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Solutions of word equations over partially commutative structures

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conference contribution
posted on 2018-02-22, 14:24 authored by Volker Diekert, Artur Jez, Manfred Kufleitner
© 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.

Funding

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.

History

School

  • Science

Department

  • Computer Science

Published in

43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016 Leibniz International Proceedings in Informatics, LIPIcs

Volume

55

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.

Publisher

Schloss Dagstuhl – Leibniz Center for Informatics

Version

  • VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/ by/4.0/

Acceptance date

2016-04-15

Publication date

2016

Notes

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/

DOI

ISBN

9783959770132

ISSN

1868-8969

Publisher version

Book series

Leibniz International Proceedings in Informatics, LIPIcs;55

Language

  • en

Location

Rome, Italy

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    Loughborough Publications

    Categories

    Keywords

    Word equationsEDT0L languageTrace monoidRight-angled Artin groupPartial commutationInformation and Computing Sciences not elsewhere classified

    Licence

    CC BY 4.0

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