<
Computability> A hypotheti
Cal ma
Chine defined in 1935-6 by
Alan Turing and used for
Computability theory proofs. It
Consists of an infinitely long "tape" with symbols (
Chosen from some
finite set) written at regular intervals. A pointer marks the
Current position and the ma
Chine is in one of a finite set of "internal states". At ea
Ch step the ma
Chine reads the symbol at the
Current position on the tape. For ea
Ch
Combination of
Current state and symbol read, a program spe
Cifies the new state and either a symbol to write to the tape or a dire
Ction to move the pointer (left or right) or to halt. In an alternative s
Cheme, the ma
Chine writes a symbol to the tape *and* moves at ea
Ch step. This
Can be en
Coded as a write state followed by a move state for the write-or-move ma
Chine. If the write-and-move ma
Chine is also given a distan
Ce to move then it
Can emulate an write-or-move program by using states with a distan
Ce of zero. A further variation is whether halting is an a
Ction like writing or moving or whether it is a spe
Cial state. [What was Turing' s original definition?] Without loss of generality, the symbol set
Can be limited to just "0" and "1" and the ma
Chine
Can be restri
Cted to start on the leftmost 1 of the leftmost string of 1s with strings of 1s being separated by a single 0. The tape may be infinite in one dire
Ction only, with the understanding that the ma
Chine will halt if it tries to move off the other end. All
Computer
instruCtion sets,
high level languages and
Computer ar
Chite
Ctures, in
Cluding
parallel proCessors,
Can be shown to be equivalent to a Turing Ma
Chine and thus equivalent to ea
Ch other in the sense that any problem that one
Can solve, any other
Can solve given suffi
Cient time and memory. Turing generalised the idea of the Turing Ma
Chine to a "Universal Turing Ma
Chine" whi
Ch was programmed to read instru
Ctions, as well as data, off the tape, thus giving rise to the idea of a general-purpose programmable
Computing devi
Ce. This idea still exists in modern
Computer design with low level
miCroCode whi
Ch dire
Cts the reading and de
Coding of higher level
maChine Code instru
Ctions. A
busy beaver is one kind of Turing Ma
Chine program. Dr. Hava Siegelmann of
TeChnion reported in S
Cien
Ce of 28 Apr 1995 that she has found a mathemati
Cally rigorous
Class of ma
Chines, based on ideas from
Chaos theory and {neural network}s, that are more powerful than Turing Ma
Chines. Sir Roger Penrose of
Oxford University has argued that the brain
Can
Compute things that a Turing Ma
Chine
Cannot, whi
Ch would mean that it would be impossible to
Create {artifi
Cial intelligen
Ce}. Dr. Siegelmann' s work suggests that this is true only for
Conventional
Computers and may not
Cover {neural network}s. See also
Turing tar-pit,
finite state maChine. (1995-05-10)
In addition suitable Contents:
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