|
|
| Line 1: |
Line 1: |
| {{lowercase|title=utm theorem}}
| | The author is called Wilber Pegues. Mississippi is exactly where her house is but her spouse desires them to move. To climb is something I really appreciate doing. Invoicing is my profession.<br><br>My page [http://www.january-yjm.com/xe/index.php?mid=video&document_srl=158289 free psychic] |
| In [[computability theory]] the '''utm theorem''', or '''[[Universal Turing machine]] theorem''', is a basic result about [[Gödel numbering]]s of the set of [[computable function]]s. 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.
| |
| | |
| [[Roger's equivalence 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 ==
| |
| | |
| Let <math>\varphi_1, \varphi_2, \varphi_3, ...</math> be an enumeration of Gödel numbers of computable functions. Then the partial function
| |
| :<math>u: \mathbb{N}^2 \to \mathbb{N}</math>
| |
| defined as
| |
| :<math>u(i,x) := \varphi_i(x) \qquad i,x \in \mathbb{N}</math>
| |
| is computable.
| |
| | |
| <math>u</math> is called the '''universal function'''.
| |
| | |
| == References ==
| |
| *{{cite book | author = Rogers, H. | title = The Theory of Recursive Functions and Effective Computability | publisher = First MIT press paperback edition | year = 1987 | origyear = 1967 | isbn = 0-262-68052-1 }}
| |
| *{{cite book | author = Soare, R.| title = Recursively enumerable sets and degrees | series = Perspectives in Mathematical Logic | publisher = Springer-Verlag | year = 1987 | isbn = 3-540-15299-7 }}
| |
| | |
| [[Category:Theory of computation]]
| |
| [[Category:Computability theory]]
| |
Revision as of 10:02, 19 February 2014
The author is called Wilber Pegues. Mississippi is exactly where her house is but her spouse desires them to move. To climb is something I really appreciate doing. Invoicing is my profession.
My page free psychic