String attractors and combinatorics on words
| Autor: | Mantaci, Sabrina, Restivo, Antonio, Romana, Giuseppe, Rosone, Giovanna, Sciortino, Marinella |
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| Přispěvatelé: | Cherubini, A, Sabadini, N, Tini, N., Mantaci S., Restivo A., Romana G., Rosone G., Sciortino M. |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Settore ING-INF/05 - Sistemi Di Elaborazione Delle Informazioni Settore INF/01 - Informatica Formal Languages and Automata Theory (cs.FL) De Brujin word Computer Science - Formal Languages and Automata Theory Burrows-Wheeler transform String attractor Computer Science - Data Structures and Algorithms Thue-Morse word Lempel-Ziv encoding Run-length encoding Data Structures and Algorithms (cs.DS) |
| Popis: | The notion of \emph{string attractor} has recently been introduced in [Prezza, 2017] and studied in [Kempa and Prezza, 2018] to provide a unifying framework for known dictionary-based compressors. A string attractor for a word $w=w[1]w[2]\cdots w[n]$ is a subset $\Gamma$ of the positions $\{1,\ldots,n\}$, such that all distinct factors of $w$ have an occurrence crossing at least one of the elements of $\Gamma$. While finding the smallest string attractor for a word is a NP-complete problem, it has been proved in [Kempa and Prezza, 2018] that dictionary compressors can be interpreted as algorithms approximating the smallest string attractor for a given word. In this paper we explore the notion of string attractor from a combinatorial point of view, by focusing on several families of finite words. The results presented in the paper suggest that the notion of string attractor can be used to define new tools to investigate combinatorial properties of the words. |
| Databáze: | OpenAIRE |
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