License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2013.215
URN: urn:nbn:de:0030-drops-41998
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/4199/
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Colcombet, Thomas ; Kuperberg, Denis ; Löding, Christof ; Vanden Boom, Michael

Deciding the weak definability of Büchi definable tree languages

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Abstract

Weakly definable languages of infinite trees are an expressive subclass of regular tree languages definable in terms of weak monadic second-order logic, or equivalently weak alternating automata. Our main result is that given a Büchi automaton, it is decidable whether the language is weakly definable. We also show that given a parity automaton, it is decidable whether the language is recognizable by a nondeterministic co-Büchi automaton.
The decidability proofs build on recent results about cost automata over infinite trees. These automata use counters to define functions from infinite trees to the natural numbers extended with infinity. We reduce to testing whether the functions defined by certain "quasi-weak" cost automata are bounded by a finite value.

BibTeX - Entry

@InProceedings{colcombet_et_al:LIPIcs:2013:4199,
  author =	{Thomas Colcombet and Denis Kuperberg and Christof L{\"o}ding and Michael Vanden Boom},
  title =	{{Deciding the weak definability of B{\"u}chi definable tree languages}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{215--230},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Simona Ronchi Della Rocca},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4199},
  URN =		{urn:nbn:de:0030-drops-41998},
  doi =		{10.4230/LIPIcs.CSL.2013.215},
  annote =	{Keywords: Tree automata, weak definability, decidability, cost automata, boundedness}
}

Keywords: Tree automata, weak definability, decidability, cost automata, boundedness
Collection: Computer Science Logic 2013 (CSL 2013)
Issue Date: 2013
Date of publication: 02.09.2013

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