Transfinite Lyndon words
Formal Languages and Automata Theory
2023-06-22 v6
Abstract
In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a relaxation of the condition used in the case of finite words. In the annex, we prove that the factorization of a rational word has a special form and that it can be computed from a rational expression describing the word.
Cite
@article{arxiv.1809.09033,
title = {Transfinite Lyndon words},
author = {Olivier Carton and Luc Boasson},
journal= {arXiv preprint arXiv:1809.09033},
year = {2023}
}