Universal computing

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 the idea of such a machine in 1936–1937. This principle is considered to be the origin of the idea of a stored-program computer used by John von Neumann in 1946 for the "Electronic Computing Instrument" that now bears von Neumann's name: the von Neumann architecture.

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

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:

Davis makes a persuasive argument that Turing's conception of what is now known as "the stored-program computer", of placing the "action table"—the instructions for the machine—in the same "memory" as the input data, strongly influenced John von Neumann's conception of the first American discrete-symbol (as opposed to analog) computer—the EDVAC. Davis quotes Time magazine to this effect, that "everyone who taps at a keyboard... is working on an incarnation of a Turing machine," and that "John von Neumann [built] on the work of Alan Turing" (Davis 2000:193 quoting Time magazine of 29 March 1999).

Davis makes a case that Turing's Automatic Computing Engine (ACE) computer "anticipated" the notions of microprogramming (microcode) and RISC processors (Davis 2000:188). Knuth cites Turing's work on the ACE computer as designing "hardware to facilitate subroutine linkage" (Knuth 1973:225); Davis also references this work as Turing's use of a hardware "stack" (Davis 2000:237 footnote 18).

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