字符串吸引子与词的组合数学
String Attractors and Combinatorics on Words
摘要：
\emph{string attractor}的概念最近在[Prezza，2017]中引入，并在[Kempa和Prezza，2018]中进行了研究，为已知的基于字典的压缩器提供了统一的框架。字$w=w[1]w[2]\cdots w[n]$的串吸引子是位置$\{1,\ldots,n\}$的子集$Γ$，使得$w$的所有不同因子具有穿过$Γ$的元素中的至少一个的出现。虽然找到单词的最小字符串吸引子是一个NP完全问题，但在[Kempa and Prezza，2018]中已经证明，字典压缩器可以被解释为近似给定单词的最小字符串吸引子的算法。在本文中，我们将探讨字符串吸引子的概念，从组合的角度来看，集中在几个家庭的有限字。结果表明，字符串吸引子的概念可以用来定义新的工具，调查的组合性质的话。
英文摘要：
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 $Γ$ of the positions $\{1,\ldots,n\}$, such that all distinct factors of $w$ have an occurrence crossing at least one of the elements of $Γ$. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
