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Title: Ehrenfeucht-Fraisse games on omega-terms
Authors: Huschenbett, Martin
Kufleitner, Manfred
Keywords: Regular language
First-order logic
Finite monoid
Ehrenfeucht-Fraisse games
Pseudoidentity
Issue Date: 2014
Publisher: Schloss Dagstuhl – Leibniz Center for Informatics
Citation: HUSCHENBETT, M. and KUFLEITNER, M., 2014. Ehrenfeucht-Fraisse games on omega-terms. Presented at the 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014), Lyon, France, Mar 5-8th. pp. 374-385.
Series/Report no.: Leibniz International Proceedings in Informatics, LIPIcs;25
Abstract: © Martin Huschenbett and Manfred Kufleitner. Fragments of first-order logic over words can often be characterized in terms of finite monoids or finite semigroups. Usually these algebraic descriptions yield decidability of the question whether a given regular language is definable in a particular fragment. An effective algebraic characterization can be obtained from identities of so-called omega-terms. In order to show that a given fragment satisfies some identity of omega-terms, one can use Ehrenfeucht-Fraïssé games on word instances of the omega-terms. The resulting proofs often require a significant amount of bookkeeping with respect to the constants involved. In this paper we introduce Ehrenfeucht-Fraïssé games on omega-terms. To this end we assign a labeled linear order to every omega-term. Our main theorem shows that a given fragment satisfies some identity of omega-terms if and only if Duplicator has a winning strategy for the game on the resulting linear orders. This allows to avoid the book-keeping. As an application of our main result, we show that one can decide in exponential time whether all aperiodic monoids satisfy some given identity of omega-terms, thereby improving a result of McCammond (Int. J. Algebra Comput., 2001).
Description: This is an Open Access Article. It is published by Schloss Dagstuhl – Leibniz Center for Informatics under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/
Sponsor: M.K. was supported by the German Research Foundation (DFG) under grant DI 435/5-1 and by the Technische Universitat Munchen, Germany.
Version: Published
DOI: 10.4230/LIPIcs.STACS.2014.374
URI: https://dspace.lboro.ac.uk/2134/31984
http://drops.dagstuhl.de/opus/volltexte/2014/4472/
Publisher Link: https://doi.org/10.4230/LIPIcs.STACS.2014.374
ISBN: 9783939897651
ISSN: 1868-8969
Appears in Collections:Conference Papers and Presentations (Computer Science)

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