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One-variable word equations in linear time

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.

preprint2014arXivOpen access
Artur Jeż
Logic in Computer ScienceFormal Languages and Automata TheoryData Structures and Algorithms
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Open access1 author3 topics
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
Citations: 0Reviews: 0Saves: 0Code: not linkedDataset: not linkedInstitutions: 0

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