
P not equal to NP - lainon
https://arxiv.org/abs/1802.03028
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Sniffnoy
Just going by the first section, I can anticipate a problem here. The last
paragraph of the first section suggests that the problem of finding a Hamilton
cycle is not in P because some cycles are maximal solutions without being a
maximum solution. However, the same could be said of the problem of finding a
maximum matching -- a maximal matching need not be a maximum matching -- and
yet that problem _is_ in P.

I haven't yet checked the formal conditions to see whether they'll apply to
the matching problems, but I bet they will. (The fact that the paper contains
no instances of the word "matching", meaning it never explains why this
condition doesn't apply to the matching problem even though it looks like it
should, is not encouraging.) If so this proof cannot be correct.

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whatshisface
[https://www.win.tue.nl/~gwoegi/P-versus-
NP.htm](https://www.win.tue.nl/~gwoegi/P-versus-NP.htm)

Here's a link to a list of P vs NP proofs that didn't work out. "Making it to
arxiv" and "sounding reasonable" are usually pretty good filters but for some
reason this problem has attracted a lot of trouble.

~~~
Sniffnoy
Note that this hasn't been updated in a while. For instance Norbert Blum's
attempt from 2017 (now acknowledged as mistaken) is missing.

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cevi
The main step seems to be Lemma 2. The fact that the reductions are logspace
is never actually used in the argument - so if this proof worked, it would
also apply to arbitrary reductions, and the same argument would show that NP
is not contained in, say, EXP.

The fact that there are no inequalities anywhere throughout the paper is the
real tip-off that this is not a serious attempt.

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unixhero
Kinda insanely difficult summary there :)

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teilo
Yawn.

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godelmachine
WOW!! Another one after Vinay Deolalikar's! I lack the mathematical expertise
but would certainly love to hear what experts have to say on this one.

~~~
Sniffnoy
Claims of P != NP are pretty common; I wouldn't get so excited just yet...

