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Title: Level Two of the quantifier alternation hierarchy over infinite words
Authors: Kufleitner, Manfred
Walter, Tobias
Issue Date: 2017
Publisher: Springer
Citation: KUFLEITNER, M. and WALTER, T., 2017. Level Two of the quantifier alternation hierarchy over infinite words. Theory of Computing Systems, 62 (3), pp.467–480
Abstract: © 2017 Springer Science+Business Media, LLC The study of various decision problems for logic fragments has a long history in computer science. This paper is on the membership problem for a fragment of first-order logic over infinite words; the membership problem asks for a given language whether it is definable in some fixed fragment. The alphabetic topology was introduced as part of an effective characterization of the fragment Σ 2 over infinite words. Here, Σ 2 consists of the first-order formulas with two blocks of quantifiers, starting with an existential quantifier. Its Boolean closure is (Formula presented.). Our first main result is an effective characterization of the Boolean closure of the alphabetic topology, that is, given an ω-regular language L, it is decidable whether L is a Boolean combination of open sets in the alphabetic topology. This is then used for transferring Place and Zeitoun’s recent decidability result for (Formula presented.) from finite to infinite words.
Description: This journal article is part of the following topical collections: Computer Science Symposium in Russia. This is a post-peer-review, pre-copyedit version of an article published in Theory of Computing Systems. The final authenticated version is available online at: https://doi.org/10.1007/s00224-017-9801-x
Sponsor: This work was supported by the German Research Foundation (DFG) under grants DI 435/5-2 and DI 435/6-1
Version: Accepted for publication
DOI: 10.1007/s00224-017-9801-x
URI: https://dspace.lboro.ac.uk/2134/31947
Publisher Link: https://doi.org/10.1007/s00224-017-9801-x
ISSN: 1432-4350
Appears in Collections:Published Articles (Computer Science)

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