# Problem Solving: Turing Machines

From the Specification : Turing Machine and the Universal Machine.
The abstract model of the Turing Machine and the Universal Machine.. |

## Contents

## Recap[edit]

Before attempting to study Turing Machines you should ensure you are familiar with Finite State machines from the AS Computing specification and the few additional FSM concepts added to the A2 course.

## Definition[edit]

Turing machines provide a general or formal model of computation and can be used to determine whether or not a task is computable.

## Universal Turing Machine[edit]

A universal Turing machine (UTM) is a Turing machine that can execute other Turing machines by simulating the behaviour of any Turing machine. If a sequence is computable then a UTM will be able to execute it. A UTM behaves as an interpreter which is just what a PC does when it runs a Java applet or Flash script.

**Principle of Universality:** A universal machine is a machine capable of simulating any other machine.

## Examples of mechanical Turing Machines[edit]

- A Turing Machine "in the classic style" has an excellent video depicting the operation of a physical Turing machine

## Simulations[edit]

- Turing Kara has some excellent instructions to help you get to grips with the basic operations of a turing machine

## Example Questions[edit]

Exercise: Turing Machines
design a TM that recoganize the language of all strings of even length over alphabets {a,b}?
A Finite State Machine that operates one or more tapes where at least one tape is infinitely long |

## Revision[edit]

- Turing machines flash cards with test and other activities