# Turing computable function

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**Computable function**— Total recursive function redirects here. For other uses of the term recursive function , see Recursive function (disambiguation). Computable functions are the basic objects of study in computability theory. Computable functions are the formalized … Wikipedia**computable function**— noun A mathematical function that can be computed using an abstract computation machine such as Turing machine … Wiktionary**Turing completeness**— For the usage of this term in the theory of relative computability by oracle machines, see Turing reduction. In computability theory, a system of data manipulation rules (such as an instruction set, a programming language, or a cellular… … Wikipedia**Computable number**— In mathematics, particularly theoretical computer science and mathematical logic, the computable numbers, also known as the recursive numbers or the computable reals, are the real numbers that can be computed to within any desired precision by a… … Wikipedia**Turing machine**— For the test of artificial intelligence, see Turing test. For the instrumental rock band, see Turing Machine (band). Turing machine(s) Machina Universal Turing machine Alternating Turing machine Quantum Turing machine Read only Turing machine… … Wikipedia**Turing reduction**— In computability theory, a Turing reduction from a problem A to a problem B, named after Alan Turing, is a reduction which solves A, assuming B is already known (Rogers 1967, Soare 1987). It can be understood as an algorithm that could be used to … Wikipedia**Function (mathematics)**— f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a … Wikipedia**Turing machine**— A mathematical device used by the English mathematician Alan Turing (1912–54) to make precise the notion of an algorithm, or an effective computation. A Turing machine is a computer with a potentially infinite linear tape in both directions,… … Philosophy dictionary**Turing's proof**— First published in January 1937 with the title On Computable Numbers, With an Application to the Entscheidungsproblem , Turing s proof was the second proof of the assertion (Alonzo Church proof was first) that some questions are undecidable :… … Wikipedia**Turing jump**— In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is intuitively described as an operation that assigns to each decision problem X a successively harder decision problem X prime; with the property that X… … Wikipedia