An Algebraic Characterization of Prefix-Strict Languages

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 i...

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 19; p. 3416
Main Authors Tian, Jing, Chen, Yizhi, Xu, Hui
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2022
Subjects
Affixes
ai-semirings variety
Algebra
embedding order
formal languages
free algebra
Grammar, Comparative and general
Language
Language and languages
Languages
Suffixes and prefixes
Words (language)
China
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10193416