Regular D-length: A tool for improved prefix-stable forward Ramsey factorisations

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2024-04-24 DOI:10.1016/j.ipl.2024.106497

Théodore Lopez, Benjamin Monmege, Jean-Marc Talbot

引用次数: 0

Abstract

Recently, Jecker has introduced and studied the regular $D$ -length of a monoid, as the length of its longest chain of regular $D$ -classes. We use this parameter in order to improve the construction, originally proposed by Colcombet, of a deterministic automaton that allows to map a word to one of its forward Ramsey splits: these are a relaxation of factorisation forests that enjoy prefix stability, thus allowing a compositional construction. For certain monoids that have a small regular $D$ -length, our construction produces an exponentially more succinct deterministic automaton. Finally, we apply it to obtain better complexity result for the problem of fast infix evaluation.

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常规 D 长度：改进前缀稳定前向拉姆齐因式分解的工具

最近，耶克尔（Jecker）引入并研究了单义体的正则 D 长度，即正则 D 类最长链的长度。我们利用这一参数改进了最初由科尔科姆贝特（Colcombet）提出的一种确定性自动机的构造，这种自动机可以将一个词映射到它的前向拉姆齐分裂中的一个：这些分裂是因式分解森林的一种放松，具有前缀稳定性，因此可以进行组合构造。对于某些具有较小规则 D 长度的单词，我们的构造会产生一种指数级的更简洁的确定性自动机。最后，我们运用它为快速下位数评估问题获得了更好的复杂性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.