String attractors and bi-infinite words

String attractors are a combinatorial tool coming from the field of data compression. It is a set of positions within a word which intersects an occurrence of every factor. While one-sided infinite words admitting a finite string attractor are eventually periodic, the situation is different for two-...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Béaur, Pierre, Gheeraert, France, Benjamin Hellouin de Menibus
Format: Article
Language:English
Subjects:
Combinatorial analysis
Data compression
Strings
Online Access:Get full text
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Summary:String attractors are a combinatorial tool coming from the field of data compression. It is a set of positions within a word which intersects an occurrence of every factor. While one-sided infinite words admitting a finite string attractor are eventually periodic, the situation is different for two-sided infinite words. In this paper, we characterise the bi-infinite words admitting a finite string attractor as the characteristic Sturmian words and their morphic images. For words that do not admit finite string attractors, we study the structure and properties of their infinite string attractors.
ISSN:2331-8422