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String Attractors and Infinite Words

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LATIN 2022: Theoretical Informatics (LATIN 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13568))

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Abstract

The notion of string attractor has been introduced by Kempa and Prezza (STOC 2018) in the context of Data Compression and it represents a set of positions of a finite word in which all of its factors can be “attracted”. The smallest size \(\gamma ^*\) of a string attractor for a finite word is a lower bound for several repetitiveness measures associated with the most common compression schemes, including BWT-based and LZ-based compressors. The combinatorial properties of the measure \(\gamma ^*\) have been studied in [Mantaci et al., TCS 2021]. Very recently, a complexity measure, called string attractor profile function, has been introduced for infinite words, by evaluating \(\gamma ^*\) on each prefix. Such a measure has been studied for automatic sequences and linearly recurrent infinite words in [Schaeffer and Shallit, arXiv 2021]. In this paper, we study the relationship between such a complexity measure and other well-known combinatorial notions related to repetitiveness in the context of infinite words, such as the factor complexity and the recurrence. Furthermore, we introduce new string attractor-based complexity measures, in which the structure and the distribution of positions in a string attractor of the prefixes of infinite words are considered. We show that such measures provide a finer classification of some infinite families of words.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Palermo, Palermo, Italy

    Antonio Restivo, Giuseppe Romana & Marinella Sciortino

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  1. Antonio Restivo
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  2. Giuseppe Romana
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  3. Marinella Sciortino
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Correspondence to Marinella Sciortino .

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Editors and Affiliations

  1. Universidad Nacional Autónoma de México, Mexico City, Mexico

    Armando Castañeda

  2. Centro de investigación y de Estudios Avanzados, Mexico City, Mexico

    Francisco Rodríguez-Henríquez

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Restivo, A., Romana, G., Sciortino, M. (2022). String Attractors and Infinite Words. In: Castañeda, A., Rodríguez-Henríquez, F. (eds) LATIN 2022: Theoretical Informatics. LATIN 2022. Lecture Notes in Computer Science, vol 13568. Springer, Cham. https://doi.org/10.1007/978-3-031-20624-5_26

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  • DOI: https://doi.org/10.1007/978-3-031-20624-5_26

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