computable nel dizionario italiano Oxford-Paravia

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inglese
Every computable number is definable, but not vice versa.
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They are also known as the recursive numbers or the computable reals.
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What is effectively calculable is computable.
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As a central result in research on computability, the expression syntax defined above (even excluding the let-variant) is able to express any computable function.
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The following classes of partial functions are coextensive, i.e. have the same members: (a) the partial recursive functions, (b) the computable functions, (c) the 1/1 computable functions.
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The non-computable numbers are a strict subset of the transcendental numbers.
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The equality relation on computable real numbers is not computable, but for unequal computable real numbers the order relation is computable.
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Post showed that these sets are strictly between the computable sets and the halting problem with respect to many-one reducibility.
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A software system is in effect a computable function implemented as an algorithm in some implementation programming language.
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In this approach logical formulas represent computational problems (or, equivalently, computational resources), and their validity means being always computable.
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