Frequency languages

Abstract

This paper deals with finite languages specified by a bigrams matrix along with introduced frequency languages on bigrams, which consist of all words with the bigrams matrix multiple of (i.e. multiplied by a positive integer) a given bigrams matrix. Connection between different characteristics of frequency languages and directed graphs and Eulerian circuits in it is established. Necessary and sufficient conditions of non-emptyness and countability of frequency languages are presented. The question of dependence of frequency language cardinality on a given bigrams matrix is analyzed. The formula for the words quantity for a specified bigrams matrix is established. Conditions of frequency languages to be regular are obtained.