limed's blog

By limed, history, 3 months ago, In English,

Thought this would be interesting to many: https://arxiv.org/abs/1708.03486

Norbert Blum

(Submitted on 11 Aug 2017)

Berg and Ulfberg and Amano and Maruoka have used CNF-DNF-approximators to prove exponential lower bounds for the monotone network complexity of the clique function and of Andreevs function. We show that these approximators can be used to prove the same lower bound for their non-monotone network complexity. This implies P not equal NP.
 
 
 
 
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3 months ago, # |
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I can't say the proof is correct or flawed, but there is a page with lots of proofs that P = NP and that P != NP here if it may be interesting to anyone

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3 months ago, # |
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Really a big new, hope it can pass through the peer review and the author can get Turing Award.

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3 months ago, # |
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I think nibabity's proof for P != NP is the shortest and the simplest. Here is the complete proof:

Suppose by contradiction that P = NP, then by basic algebra if we reduce P we obtain N = 1 for every N integer which is clearly a contradiction thus the proof is complete.

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    3 months ago, # ^ |
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    It's wrong if P=0, world rescued

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      3 months ago, # ^ |
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      nibabity, what do you say about it?

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        3 months ago, # ^ |
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        Obviously P!=0 since it stands for Positive :)

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          3 months ago, # ^ |
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          Alternative argument :

          P is a polynomial complexity , if it was 0, it would have been constant( O(1) ), which is not polynomial complexity, therefore P != 0 and the proof is correct, where is my 1kk ?

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            3 months ago, # ^ |
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            Actually, at least in some definitions f(x) = 1 is a polynomial of degree 0.

            Also, O(1) is a subset of O(N).

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              3 months ago, # ^ |
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              So many wrong proofs nowadays...

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3 months ago, # |
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And it's wrong apparently?