Turing machine (redirected from Infinite time Turing machine)

Turing machine, a mathematical model of a device that computes via a series of discrete steps and is not limited in use by a fixed maximum amount of data storage. Introduced by the British mathematician Alan Turing in 1936, a Turing machine is a particularly simple computer, one whose operations are limited to reading and writing symbols on tape, or moving along the tape to the left or to the right one symbol at a time. Its behavior at a given moment is determined by the symbol in the square currently being read and by the current state of the machine. The theoretical prototype of the electronic digital computer, Turing machines are one of the key abstractions used in modern computability theory, the study of what computers can and cannot do. Appropriate Turing machines have found application in the study of artificial intelligence, the structure of languages, and pattern recognition.

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Turing machine

Hypothetical computing device proposed by Alan M. Turing (1936). Not actually a machine, it is an idealized mathematical model that reduces the logical structure of any computing device to its essentials. It consists of an infinitely extensible tape, a tape head that is capable of performing various operations on the tape, and a modifiable control mechanism in the head that can store instructions. As envisaged by Turing, it performs its functions in a sequence of discrete steps. His extrapolation of the essential features of information processing was instrumental in the development of modern digital computers, which share his basic scheme of an input/output device (tape and tape reader), central processing unit (CPU, or control mechanism), and stored memory.

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Turing machine [′tu̇r·iŋ mə‚shēn]

(computer science)

A mathematical idealization of a computing automation similar in some ways to real computing machines; used by mathematicians to define the concept of computability.

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(computability)

Turing Machine - A hypothetical machine defined in 1935-6 by Alan Turing and used for computability theory proofs. It consists of an infinitely long "tape" with symbols (chosen from some finite set) written at regular intervals. A pointer marks the current position and the machine is in one of a finite set of "internal states". At each step the machine reads the symbol at the current position on the tape. For each combination of current state and symbol read, a program specifies the new state and either a symbol to write to the tape or a direction to move the pointer (left or right) or to halt. In an alternative scheme, the machine writes a symbol to the tape *and* moves at each step. This can be encoded as a write state followed by a move state for the write-or-move machine. If the write-and-move machine is also given a distance to move then it can emulate an write-or-move program by using states with a distance of zero. A further variation is whether halting is an action like writing or moving or whether it is a special state. Without loss of generality, the symbol set can be limited to just "0" and "1" and the machine can be restricted to start on the leftmost 1 of the leftmost string of 1s with strings of 1s being separated by a single 0. The tape may be infinite in one direction only, with the understanding that the machine will halt if it tries to move off the other end. All computer instruction sets, high level languages and computer architectures, including parallel processors, can be shown to be equivalent to a Turing Machine and thus equivalent to each other in the sense that any problem that one can solve, any other can solve given sufficient time and memory. Turing generalised the idea of the Turing Machine to a "Universal Turing Machine" which was programmed to read instructions, as well as data, off the tape, thus giving rise to the idea of a general-purpose programmable computing device. This idea still exists in modern computer design with low level microcode which directs the reading and decoding of higher level machine code instructions. A busy beaver is one kind of Turing Machine program. Dr. Hava Siegelmann of Technion reported in Science of 28 Apr 1995 that she has found a mathematically rigorous class of machines, based on ideas from chaos theory and neural networks, that are more powerful than Turing Machines. Sir Roger Penrose of Oxford University has argued that the brain can compute things that a Turing Machine cannot, which would mean that it would be impossible to create artificial intelligence. Dr. Siegelmann's work suggests that this is true only for conventional computers and may not cover neural networks. See also Turing tar-pit, finite state machine.