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arXiv · 1302.3481

One-variable word equations in linear time

Artur Jeż
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Abstract

In this paper we consider word equations with one variable (and arbitrary many appearances of it). A recent technique of recompression, which is applicable to general word equations, is shown to be suitable also in this case. While in general case it is non-deterministic, it determinises in case of one variable and the obtained running time is O(n + #_X log n), where #_X is the number of appearances of the variable in the equation. This matches the previously-best algorithm due to Dąbrowski and Plandowski. Then, using a couple of heuristics as well as more detailed time analysis the running time is lowered to O(n) in RAM model. Unfortunately no new properties of solutions are shown.

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Artur Jeż. 2014-01-22. One-variable word equations in linear time. https://arxiv.org/abs/1302.3481

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