String attractors and bi-infinite words
Provides a theoretical characterization of string attractors for bi-infinite words, advancing combinatorial understanding in data compression.
The paper characterizes bi-infinite words that admit a finite string attractor as characteristic Sturmian words and their morphic images, and studies infinite string attractors for other words.
String attractors are a combinatorial tool coming from the field of data compression. It is a set of positions within a word which captures 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 article, 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.