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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).
In computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, [1] as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Common sense might say that a universal machine is impossible, but Turing proves that it is possible.
The statement that the halting problem cannot be solved by a Turing machine [7] is one of the most important results in computability theory, as it is an example of a concrete problem that is both easy to formulate and impossible to solve using a Turing machine. Much of computability theory builds on the halting problem result.
Turing completeness is significant in that every real-world design for a computing device can be simulated by a universal Turing machine. The Church–Turing thesis states that this is a law of mathematics – that a universal Turing machine can, in principle, perform any calculation that any other programmable computer can.
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.
Turing's a-machine model. Turing's a-machine (as he called it) was left-ended, right-end-infinite. He provided symbols əə to mark the left end. A finite number of tape symbols were permitted. The instructions (if a universal machine), and the "input" and "out" were written only on "F-squares", and markers were to appear on "E-squares".
tape Turing machine can be formally defined as a 7-tuple = ,,,,, , following the notation of a Turing machine: is a finite, non-empty set of tape alphabet symbols;; is the blank symbol (the only symbol allowed to occur on the tape infinitely often at any step during the computation);
In his 1936 paper, Turing described his idea as a "universal computing machine", but it is now known as the Universal Turing machine. [citation needed] Turing was sought by Womersley to work in the NPL on the ACE project; he accepted and began work on 1 October 1945 and by the end of the year he completed his outline of his 'Proposed electronic ...