An Algebraic Characterization of Prefix-Strict Languages
-
Published:2022-09-20
Issue:19
Volume:10
Page:3416
-
ISSN:2227-7390
-
Container-title:Mathematics
-
language:en
-
Short-container-title:Mathematics
Author:
Tian Jing,Chen Yizhi,Xu Hui
Abstract
Let Σ+ be the set of all finite words over a finite alphabet Σ. A word u is called a strict prefix of a word v, if u is a prefix of v and there is no other way to show that u is a subword of v. A language L⊆Σ+ is said to be prefix-strict, if for any u,v∈L, u is a subword of v always implies that u is a strict prefix of v. Denote the class of all prefix-strict languages in Σ+ by P(Σ+). This paper characterizes P(Σ+) as a universe of a model of the free object for the ai-semiring variety satisfying the additional identities x+yx≈x and x+yxz≈x. Furthermore, the analogous results for so-called suffix-strict languages and infix-strict languages are introduced.
Funder
National Natural Science Foundation of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference18 articles.
1. Codes and Automata;Berstel,2010
2. Outfix and infix codes and related classes of languages
3. Hypercodes
4. Codes and binary relations;Shyr,1977
5. Convex languages;Thierrin,1973