Nondeterminism in the presence of a diverse or unknown future

Udi Boker, Denis Kuperberg, Orna Kupferman, Michał Skrzypczak

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

25 Scopus citations

Abstract

Choices made by nondeterministic word automata depend on both the past (the prefix of the word read so far) and the future (the suffix yet to be read). In several applications, most notably synthesis, the future is diverse or unknown, leading to algorithms that are based on deterministic automata. Hoping to retain some of the advantages of nondeterministic automata, researchers have studied restricted classes of nondeterministic automata. Three such classes are nondeterministic automata that are good for trees (GFT; i.e., ones that can be expanded to tree automata accepting the derived tree languages, thus whose choices should satisfy diverse futures), good for games (GFG; i.e., ones whose choices depend only on the past), and determinizable by pruning (DBP; i.e., ones that embody equivalent deterministic automata). The theoretical properties and relative merits of the different classes are still open, having vagueness on whether they really differ from deterministic automata. In particular, while DBP ⊆ GFG ⊆ GFT, it is not known whether every GFT automaton is GFG and whether every GFG automaton is DBP. Also open is the possible succinctness of GFG and GFT automata compared to deterministic automata. We study these problems for ω-regular automata with all common acceptance conditions. We show that GFT=GFG⊃DBP, and describe a determinization construction for GFG automata.

Original languageAmerican English
Title of host publicationAutomata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Proceedings
Pages89-100
Number of pages12
EditionPART 2
DOIs
StatePublished - 2013
Event40th International Colloquium on Automata, Languages, and Programming, ICALP 2013 - Riga, Latvia
Duration: 8 Jul 201312 Jul 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume7966 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference40th International Colloquium on Automata, Languages, and Programming, ICALP 2013
Country/TerritoryLatvia
CityRiga
Period8/07/1312/07/13

Bibliographical note

Funding Information:
This work was supported in part by the Polish Ministry of Science grant no. N206 567840, Poland’s NCN grant no. DEC-2012/05/N/ST6/03254, Austrian Science Fund NFN RiSE (Rigorous Systems Engineering), ERC Advanced Grant QUAREM (Quantitative Reactive Modeling), and ERC Grant QUALITY. The full version is available at the authors’ URLs.

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