Degrees of Ambiguity for Parity Tree Automata

Authors Alexander Rabinovich , Doron Tiferet

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Alexander Rabinovich
  • Tel Aviv University, Israel
Doron Tiferet
  • Tel Aviv University, Israel


We would like to thank the reviewers for their useful suggestions. The first author is grateful to Michał Skrzypczak for very fruitful discussions.

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Alexander Rabinovich and Doron Tiferet. Degrees of Ambiguity for Parity Tree Automata. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is finitely (respectively, countably) ambiguous if for every input it has at most finitely (respectively, countably) many accepting computations. An automaton is boundedly ambiguous if there is k ∈ ℕ, such that for every input it has at most k accepting computations. We consider Parity Tree Automata (PTA) and prove that the problem whether a PTA is not unambiguous (respectively, is not boundedly ambiguous, not finitely ambiguous) is co-NP complete, and the problem whether a PTA is not countably ambiguous is co-NP hard.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • automata on infinite trees
  • degree of ambiguity
  • omega word automata
  • parity automata


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