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)
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Famous quotes containing the words universal and/or machines:
“I had rather believe all the fables in the Legend, and the Talmud, and the Alcoran, than that this universal frame is without a Mind; and, therefore, God never wrought miracle to convince atheism, because his ordinary works convince it.”
—Francis Bacon (1561–1626)
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Irregular verbs to learn, the Time Being to redeem
From insignificance.”
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