On the Solvability Problem for Restricted Classes of Word Equations

  • Florin Manea
  • Dirk Nowotka
  • Markus L. SchmidEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9840)


We investigate the complexity of the solvability problem for restricted classes of word equations with and without regular constraints. For general word equations, the solvability problem remains \({{\mathrm{\mathsf {NP}}}}\)-hard, even if the variables on both sides are ordered, and for word equations with regular constraints, the solvability problems remains \({{\mathrm{\mathsf {NP}}}}\)-hard for variable disjoint (i. e., the two sides share no variables) equations with two variables, only one of which is repeated. On the other hand, word equations with only one repeated variable (but an arbitrary number of variables) and at least one non-repeated variable on each side, can be solved in polynomial-time.


Word equations Regular constraints NP-hardness 



We are indebted to Artur Jeż for valuable discussions. Markus L. Schmid gratefully acknowledges partial support for this research from DFG, that in particular enabled his visit at the University of Kiel.


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceKiel UniversityKielGermany
  2. 2.Fachbereich IV – Abteilung InformatikwissenschaftenTrier UniversityTrierGermany

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