Introduction

An Automaton is a device which recognises or accepts certain elements of ${\Sigma }^{\mathrm{*}}$, where $\Sigma$ is a finite alphabet. Since the elements accepted by an automaton are a subset of ${\Sigma }^{\mathrm{*}}$, they form a language. Therefore each automaton will recognise or accept a language contained in ${\Sigma }^{\mathrm{*}}$. The language of ${\Sigma }^{\mathrm{*}}$ consisting of the words accepted by an automaton $M$ is the language over ${\Sigma }^{\mathrm{*}}$ accepted by $M$ and denoted by $M\left(L\right)$>

Definition 3.1

A deterministic automaton, denoted by $(\Sigma ,Q,s_0,\Upsilon ,F)$ , consists of a finite alphabet $\Sigma$, a finite set $Q$ of states, and a function called the transition function and a set $F$ of acceptance states.