Turing machine

The Turing machine is a computing device which consists of a read and write head , which is better known today as a scanner and a paper tape that passes through the machine. This ribbon was divided into squares , and each of them had a symbol at the same time . This tape was in charge of storing the machine, and was a kind of input and output vehicle , as well as working as a working memory to store the results of the intermediate steps of the calculation.

Characteristics of the Turing machine

The main characteristics of the Turing machine were the following:

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

History of the Turing machine

Alan Mathison Turing was the inventor of the Turing machine. He was known as an extremely talented man, who had great influences in the development of computer science and in 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 first described it in his article published in 1936 on 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, who runs these deterministic mechanical rules carelessly.

How does it work

The Turing machine works by means of a finite control , a playhead and a tape on which there can be different characters , and on which the input word is found. Towards the right side the tape has a length that is the place where the spaces are filled with the white character which is represented by the letter “t” . Towards its left side, the opposite happens because the tape is not infinite, which is why there is a box of the tape that is the extreme left. In addition, it has a head that moves to the left and right, so it has the ability to cycle through the same segment of the belt.

The machine is made up of an input alphabet and an output alphabet , by a special symbol known by the name of target which is normally represented by a b, Δ or 0, by a group of finite states and by 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 cell on the tape, erasing 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 a state of acceptance , thus representing the output.

Uses of the Turing machine

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

In ancient times it was used in machines such as the “Bombe” which was a device used by British cryptologists to be able to decipher signals encrypted by the German “enigma” machine during World War II . Also in the “colossus” machines that deciphered the encrypted messages intercepted in the communications of the Nazis.

Examples

Some examples of the Turing machine are:

• A string of X followed by a string of Y. Both of the same length.
• {X ^ n Y ^ n, n> 0}
• Ribbon Initial Status: 000111 #
• Transitions:
  • 0 0 X r 1
  • 1 0 0 r 1
  • 1 YY r 1
  • 2 XX r 0
  • 3 YY r 3
  • 0 YY r 3
  • 1 1 AND l 2
  • 2 0 0 l 2
  • 2 YY l 2
  • 3 # # r 4
  • 4 * * r halt