# What is the Turing machine? – Function, operation and historical importance

The Turing machine is a device that can **read and write information **on a paper tape. Although it is an abstract concept, the Turing machine has been fundamental to the development of computing.

In this article we will explore in detail **what is turing machine**how it works and why it is so important in the historical context of computing and mathematics.

## Definition and concept of the Turing machine

The Turing machine is a theoretical model of an abstract mechanical device that can **perform calculations** by reading and writing information on a paper tape.

This device is composed of a **read/write head** that moves along the tape, a set of internal states, and a set of instructions that tell how the machine should behave based on the information it reads. He is able to **perform any computational operation **that can be performed by a computer, which is why it is considered the simplest and most powerful computational model ever created.

### What is the universal Turing machine?

The universal Turing machine is a **Turing machine variant**.** **The idea behind the universal Turing machine is that it can simulate any other Turing machine, that is, it can run any program that a Turing machine can run.

The idea of the universal Turing machine was revolutionary, as it showed that any problem that could be solved by a Turing machine could be **solved by any other Turing machine**, as long as they had enough time and memory to do it. This idea is the basis of modern computing theory, and is a fundamental concept in computer programming and design.

In addition, it allowed us to demonstrate that computing was a mechanical activity that could be **formally described** **and accurate** using algorithms, and that any problem that could be solved by a computer could be solved by any other computer, as long as it had sufficient capacity.

The universal Turing machine also allowed researchers to show that certain problems were mathematically undecidable, that is, they could not be solved by any Turing machine, including the universal Turing machine. These problems include the stall problem** **(**halting problem**)** **and the string equality problem (**string equality problem**), among others.

## What is the Turing machine used for?

Although the Turing machine **not a real physical machine**is considered the simplest and most powerful model of computation that has been created, having a great influence on the theory of computation and computer science.

Among the practical applications of the Turing machine is its use in **algorithm creation and analysis**the demonstration of the existence of mathematically undecidable problems and the simulation of computers and complex computer systems.

The Turing machine has also been used as the basis for the **programming language development **and modern computing systems, and has been an important tool in the design and analysis of algorithms, as well as in the teaching of computing theory and informatics.

In addition to the applications mentioned, the Turing machine has been fundamental in the **study of computational complexity** and the classification of problems based on their computational difficulty.

## How does the Turing machine work?

The Turing machine works through the **manipulation of stored information** on a paper tape, using a read/write head that moves along the tape and reads or writes symbols at each position on the tape.

It consists of three main components: the paper ribbon, the read/write head, and a **transition table** **which specifies the rules** machine transition. The paper strip is infinitely long and is divided into cells, each of which can contain one symbol from a finite set of symbols. The read/write head moves left or right along the tape, and can read or write symbols in each cell. The operation of the Turing machine is based on:

- A ‘current state’, which represents the
**machine status**at one point. - A ‘current symbol’, which represents the symbol at the current position on the tape.
- A transition table, which manages to specify the action the machine should take based on the current state and the current symbol.

The transition table indicates what the **next machine status**what symbol to write at the current tape position, whether the read/write head should move left or right, and what the next state of the machine will be.

At each step, the Turing machine **read the symbol** **in current position **on the tape, determines the action to take based on the current state and the current symbol, writes a new symbol at the current position on the tape, moves the play/write head left or right according to the instructions in the table transition, and changes to the new state of the machine. The process is repeated until the machine reaches a **accept or reject status**according to the rules specified by the designer of the machine.

The Turing machine is capable of solving any computable problem that can be **described in terms of a sequence **of finite instructions, and is considered the simplest and most powerful model of computing ever created.

## What are the characteristics of the Turing machine?

The Turing machine is characterized by its universality, since it can carry out any task that can be described in terms of a **finite sequence of instructions**.

It is very flexible, as it can **work with different types of information**, such as numbers, letters, symbols and other data that can be represented on a paper tape. Despite its power and versatility, the Turing machine is a relatively simple computational model, with few rules and components.

It’s a **abstract pattern** **from a computer**, focused on the essential operations and processes of computing, which makes it precise and mathematical. Its operation is deterministic, that is, its behavior is completely determined by its current state and the inputs it receives.

Another important feature of the Turing machine is that it is based on the **symbol manipulation **on a paper tape, which makes it very different from modern computers that use electronic components.

### Who made the Turing machine? – History

The Turing machine was invented by the **British mathematician and cryptographer** **alan turing** in 1936. At the time, Turing was a graduate student at King’s College, Cambridge University, working on the theory of computation and mathematical logic.

Turing was interested in the question of whether there were any mathematical problems that could not be solved by a computer, and whether it was possible to develop a theoretical model of computation that could address any mathematical problem. With this idea in mind, he developed the Turing machine as a theoretical model of a computer that could **carry out any task** that could be described in terms of a finite sequence of instructions.

Although the Turing machine was not physically built during Turing’s lifetime, his theoretical model was fundamental to the **development of modern computing** and laid the foundations of programming and computer theory.

## Why is the Turing machine considered relevant?

The Turing machine is considered relevant for several reasons:

- It’s a
**theoretical model of universal computing**: The Turing machine is a theoretical model of a computer that can perform any task that can be described in terms of a finite sequence of instructions, being**able to perform any mathematical calculation**that can be assigned. This makes it a theoretical model of universal computing that laid the foundations of computing theory. **laid the****basics of programming**: Turing machine**laid the foundations of programming**, since it provided a systematic way to describe an algorithm. This allowed programmers to write computer programs that could be executed by real machines.**contributed to cryptography**: The Turing machine was also of great importance in cryptography, as Turing used his knowledge of cryptography and computing to work on the**decryption of encrypted messages**of the ‘Enigma’ encryption machine used by German forces during World War II. Turing and his team developed the Turing ‘bomb’, an electromechanical machine capable of deciphering encrypted Enigma messages and which played a key role in the Allied victory in the war.**He pioneered artificial intelligence**: The Turing machine is also relevant in the field of artificial intelligence, as Turing proposed the idea of the ‘Turing test’ as a way of**assess the intelligence of a machine**. This test consists of determining if a machine can be considered intelligent if its responses are indistinguishable from those of a human being.