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 Hyper operators in computability theory tommy1729 Ultimate Fellow Posts: 1,365 Threads: 333 Joined: Feb 2009 02/13/2017, 12:09 AM (02/07/2017, 07:59 AM)JmsNxn Wrote: Recently I asked this question on MO http://mathoverflow.net/questions/261538...n-analysis 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 $\sqrt{2}\uparrow^n x$ grows hyper operationally with $n$. 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. Sorry Regards Tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Hyper operators in computability theory - by JmsNxn - 02/07/2017, 07:59 AM RE: Hyper operators in computability theory - by tommy1729 - 02/13/2017, 12:09 AM RE: Hyper operators in computability theory - by MphLee - 02/14/2017, 06:53 PM RE: Hyper operators in computability theory - by MphLee - 02/15/2017, 10:10 AM RE: Hyper operators in computability theory - by JmsNxn - 02/15/2017, 04:19 PM RE: Hyper operators in computability theory - by MphLee - 02/15/2017, 10:07 PM

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