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An Algebraic Characterization of Prefix-Strict Languages

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jing Tian & Yizhi Chen & Hui Xu, 2022. "An Algebraic Characterization of Prefix-Strict Languages," Mathematics, MDPI, vol. 10(19), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3416-:d:919713
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