2000 character limit reached
String attractors and bi-infinite words (2403.13449v1)
Published 20 Mar 2024 in math.CO and cs.DM
Abstract: 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.
- Pascal Alessandri. Codages de rotation et suites de basses complexités, 1996. PhD Thesis, Université d’Aix-Marseille II.
- Pierre Arnoux. Sturmian sequences. In V. Berthé, S. Ferenczi, C. Mauduit, and A. Siegel, editors, Substitutions in Dynamics, Arithmetics and Combinatorics, chapter 6, pages 143–198. Springer Berlin Heidelberg, 2002.
- Rigidity and substitutive dendric words. Internat. J. Found. Comput. Sci., 29(5):705–720, 2018.
- Structural aspects of tilings. In STACS 2008: 25th International Symposium on Theoretical Aspects of Computer Science, volume 1 of LIPIcs. Leibniz Int. Proc. Inform., pages 61–72. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2008.
- A characterization of Sturmian sequences by indistinguishable asymptotic pairs. European J. Combin., 95:Paper No. 103318, 22, 2021.
- Julien Cassaigne. Sequences with grouped factors. In Developments in Language Theory, pages 211–222. 1997.
- New string attractor-based complexities for infinite words, 2023.
- On a new notion of complexity on infinite words. Acta Univ. Sapientiae Math., 2(2):127–136, 2010.
- Ethan M. Coven. Sequences with minimal block growth. II. Math. Systems Theory, 8(4):376–382, 1974/75.
- Fabien Durand. A characterization of substitutive sequences using return words. Discrete Math., 179(1-3):89–101, 1998.
- France Gheeraert. A study of dendricity through the lens of morphisms, 2023. PhD Thesis, University of Liège.
- Alex Heinis. Arithmetics and cominatorics of words of low complexity, 2001. PhD Thesis, Leiden University.
- On repetitiveness measures of Thue-Morse words. In String processing and information retrieval, volume 12303 of Lecture Notes in Comput. Sci., pages 213–220. Springer, Cham, 2020.
- At the roots of dictionary compression: string attractors. In STOC’18—Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, pages 827–840. ACM, New York, 2018.
- Combinatoire de mots récurrents de complexité n+2𝑛2n+2italic_n + 2. Theor. Inform. Appl., 41(4):425–446, 2007.
- An introduction to symbolic dynamics and coding. Cambridge Mathematical Library. Cambridge University Press, Cambridge, second edition, 2021.
- M. Lothaire. Algebraic combinatorics on words, volume 90 of Encycl. Math. Appl. Cambridge University Press, Cambridge, 2002.
- A combinatorial view on string attractors. Theoret. Comput. Sci., 850:236–248, 2021.
- Michael E. Paul. Minimal symbolic flows having minimal block growth. Math. Systems Theory, 8(4):309–315, 1974/75.
- String attractors and infinite words. In LATIN 2022: theoretical informatics, volume 13568 of Lecture Notes in Comput. Sci., pages 426–442. Springer, Cham, 2022.
- String attractors for automatic sequences, 2021. arXiv:2012.06840.
- Luca Q. Zamboni. On the character of words of sublinear complexity. Acta Arith., 184(3):201–213, 2018.