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Title: Solutions of word equations over partially commutative structures
Authors: Diekert, Volker
Jez, Artur
Kufleitner, Manfred
Keywords: Word equations
EDT0L language
Trace monoid
Right-angled Artin group
Partial commutation
Issue Date: 2016
Publisher: Schloss Dagstuhl – Leibniz Center for Informatics
Citation: DIEKERT, V., JEZ, A. and KUFLEITNER, M., 2016. Solutions of word equations over partially commutative structures. Presented at the 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016), Rome, Italy, 12-15th July.
Series/Report no.: Leibniz International Proceedings in Informatics, LIPIcs;55
Abstract: © Volker Diekert, Artur Jez, and Manfred Kufleitner. We give NSPACE(n log n) algorithms solving the following decision problems. Satisfiability: Is the given equation over a free partially commutative monoid with involution (resp. a free partially commutative group) solvable? Finiteness: Are there only finitely many solutions of such an equation? PSPACE algorithms with worse complexities for the first problem are known, but so far, a PSPACE algorithm for the second problem was out of reach. Our results are much stronger: Given such an equation, its solutions form an EDT0L language effectively representable in NSPACE(n log n). In particular, we give an effective description of the set of all solutions for equations with constraints in free partially commutative monoids and groups.
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: Artur Jez was supported by a return fellowship of the Alexander von Humboldt Foundation. Manfred Kufleitner was supported by the grants DI 435/5-2 and KU 2716/1-1 of the DFG.
Version: Published
DOI: 10.4230/LIPIcs.ICALP.2016.127
URI: https://dspace.lboro.ac.uk/2134/31951
Publisher Link: https://doi.org/10.4230/LIPIcs.ICALP.2016.127
ISBN: 9783959770132
ISSN: 1868-8969
Appears in Collections:Conference Papers and Presentations (Computer Science)

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