A Turing machine is a finite automaton with access to memory. It’s a mathematical model of computation that describes an abstract machine.
It is assumed with unbounded memory, provided by an infinite tape of discrete cells with each cell containing a character (including an ‘empty’ or blank character).
A Turing machine consists of
The transition function
When annotating this on a state diagram, convention is to mark each edge with
The language of a given Turing machine,
A language is recognisable is it is accepted by a Turing machine. The machine itself is termed the recogniser of
Turing machines that do not enter infinite loops are called deciders. A language is decidable always result in an explicit accept or reject state being reached.