One-variable word equations in linear time
Year: 2013
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Jeż, Artur
Institutions: University of Wrocław, Max Planck Institute for Informatics
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Alexander von Humboldt-Stiftung
OpenAlex ID: W2951371041