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.FSTTCS.2018.16
URN: urn:nbn:de:0030-drops-99157
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9915/
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Bagnol, Marc ; Kuperberg, Denis

Büchi Good-for-Games Automata Are Efficiently Recognizable

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Abstract

Good-for-Games (GFG) automata offer a compromise between deterministic and nondeterministic automata. They can resolve nondeterministic choices in a step-by-step fashion, without needing any information about the remaining suffix of the word. These automata can be used to solve games with omega-regular conditions, and in particular were introduced as a tool to solve Church's synthesis problem. We focus here on the problem of recognizing Büchi GFG automata, that we call Büchi GFGness problem: given a nondeterministic Büchi automaton, is it GFG? We show that this problem can be decided in P, and more precisely in O(n^4m^2|Sigma|^2), where n is the number of states, m the number of transitions and |Sigma| is the size of the alphabet. We conjecture that a very similar algorithm solves the problem in polynomial time for any fixed parity acceptance condition.

BibTeX - Entry

@InProceedings{bagnol_et_al:LIPIcs:2018:9915,
  author =	{Marc Bagnol and Denis Kuperberg},
  title =	{{B{\"u}chi Good-for-Games Automata Are Efficiently Recognizable}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{16:1--16:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Sumit Ganguly and Paritosh Pandya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9915},
  URN =		{urn:nbn:de:0030-drops-99157},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.16},
  annote =	{Keywords: B{\"u}chi, automata, games, polynomial time, nondeterminism}
}

Keywords: Büchi, automata, games, polynomial time, nondeterminism
Collection: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)
Issue Date: 2018
Date of publication: 05.12.2018

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