Computer Science > Formal Languages and Automata Theory
[Submitted on 24 Sep 2018 (v1), last revised 9 Nov 2020 (this version, v6)]
Title:Transfinite Lyndon words
View PDFAbstract: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.
Submission history
From: Olivier Carton [view email] [via Logical Methods In Computer Science as proxy][v1] Mon, 24 Sep 2018 16:20:26 UTC (43 KB)
[v2] Tue, 18 Feb 2020 18:16:05 UTC (45 KB)
[v3] Tue, 25 Aug 2020 09:05:29 UTC (45 KB)
[v4] Wed, 26 Aug 2020 13:08:53 UTC (45 KB)
[v5] Fri, 28 Aug 2020 06:55:43 UTC (45 KB)
[v6] Mon, 9 Nov 2020 14:47:58 UTC (71 KB)
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
Connected Papers (What is Connected Papers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.