On Guidable Index of Tree Automata

Authors Damian Niwiński , Michał Skrzypczak

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Damian Niwiński
  • Institute of Informatics, University of Warsaw, Poland
Michał Skrzypczak
  • Institute of Informatics, University of Warsaw, Poland

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Damian Niwiński and Michał Skrzypczak. On Guidable Index of Tree Automata. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 81:1-81:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We study guidable parity automata over infinite trees introduced by Colcombet and Löding, which form an expressively complete subclass of all non-deterministic tree automata. We show that, for any non-deterministic automaton, an equivalent guidable automaton with the smallest possible index can be effectively found. Moreover, if an input automaton is of a special kind, i.e. it is deterministic or game automaton then a guidable automaton with an optimal index can be deterministic (respectively game) automaton as well. Recall that the problem whether an equivalent non-deterministic automaton with the smallest possible index can be effectively found is open, and a positive answer is known only in the case when an input automaton is a deterministic, or more generally, a game automaton.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • guidable automata
  • index problem
  • ω-regular games


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