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 < n/logn it yields time complexity of O(n) which is optimal. Additionally, we prove that the set of solutions of one-variable word equations is either of the form F where F is a set of O(logn) words or of the form F ∪ (uv)+ u where F is a set of O(logn) words and u, v are some words such that uv is a primitive word.
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Dabrowski, R., Plandowski, W. (2002). On Word Equations in One Variable. In: Diks, K., Rytter, W. (eds) Mathematical Foundations of Computer Science 2002. MFCS 2002. Lecture Notes in Computer Science, vol 2420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45687-2_17
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DOI: https://doi.org/10.1007/3-540-45687-2_17
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