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DOI: 10.4230/LIPIcs.ICALP.2016.99
URN: urn:nbn:de:0030-drops-62346
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6234/
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Skrzypczak, Michal ; Walukiewicz, Igor

Deciding the Topological Complexity of Büchi Languages

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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.

BibTeX - Entry

@InProceedings{skrzypczak_et_al:LIPIcs:2016:6234,
  author =	{Michal Skrzypczak and Igor Walukiewicz},
  title =	{{Deciding the Topological Complexity of B{\"u}chi Languages}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{99:1--99:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6234},
  URN =		{urn:nbn:de:0030-drops-62346},
  doi =		{10.4230/LIPIcs.ICALP.2016.99},
  annote =	{Keywords: tree automata, non-determinism, Borel sets, topological complexity, decidability}
}

Keywords: tree automata, non-determinism, Borel sets, topological complexity, decidability
Seminar: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 17.08.2016


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