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Title: The half-levels of the FO2 alternation hierarchy
Authors: Fleischer, Lukas
Kufleitner, Manfred
Lauser, Alexander
Keywords: Regular language
Finite monoid
Positive variety
First-order logic
Issue Date: 2017
Publisher: © Springer
Citation: FLEISCHER, L., KUFLEITNER, M. and LAUSER, A., 2017. The Half-Levels of the FO2 Alternation Hierarchy. Theory of Computing Systems, 61(2), pp. 352-370.
Abstract: © 2016, Springer Science+Business Media New York. The alternation hierarchy in two-variable first-order logic FO 2 [ < ] over words was shown to be decidable by Kufleitner and Weil, and independently by Krebs and Straubing. We consider a similar hierarchy, reminiscent of the half levels of the dot-depth hierarchy or the Straubing-Thérien hierarchy. The fragment Σm2 of FO 2 is defined by disallowing universal quantifiers and having at most m−1 nested negations. The Boolean closure of Σm2 yields the m th level of the FO 2 -alternation hierarchy. We give an effective characterization of Σm2, i.e., for every integer m one can decide whether a given regular language is definable in Σm2. Among other techniques, the proof relies on an extension of block products to ordered monoids.
Description: 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/s00224-016-9712-2
Sponsor: Supported by the German Research Foundation (DFG) under grant DI 435/5-2.
Version: Accepted for publication
DOI: 10.1007/s00224-016-9712-2
URI: https://dspace.lboro.ac.uk/2134/31948
Publisher Link: https://doi.org/10.1007/s00224-016-9712-2
ISSN: 1432-4350
Appears in Collections:Published Articles (Computer Science)

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