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Title: The word problem for omega-terms over the Trotter-Weil hierarchy
Authors: Kufleitner, Manfred
Wachter, Jan Philipp
Keywords: Regular language
Finite monoid
Separation problem
Trotter-Weil hierarchy
FO2 alternation hierarchy
Issue Date: 2017
Publisher: © Springer
Citation: KUFLEITNER, M. and WACHTER, J.P., 2017. The Word Problem for Omega-Terms over the Trotter-Weil Hierarchy. Theory of Computing Systems, 62 (3), pp.682–738.
Abstract: © 2017 Springer Science+Business Media New York For two given ω-terms α and β, the word problem for ω-terms over a variety V asks whether α = β in all monoids in V. We show that the word problem for ω-terms over each level of the Trotter-Weil Hierarchy is decidable. More precisely, for every fixed variety in the Trotter-Weil Hierarchy, our approach yields an algorithm in nondeterministic logarithmic space (NL). In addition, we provide deterministic polynomial time algorithms which are more efficient than straightforward translations of the NL-algorithms. As an application of our results, we show that separability by the so-called corners of the Trotter-Weil Hierarchy is witnessed by ω-terms (this property is also known as ω-reducibility). In particular, the separation problem for the corners of the Trotter-Weil Hierarchy is decidable.
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: http://dx.doi.org/10.1007/s00224-017-9763-z.
Sponsor: The first author was supported by the German Research Foundation (DFG) under grants DI 435/5-2 and KU 2716/1-1
Version: Accepted for publication
DOI: 10.1007/s00224-017-9763-z
URI: https://dspace.lboro.ac.uk/2134/31950
Publisher Link: https://doi.org/10.1007/s00224-017-9763-z
ISSN: 1432-4350
Appears in Collections:Published Articles (Computer Science)

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