing to infinite duration games with ω-regular winning conditions and applying the finite-memory determinacy theorem of Büchi and Landweber.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Tree languages
  • separation
  • infinite trees
  • regular languages
  • deterministic automata
  • game automata


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