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Hyper operators in computability theory
(02/07/2017, 07:59 AM)JmsNxn Wrote: Recently I asked this question on MO

And I'm curious if anyone has encountered anything similar. As in, the main value of the hyper-operators defined for natural numbers is its computational aspect. Is there a similar idea in analysis? Can anyone give me any ideas of where to talk about these things. About how to phrase the fact that the computational complexity of grows hyper operationally with .

In the most General case computational complexity is a very hard and unsolved area of research.
For instance take euler's gamma : if irrational , the complexity is finite. But we do not know.
The fastest algorithm or even a quadratic speed algorithm for its digits is unknown.

As for your case : 

I hope you meant superexponentially INSTEAD of hyper operationally.

Second , it seems you want a fastcut for functions like exp exp and exp exp exp.

Well if the stirling Numbers or its generalisations will not help , I assume it can not be done.

Reminds me of Stephen Wolfram's irreducible complexity.

Besides the acceleration by 2 or 3 iterates at once and the alike , one could try a nonconstant iteration speedup, but that would require a superfunction or Abel function AND a fast method for THAT Abel or super.

Combinatorical methods probably reduce to the above.

Number theory seems unrelated in a noncombinatorical sense.

Fake function theory can be fast but not precise.

Contour integrals ??

Im not optimistic since i just Summarized imho the most realistic ideas.




Messages In This Thread
RE: Hyper operators in computability theory - by tommy1729 - 02/13/2017, 12:09 AM

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