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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).
A configuration, also called an instantaneous description (ID), is a finite representation of the machine at a given time. For example, for a finite automata and a given input, the configuration will be the current state and the number of read letters, for a Turing machine it will be the state, the content of the tape and the position of the head.
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 model describes how units of computations, memories, and communications are organized. [1] The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology.
A Turing machine that "solves" a problem is generally meant to mean one that decides the language. Turing machines enable intuitive notions of "time" and "space". The time complexity of a TM on a particular input is the number of elementary steps that the Turing machine takes to reach either an accept or reject state.
In it he stated another notion of "effective computability" with the introduction of his a-machines (now known as the Turing machine abstract computational model). And in a proof-sketch added as an "Appendix" to his 1936–1937 paper, Turing showed that the classes of functions defined by λ-calculus and Turing machines coincided. [32]
In short the modern Church-Turing thesis states that any computational model can be simulated in polynomial time with a probabilistic Turing machine. [1] [2] However, questions around the Church-Turing thesis arise in the context of quantum computing. It is unclear whether the Church-Turing thesis holds for the quantum computation model.
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".