Fresnel diffraction

Template:Lowercase 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

Let $\varphi _{1},\varphi _{2},\varphi _{3},...$ be an enumeration of Gödel numbers of computable functions. Then the partial function

$u:\mathbb {N} ^{2}\to \mathbb {N}$

defined as

$u(i,x):=\varphi _{i}(x)\qquad i,x\in \mathbb {N}$

is computable.

$u$ is called the universal function.

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534