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 $M\left(L\right)$>

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.