文章基本信息

标题：Good for Games Automata: From Nondeterminism to Alternation
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作者：Udi Boker ; Karoliina Lehtinen
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：140
页码：1-16
DOI：10.4230/LIPIcs.CONCUR.2019.19
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：A word automaton recognizing a language L is good for games (GFG) if its composition with any game with winning condition L preserves the game's winner. While all deterministic automata are GFG, some nondeterministic automata are not. There are various other properties that are used in the literature for defining that a nondeterministic automaton is GFG, including "history-deterministic", "compliant with some letter game", "good for trees", and "good for composition with other automata". The equivalence of these properties has not been formally shown. We generalize all of these definitions to alternating automata and show their equivalence. We further show that alternating GFG automata are as expressive as deterministic automata with the same acceptance conditions and indices. We then show that alternating GFG automata over finite words, and weak automata over infinite words, are not more succinct than deterministic automata, and that determinizing Büchi and co-Büchi alternating GFG automata involves a 2^{Theta(n)} state blow-up. We leave open the question of whether alternating GFG automata of stronger acceptance conditions allow for doubly-exponential succinctness compared to deterministic automata.
关键词：Good for games; history-determinism; alternation