Universal Turing machine

In computer science, a universal Turing machine (UTM) is a Turing machine that can simulate an arbitrary Turing machine on arbitrary input. The universal machine essentially achieves this by reading both the description of the machine to be simulated as well as the input thereof from its own tape. Alan Turing introduced this machine in 1936–1937. This model is considered by some (for example, Martin Davis (2000)) to be the origin of the stored program computer—used by John von Neumann (1946) for the "Electronic Computing Instrument" that now bears von Neumann's name: the von Neumann architecture. It is also known as universal computing machine, universal machine (UM), machine U, U.

In terms of computational complexity, a multi-tape universal Turing machine need only be slower by logarithmic factor compared to the machines it simulates.

Introduction

Every Turing machine computes a certain fixed partial computable function from the input strings over its alphabet. In that sense it behaves like a computer with a fixed program. However, we can encode the action table of any Turing machine in a string. Thus we can construct a Turing machine that expects on its tape a string describing an action table followed by a string describing the input tape, and computes the tape that the encoded Turing machine would have computed. Turing described such a construction in complete detail in his 1936 paper:

Turing machine

A Turing machine is an abstract machine that manipulates symbols on a strip of tape according to a table of rules; to be more exact, it is a mathematical model that defines such a device. Despite the model's simplicity, given any computer algorithm, a Turing machine can be constructed that is capable of simulating that algorithm's logic.

The machine operates on an infinite memory tape divided into cells. The machine positions its head over a cell and "reads" (scans) the symbol there. Then per the symbol and its present place in a finite table of user-specified instructions the machine (i) writes a symbol (e.g. a digit or a letter from a finite alphabet) in the cell (some models allowing symbol erasure and/or no writing), then (ii) either moves the tape one cell left or right (some models allow no motion, some models move the head), then (iii) (as determined by the observed symbol and the machine's place in the table) either proceeds to a subsequent instruction or halts the computation.

Wolfram's 2-state 3-symbol Turing machine

In his book A New Kind of Science, Stephen Wolfram described a universal 2-state 5-color Turing machine, and conjectured that a particular 2-state 3-color Turing machine (hereinafter (2,3) Turing machine) might be universal as well.

On May 14, 2007, Wolfram announced a $25,000 prize to be won by the first person to prove or disprove the universality of the (2,3) Turing machine. On 24 October 2007, it was announced that the prize had been won by Alex Smith, a student in electronics and computing at the University of Birmingham.

Description

The following table indicates the actions to be performed by the Turing machine depending on whether its current state is A or B, and the symbol currently being read is 0, 1 or 2. The table entries indicate the symbol to be printed, the direction in which the tape head is to move, and the subsequent state of the machine.

The (2,3) Turing machine:

Turing Machine (band)

Turing Machine is an instrumental rock band formed in New York City in 1998 by Justin Chearno and Scott DeSimon, late of DC's noise-rockers Pitchblende and Gerhardt 'Jerry' Fuchs, who had moved to New York to play with Bitch Magnet guitarist Jon Fine's new band, Vineland. Their music has been described as "Angular instrumental indie rock," that has "influences as vast as vintage prog, Krautrock and post-punk."

On November 7, 2009, drummer Fuchs died in an elevator shaft accident. The last of Fuchs' studio work with Turing Machine was included posthumously in the 2012 album, What Is The Meaning of What. Some of the friends of the band such as Pat Mahoney of LCD Soundsystem and Brian Chase helped to complete the unfinished album after Fuchs' death.

The name comes from the hypothetical device defined by Alan Turing with the same name.

Discography

References

External links