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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).
Smith's proof has unleashed a debate on the precise operational conditions a Turing machine must satisfy in order for it to be candidate universal machine. 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.
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.
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'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".
Arithmetic-based Turing-complete machines use an arithmetic operation and a conditional jump. Like the two previous universal computers, this class is also Turing-complete. The instruction operates on integers which may also be addresses in memory. Currently there are several known OISCs of this class, based on different arithmetic operations:
Configurations and the yields relation on configurations, which describes the possible actions of the Turing machine given any possible contents of the tape, are as for standard Turing machines, except that the yields relation is no longer single-valued. (If the machine is deterministic, the possible computations are all prefixes of a single ...