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Deciding the Topological Complexity of Büchi Languages

Authors Michal Skrzypczak, Igor Walukiewicz

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Michal Skrzypczak
Igor Walukiewicz

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Michal Skrzypczak and Igor Walukiewicz. Deciding the Topological Complexity of Büchi Languages. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 99:1-99:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ICALP.2016.99

Abstract

We study the topological complexity of languages of Büchi automata on infinite binary trees. We show that such a language is either Borel and WMSO-definable, or Sigma_1^1-complete and not WMSO-definable; moreover it can be algorithmically decided which of the two cases holds. The proof relies on a direct reduction to deciding the winner in a finite game with a regular winning condition.

Subject Classification

Keywords
  • tree automata
  • non-determinism
  • Borel sets
  • topological complexity
  • decidability

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