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Algorithmica

, Volume 60, Issue 4, pp 819–828 | Cite as

On Word Equations in One Variable

  • Robert DąbrowskiEmail author
  • Wojciech Plandowski
Article

Abstract

For a word equation E of length n in one variable x occurring # x times in E a resolution algorithm of O(n+# x log n) time complexity is presented here. This is the best result known and for the equations that feature \(\#_{x}<\frac{n}{\log n}\) it yields time complexity of O(n) which is optimal. Additionally it is proven here that the set of solutions of any one-variable word equation is either of the form F or of the form F∪(uv)+ u where F is a set of O(log n) words and u, v are some words such that uv is a primitive word.

Word equation Equation in free semigroup Algorithm analysis and design Computational complexity 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institute of InformaticsUniversity of WarsawWarsawPoland

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