# Automata

## Introduction

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

## Definition 3.1

A deterministic automaton, denoted by $\left(\Sigma ,Q,{s}_{0},\Upsilon ,F\right)$ , 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.