How deterministic are good-for-games automata?

Udi Boker, Orna Kupferman, Michal Skrzypczak

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations

Abstract

In good for games (GFG) automata, it is possible to resolve nondeterminism in a way that only depends on the past and still accepts all the words in the language. The motivation for GFG automata comes from their adequacy for games and synthesis, wherein general nondeterminism is inappropriate. We continue the ongoing effort of studying the power of nondeterminism in GFG automata. Initial indications have hinted that every GFG automaton embodies a deterministic one. Today we know that this is not the case, and in fact GFG automata may be exponentially more succinct than deterministic ones. We focus on the typeness question, namely the question of whether a GFG automaton with a certain acceptance condition has an equivalent GFG automaton with a weaker acceptance condition on the same structure. Beyond the theoretical interest in studying typeness, its existence implies efficient translations among di erent acceptance conditions. This practical issue is of special interest in the context of games, where the Büchi and co-Büchi conditions admit memoryless strategies for both players. Typeness is known to hold for deterministic automata and not to hold for general nondeterministic automata. We show that GFG automata enjoy the benefits of typeness, similarly to the case of deterministic automata. In particular, when Rabin or Streett GFG automata have equivalent Büchi or co-Büchi GFG automata, respectively, then such equivalent automata can be defined on a substructure of the original automata. Using our typeness results, we further study the place of GFG automata in between deterministic and nondeterministic ones. Specifically, considering automata complementation, we show that GFG automata lean toward nondeterministic ones, admitting an exponential state blow-up in the complementation of a Streett automaton into a Rabin automaton, as opposed to the constant blow-up in the deterministic case.

Original languageAmerican English
Title of host publication37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017
EditorsSatya Lokam, R. Ramanujam
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770552
DOIs
StatePublished - 1 Jan 2018
Event37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017 - Kanpur, India
Duration: 12 Dec 201714 Dec 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume93
ISSN (Print)1868-8969

Conference

Conference37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017
Country/TerritoryIndia
CityKanpur
Period12/12/1714/12/17

Bibliographical note

Publisher Copyright:
© Udi Boker, Orna Kupferman, and Michal Skrzypczak.

Keywords

  • Determinism
  • Finite automata on infinite words
  • Good-for-games

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