A free monoid containing all strongly Bi-singular languages and non-primitive words

摘要

Let Q~((i)), where i ≥ 1, be the set of ith powers of primitive words. A language is called strongly bi-singular if the minimal-length words in it are neither prefixes nor suffixes of any other word in the language. Strongly bi-singular languages forms a free monoid with respect to the concatenation of languages. The main result of this paper is that if we start with the basis of this free monoid together with the languages Q~((i)) for all i ≥ 2, then the resulting family of languages is a code. So we find a free monoid which properly contains the free monoid of all strongly bi-singular languages.