On the periodicity of regular languages

A subclass of regular languages called periodic languages and the corresponding finite automata having nontrivial periodic structure are characterized in this paper. Canonical forms of the regular expressions representing such periodic languages are presented. A systematic procedure to determine the periodicity of any given regular expression is devised through a differential approach. Closure properties of periodic languages are found. Relationships between periodic languages and other subclasses of regular languages, such as finite sets and definite languages, are established. We demonstrate a periodic formation of the grammatical production rules for periodic languages. The reducibility of periodic automata and languages is also studied