An Algebraic Characterization of Prefix-Strict Languages

An Algebraic Characterization of Prefix-Strict Languages

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Let
.org/1998/Math/MathML" display="inline">Σ+ be the set of all finite words over a finite alphabet .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 $L\subseteq {\mathsf{\Sigma }}^{+}$ is said to be prefix-strict, if for any , 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 by
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org/1998/Math/MathML" display="inline">P(Σ+).This paper characterizes as a universe of a model of the free object for the ai-semiring variety satisfying the additional identities $x+yx\approx x$ and .Furthermore, the analogous results for so-called suffix-strict languages and infix-strict languages are introduced.