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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.
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 universal (2,3) Turing machine has conceivable applications. [19] For instance, a machine that small and simple can be embedded or constructed using a small number of particles or molecules. But the "compiler" Smith's algorithm implies does not produce compact or efficient code, at least for anything but the simplest cases.
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".
In computability theory, the UTM theorem, or universal Turing machine theorem, is a basic result about Gödel numberings of the set of computable functions.It affirms the existence of a computable universal function, which is capable of calculating any other computable function. [1]
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 quantum Turing machine (QTM) or universal quantum computer is an abstract machine used to model the effects of a quantum computer.It provides a simple model that captures all of the power of quantum computation—that is, any quantum algorithm can be expressed formally as a particular quantum Turing machine.
A Turing machine which has the ability to simulate any other Turing machine is called universal - in other words, a Turing machine (TM) is said to be a universal Turing machine (or UTM) if, given any other TM, there is a some input (or "header") such that the first TM given that input "header" will forever after behave like the second TM.