utm theoremFrom Wikipedia, the free encyclopedia (Redirected from Universal Function) Jump to: navigation, search In computability theory the utm theorem, or Universal Turing machine theorem, is a basic result about Gödel numberings of the set of computable functions. It affirms the existence of a computable universal function which is capable of calculating any other computable function. The universal function is an abstract version of the universal turing machine, thus the name of the theorem. Rogers equivalence theorem provides a characterization of the Gödel numbering of the computable functions in terms of the smn theorem and the utm theorem. utm theorem[edit]Let be an enumeration of Gödel numbers of computable functions. Then the partial function defined as is computable. is called the universal function.
Posted on: Wed, 03 Jul 2013 21:52:51 +0000
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