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Informatics# Turing machine

## What is the Turing machine?

## Features of Turing Machine

## History of Turing machine

## How it works

## Uses of the Turing machine

## Examples

The **Turing machine** is a **computer device** which consists of a **read** and **write header**, what we know best today as a **scanner** and a paper ribbon that passes through the machine. This tape was divided into **squares**, and each of them had a **symbol** at the same time. It was responsible for the **storage** of the machine and was a kind of vehicle for **entry** and **exit**, as well as working memory to store the results of the intermediate steps of the calculation.

**Who invented it**? Alan Turing**Year of invention**? 1936

It is a more general language **recognition** **module** that any **Finite** and **Stack** automaton has, as it has the ability to recognize **regular** and context-**independent** languages, as well as many other types of languages.

The main features of the Turing machine were as follows:

- The input that the tape has before the calculation begins, must consist of a finite number of symbols.
- The machine tape has an unlimited length.
- The read/write head can be programmable.
- The Turing machine is capable of doing six types of fundamental operations: read, write, move left, move right, change state and stop.
- It has the ability to compute anything any modern computer can calculate.
- It consists of an input and output alphabet and a special symbol called white.

**Alan Mathison Turing** was the inventor of the Turing machine. He was known as an extremely talented man, who had great influences on the development of **computing** and on the formalization of the concept of **algorithm** and **computation** through his Turing machine, which played a very important role in the creation of the modern computer.

Turing described it for the first time in his 1936 article dealing with issues concerning **computable** **numbers**. In his article, Turing imagines that his creation is not a mechanical machine, but rather a person he decided to call a computer, which carelessly executes these deterministic mechanical rules.

The Turing machine operates through a **finite control**, a **reader head** and a **ribbon** on which there may be different **characters**, and on which the input word is found. To the **right side,** the ribbon has a length which is the place where the spaces are filled with the white character which is represented by the letter **“t”.** To its left side, the opposite happens because the tape is not infinite, reason why there is a picture of the tape that is the left side. In addition, it has a head that moves to the left and right, so it has the ability to pass in repeated cycles over the same segment of the tape.

The machine consists of an input and output **alphabet**, a **special symbol** known as **white** which is normally represented by a b, Δ or 0, a group of finite states, and a set of **transitions** between these states.

Its operation is based on the **transition**, which is responsible for receiving an **initial state** and a **string of characters** which belong to the input alphabet. From that moment on, the machine begins to read a **band cell**, **deleting** the symbol, and **writing** the new symbol that belongs to the output alphabet and then advances to the left or right, one time at a time and repeating the process as indicated in the transition function. At the end of the process it stops in an **acceptance** state, thus representing the output.

The Turing machine has been, for example, used as a **language generator**, because this type of machine has several tapes including an output tape that is empty at first and then filled with words of language. It is also used in **compilers I and II**, state machines, **automaton** machines and **code generators**.

In the antiquity it was used in machines as the “**Bombe**” that was a device used by the British cryptologists to decipher signals encrypted by the German machine “enigma” during the Second World War. Also in the “**colossus**” machines that deciphered the encrypted messages intercepted in the communications of the Nazis.

Some examples of the Turing machine are:

- An X chain followed by a Y chain. Both of the same length.
- X^n Y^n, n>0}
- Tape initial state: 000111#
- Transitions:
- 0 0 X r 1
- 1 0 0 r 1
- 1 Y Y r 1
- 2 X X r 0
- 3 Y Y r 3
- 0 Y Y r 3
- 1 1 Y l 2
- 2 0 0 l 2
- 2 Y Y l 2
- 3 # # r 4
- 4 * * r halt

Written by Gabriela Briceño V.

Briceño V., Gabriela. (2019). *Turing machine*. Recovered on 8 March, 2023, de Euston96: https://www.euston96.com/en/turing-machine/