An Algebraic Characterization of Prefix-Strict Languages

Jing Tian (), Yizhi Chen and Hui Xu
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Jing Tian: School of Economics and Finance, Xi’an International Studies University, Xi’an 710128, China
Yizhi Chen: School of Mathematics and Statistics, Huizhou University, Huizhou 516007, China
Hui Xu: School of Science, Air Force Engineering University, Xi’an 710051, China

Mathematics, 2022, vol. 10, issue 19, 1-17

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 + y x ≈ x and x + y x z ≈ x . Furthermore, the analogous results for so-called suffix-strict languages and infix-strict languages are introduced.

Keywords: free algebra; formal languages; embedding order; ai-semirings variety (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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