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Download fileThe hardness of solving simple word equations
conference contribution
posted on 2019-04-24, 09:58 authored by Joel DayJoel Day, Florin Manea, Dirk NowotkaWe investigate the class of regular-ordered word equations. In such equations, each variable occurs at most once in each side and the order of the variables occurring in both left and right hand sides is preserved (the variables can be, however, separated by potentially distinct constant factors). Surprisingly, we obtain that solving such simple equations, even when the sides contain exactly the same variables, is NP-hard. By considerations regarding the combinatorial structure of the minimal solutions of the more general quadratic equations we obtain that the satisfiability problem for regular-ordered equations is in NP. The complexity of solving such word equations under regular constraints is also settled. Finally, we show that a related class of simple word equations, that generalises one-variable equations, is in P.
History
School
- Science
Department
- Computer Science
Published in
42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)Volume
83Pages
18:1 - 18:14 (14)Citation
DAY, J.D., MANEA, F. and NOWOTKA, D., 2017. The hardness of solving simple word equations. IN: Larsen, K.G., Bodlaender, H.L. and Raskin, J-F. (eds). 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017), Aalborg, Denmark, 21-25 August 2017, Article No. 18, pp.18:1-18:14.Publisher
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik © The AuthorsVersion
- VoR (Version of Record)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/3.0/Publication date
2017-12-01Notes
This is an Open Access article. It is published by Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik under the Creative Commons Attribution 3.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/3.0/ISBN
9783959770460ISSN
1868-8969Publisher version
Book series
Leibniz International Proceedings in Informatics (LIPIcs);83Language
- en