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Computable function - Wikipedia, the free encyclopedia (1960 words) |
 | If a computable function is defined then it returns a single natural number as output (this output can be interpreted as a list of numbers using a pairing function). |
| The fact that these models give equivalent classes of computable functions stems from the fact that each model is capable of reading and mimicking a procedure for any of the other models, much as a compiler is able to read instructions in one computer language and emit instructions in another language. |
| The notion of computability of a function can be relativized to an arbitrary set of natural numbers A, or equivalently to an arbitrary function f from the naturals to the naturals, by using Turing machines (or any other model of computation) extended by an oracle for A or f. |
| PlanetMath: alternative characterizations of recursive functions (348 words) |
| The class of recursive functions may be characterized by considerably weaker conditions than those given in the entry “recursive function” of this encyclopaedia. |
| By means of a pairing function, the definition may be simplified considerably. |
| This is version 8 of alternative characterizations of recursive functions, born on 2004-09-04, modified 2006-10-08. |
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