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Büchi Good-for-Games Automata Are Efficiently Recognizable

Authors Marc Bagnol, Denis Kuperberg

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Author Details

Marc Bagnol
  • LIP, École Normale Supérieure, Lyon, France
Denis Kuperberg
  • CNRS, LIP, École Normale Supérieure, Lyon, France

Funding

  • Bagnol, Marc: This work has been funded by the European Research Council (ERC) under the European Union’s Horizon 2020 programme (CoVeCe, grant agreement No 678157).

Cite AsGet BibTex

Marc Bagnol and Denis Kuperberg. Büchi Good-for-Games Automata Are Efficiently Recognizable. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FSTTCS.2018.16

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Formal languages and automata theory
Keywords
  • Büchi
  • automata
  • games
  • polynomial time
  • nondeterminism

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