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A multi-tape Turing machine is a variant of the Turing machine that utilizes several tapes. Each tape has its own head for reading and writing. Each tape has its own head for reading and writing. Initially, the input appears on tape 1, and the others start out blank.
A Turing machine is a hypothetical computing device, first conceived by Alan Turing in 1936. Turing machines manipulate symbols on a potentially infinite strip of tape according to a finite table of rules, and they provide the theoretical underpinnings for the notion of a computer algorithm.
An oracle machine or o-machine is a Turing a-machine that pauses its computation at state "o" while, to complete its calculation, it "awaits the decision" of "the oracle"—an entity unspecified by Turing "apart from saying that it cannot be a machine" (Turing (1939), The Undecidable, p. 166–168).
A Multitrack Turing machine is a specific type of multi-tape Turing machine. In a standard n-tape Turing machine, n heads move independently along n tracks. In a n-track Turing machine, one head reads and writes on all tracks simultaneously. A tape position in an n-track Turing Machine contains n symbols from the tape alphabet. It is equivalent ...
Starting from the above encoding, in 1966 F. C. Hennie and R. E. Stearns showed that given a Turing machine M α that halts on input x within N steps, then there exists a multi-tape universal Turing machine that halts on inputs α, x (given on different tapes) in CN log N, where C is a machine-specific constant that does not depend on the ...
With regard to what actions the machine actually does, Turing (1936) [2] states the following: "This [example] table (and all succeeding tables of the same kind) is to be understood to mean that for a configuration described in the first two columns the operations in the third column are carried out successively, and the machine then goes over into the m-configuration in the final column."
Informally, these theorems say that given more time, a Turing machine can solve more problems. For example, there are problems that can be solved with n 2 time but not n time, where n is the input length. The time hierarchy theorem for deterministic multi-tape Turing machines was first proven by Richard E. Stearns and Juris Hartmanis in 1965. [1]
Wang (1957, but presented to the ACM in 1954) is often cited (cf. Minsky (1967), p. 200) as the source of the "program formulation" of binary-tape Turing machines using numbered instructions from the set write 0 write 1 move left move right if scanning 0 then go to instruction i if scanning 1 then go to instruction j