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Open AccessArticle

by Jing Tian, Yizhi Chen and Hui Xu

Mathematics 2022, 10(19), 3416; https://doi.org/10.3390/math10193416 - 20 Sep 2022

Viewed by 1387

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 [...] Read more.

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 \subseteq Σ^{+}

is said to be prefix-strict, if for any

u, v \in 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^{+}

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 + y x \approx x

and

x + y x z \approx x

. Furthermore, the analogous results for so-called suffix-strict languages and infix-strict languages are introduced. Full article

(This article belongs to the Special Issue Rota-Baxter Algebra and Related Topics)

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