## ★ Turing machine

Turing machine is a term from computer science. A Turing machine is a system of rules, states and transitions rather than a real machine. It was first described in 1936 by English mathematician and computer scientist Alan Turing. There are two purposes for a Turing machine: deciding formal languages and solving mathematical functions. Turing machines are one of the most important formal models in the study of computer science.

## 1. Common basics

A Turing machine consists of the following components simplified:

- A limited set of states with one state marked as start state, while running, a Turing machine always has a current state.
- A definition of a so-called transition function.
- An infinite tape with storage cells and a read / write-device that can move on the tape.

Also, a working-alphabet set of characters has to be defined.

When a Turing machine is started, a word out of the working-alphabet must be present on the infinite tape of the machine. The read / write-device on the first character now reads the first character and depending on the current state of Turing machine the read / write-device overwrites the character with a new one or moves one cell to the left or to the right. Furthermore, the current state of the machine can be switched.

### * 1.1. Common basics * Turing machines that decide languages

For decidability theory a Turing machine is said to decide a language if it is always able to determine whether a given word is contained in a certain language or not. Therefore, the machine usually has two special states marked as Accept and Reject. After a while one of the two states will be reached depending on the input word and the machine is halted. If only one of the two states will ever be reached, the Turing machine is said to semi-decide a language.

### * 1.2. Common basics * Turing machines that compute functions

If a Turing machine is used for the computation of functions it only has one end state. When the machine comes to that state it is halted and the result of the function depending on the input can be found on the tape.

## 2. Impact of Turing machines

Turing machines were not invented to be built in reality, but they are very important for theoretical computer science as they are one of the simplest models for computers. The Church-Turing thesis states that all computers are only as powerful as Turing machines. This can be used to prove if a problem is solvable by a computer or not.

## 3. Variations

- A Turing machine can consist of multiple infinite tapes and multiple read / write-devices. However it is proven that such machines are only as powerful as single-tape machines. Multi-tape machines are useful when dealing with more complex problems.
- If a Turing machine has a nondeterministic transition function there can be multiple transitions from one state to many others when reading a character. Again this does not enhance the power of Turing machines. However nondeterministic Turing machines as they are called then may possibly decrease the computation time by a strong amount. This question is covered in the P versus NP-discussion and is not solved yet. Most scientists assume however that nondeterministic machines can work much faster on certain problems.
- A Universal Turing Machine is a variation which can simulate a Turing Machine with an input.

- A Turing machine is an idea from computer science that tries to describe how some computers work. Deterministic Turing machines use a function. Given
- both together can be made Turing complete. The standard regular expressions, which most programming languages use, are not Turing complete either. Most regular
- The Church - Turing thesis also known as Church s thesis, Church s conjecture and Turing s thesis is a statement about computers. It says that a very simple
- married Julius Mathison Turing latter son of Reverend John Robert Turing and Fanny Boyd, in Dublin. Born on June 23rd 1912, Alan Turing would go on to be regarded
- Turing may refer to: Alan Turing a computer scientist Turing test, a test to see if a computer can act like a person Turing machine an idea in computer
- parameter link p. 317. Bibliography of Turing Award lectures, DBLP Steven Geringer 27 July 2007 ACM S Turing Award Prize Raised To 250, 000 ACM press
- Turing machine A Turing machine basically is a special typewriter with an endless ribbon. The machine is named after the mathematician Alan Turing
- to the PHB Pointy Haired Boss failing the Turing test. Harnad, Stevan 2008. The Annotation Game: on Turing 1950 on Computing, Machinery and Intelligence
- a test that is used to separate humans and machines CAPTCHA stands for Completely Automated Public Turing test to tell Computers and Humans Apart. It
- If it is not minimal, there must be another automaton with fewer states that can do the same thing. An example of an automaton is the turing machine

- solution for the Entscheidungsproblem This was proven by Alan Turings Turing Machine which was created in the 1930s. This short article about mathematics
- most of the time. The language is Turing complete. This means that anything that can be computed by a Turing machine can also be done in XSLT. Uses for
- complexity in complexity theory, a string with extra information used by Turing machine or other computing device Pay advice, whereby employees are advised
- and his long - time partner Jeffrey Ullman are the recipients of the 2020 Turing Award. Alfred Vaino Aho at the Mathematics Genealogy Project Aho, A. Gottlob
- management systems. The Bachman diagrams are named after him. He won the Turing Award in 1973. Bachman died on July 13, 2017 at his home in Lexington, Massachusetts
- a given programming language The set of inputs upon which a certain Turing machine halts A formal language can be specified in a great variety of ways
- 1996 The Turing Test: AI s Biggest Blind Alley? in Millican, Peter & Clark, Andy ed. Machines and Thought: The Legacy of Alan Turing 1, Oxford
- an algorithm is a precise list of operations that could be done by a Turing machine For the purpose of computing, algorithms are written in pseudocode
- known for his research in the theory of algorithms, for which he received a Turing Award in 1985, The Benjamin Franklin Medal in Computer and Cognitive Science
- data and perform operations on it. A theoretical model is the quantum Turing machine also known as the universal quantum computer. The idea of quantum computing

- no real computers are used. They are replaced by a system called the Turing machine Once it is known if such a solution exists, computer scientists want
- the Boolean satisfiability problem is NP - complete. A deterministic Turing machine can change a problem in NP in polynomial time to the problem of determining
- as the Turing machine formalism. However, lambda calculus emphasizes the use of transformation rules. It does not care about the actual machine that implements
- died in 1871 Alan Turing he was important in the development of theoretical computer science, and is known for the Turing machine which can be considered
- systems, which study theoretical objects, ideas or concepts such as the Turing machine System Thermodynamic system An Essay on the Investigation of the First
- States Navy Alonzo Church 1905 1995 a logician, famous for the Church - Turing thesis and lambda calculus Benjamin Church 1734 1776 the first Surgeon
- an award given out every year to a chatterbot. The winner is chosen by a Turing test: Each judge talks text - based to a chatterbot and to a human. The
- together. You could also program it. In 1998 the Z3 was proved to be Turing complete. Turing complete means that it is possible to tell this particular computer
- Thompson, the UNIX operating system. Ritchie and Thompson received the Turing Award from the ACM in 1983, the Hamming Medal from the IEEE in 1990 and
- field of artificial intelligence. He is a joint winner of the 1994 ACM Turing Award. He is often called the father of expert systems. Elected AAAI Fellows

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