The second step in characterizing a three-word code

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS Acta Informatica Pub Date : 2023-09-08 DOI:10.1007/s00236-023-00444-6

Chunhua Cao, Jiao Xu, Lei Liao, Di Yang, Guichuan Jia, Qian Du

引用次数: 0

Abstract

In the fields of combinatorics on words and theory of codes, a two-word language \(\{x, y\}\) is a code if and only if \(xy \not = yx\). But up to now, corresponding characterizations for a three-word language, which forms a code, have not been completely found. Let \(X=\{x,\ y,\ z\}\) be a three-word language and \(|x|,\ |y|,\ |z|\) be their lengths. When \(|x| = |y| < |z|\), a necessary and sufficient condition for X to be a code was obtained in 2018. If \(|x| < |y| = |z| \le 2|x|\), a necessary and sufficient condition for X to be a code is proposed in this paper.

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描述三字代码的第二步

在词的组合学领域和码理论中，两个词的语言\(\{x, y\}\)是一个码当且仅当\(xy \not = yx\)。但是到目前为止，对于构成一个码的三字语言，还没有完全找到相应的表征。让\(X=\{x,\ y,\ z\}\)是一个三个单词的语言，\(|x|,\ |y|,\ |z|\)是它们的长度。当\(|x| = |y| < |z|\), 2018年获得X为代码的充分必要条件。如果\(|x| < |y| = |z| \le 2|x|\)，本文给出了X为码的充分必要条件。

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

Acta Informatica 工程技术-计算机：信息系统

CiteScore

2.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics. Topics of interest include: • semantics of programming languages • models and modeling languages for concurrent, distributed, reactive and mobile systems • models and modeling languages for timed, hybrid and probabilistic systems • specification, program analysis and verification • model checking and theorem proving • modal, temporal, first- and higher-order logics, and their variants • constraint logic, SAT/SMT-solving techniques • theoretical aspects of databases, semi-structured data and finite model theory • theoretical aspects of artificial intelligence, knowledge representation, description logic • automata theory, formal languages, term and graph rewriting • game-based models, synthesis • type theory, typed calculi • algebraic, coalgebraic and categorical methods • formal aspects of performance, dependability and reliability analysis • foundations of information and network security • parallel, distributed and randomized algorithms • design and analysis of algorithms • foundations of network and communication protocols.

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