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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.
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 ...
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."
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.
With a single infinite stack the model can parse (at least) any language that is computable by a Turing machine in linear time. [2] In particular, the language {a n b n c n } can be parsed by an algorithm which verifies first that there are the same number of a's and b's, then rewinds and verifies that there are the same number of b's and c's.
Langton's ant is a two-dimensional Turing machine with a very simple set of rules but complex emergent behavior. It was invented by Chris Langton in 1986 and runs on a square lattice of black and white cells. [1] The idea has been generalized in several different ways, such as turmites which add more colors and more states.
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".
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