Universal Turing Machines
As Turing wrote in Undecidable, p. 128 (italics added):
It is possible to invent a single machine which can be used to compute any computable sequence. If this machine U is supplied with the tape on the beginning of which is written the string of quintuples separated by semicolons of some computing machine M, then U will compute the same sequence as M.This finding is now taken for granted, but at the time (1936) it was considered astonishing. The model of computation that Turing called his "universal machine"—"U" for short—is considered by some (cf Davis (2000)) to have been the fundamental theoretical breakthrough that led to the notion of the Stored-program computer.
Turing's paper ... contains, in essence, the invention of the modern computer and some of the programming techniques that accompanied it. —Minsky (1967), p. 104In terms of computational complexity, a multi-tape universal Turing machine need only be slower by logarithmic factor compared to the machines it simulates. This result was obtained in 1966 by F. C. Hennie and R. E. Stearns. (Arora and Barak, 2009, theorem 1.9)
Read more about this topic: Turing Machine
Famous quotes containing the words universal and/or machines:
“There is an universal tendency among mankind to conceive all beings like themselves, and to transfer to every object, those qualities, with which they are familiarly acquainted, and of which they are intimately conscious. We find human faces in the moon, armies in the clouds; and by a natural propensity, if not corrected by experience and reflection, ascribe malice or good-will to every thing, that hurts or pleases us.”
—David Hume (1711–1776)
“In Hell all the messages you ever left on answering machines will be played back to you.”
—Judy Horacek (b. 1961)