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 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, machine U, U.
| Universal Turing Machines and Diagonalization |
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:
- "It is possible to invent a single machine which can be used to compute any computable sequence. If this machine U is supplied with a tape on the beginning of which is written the S.D ["standard description" of an action table] of some computing machine M, then U will compute the same sequence as M."
0 comments