Synopsis

Mathematical models in classical computation, automata have been an important area in theoretical computer science [1]. It started from a seminal paper of Kleene [2], and within a few years developed into a rich mathematical research topic. From the very beginning finite automata constituted a core of computer science. Part of the reason is that they capture something very fundamental as is witnessed by a numerous different characterizations of the family of rational languages, i.e. languages defined by finite automata [1]. In fact, the interrelation of finite automata and their applications in computer science is a splendid example of a really fruitful connection of theory and practice and these will accept regular language [3]. Finite automata played a crucial role in the theory of programming languages, compiler constructions, switching circuit designing, computer controller, neuron net, text editor and lexical analyzer [4]. The Myhill–Nerode theory [5] is a branch of the algebraic theory of languages and automata in which formal languages and deterministic automata are studied through right invariant equivalence classes (also studied through right congruences and congruences on a free monoid). It provides necessary and sufficient conditions for a language to be regular, in term