Logical Methods in Computer Science (Nov 2020)

Transfinite Lyndon words

  • Olivier Carton,
  • Luc Boasson

DOI
https://doi.org/10.23638/lmcs-16(4:9)2020
Journal volume & issue
Vol. Volume 16, Issue 4

Abstract

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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.

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