Word-paired insertions of languages

Abstract

In this article, we focus on the properties of word-paired insertions of languages. We show that the word-paired insertions of discrete dense languages, the set of all d-primitive words, and the set of all primitive words are disjunctive (hence, dense and not regular). The equalities and the intersection-properties concerning word-paired insertions of languages are studied too

Word-paired catenations of regular languages

“…For a non-empty language L and its image h(L) equipped with some total orders 1 and 2 respectively, h is said to be order-preserving on L if h(u) 2 h(v) holds whenever u, v ∈ L with u 1 v. Note that the word-paired catenation h (L) and the ordered catenation L$h(L) coincide whenever h is order-preserving on L. Especially, h (L) = {w 2 | w ∈ L} is the ordered catenation of L and itself, denoted by L (2) , when h(w) = w for every w ∈ X * . Moreover, some other word-paired operations such as the word-paired insertions of languages [4] can also be considered. The insertion-primitive words [5] can be defined by using the word-paired insertions.…”