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On Word Equations in One Variable

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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.

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Robert Dąbrowski & Wojciech Plandowski

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  1. Robert Dąbrowski
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  2. Wojciech Plandowski
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Correspondence to Robert Dąbrowski.

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Dąbrowski, R., Plandowski, W. On Word Equations in One Variable. Algorithmica 60, 819–828 (2011). https://doi.org/10.1007/s00453-009-9375-3

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  • DOI: https://doi.org/10.1007/s00453-009-9375-3

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