
P = NP - Anon84
http://arxiv.org/abs/1208.0954
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robinhouston
It’s fascinating how this sort of thing keeps attracting interest. Here’s a
list of 100 proofs that P=NP or P≠NP, which includes this one:
[http://www.win.tue.nl/~gwoegi/P-versus-
NP.htm](http://www.win.tue.nl/~gwoegi/P-versus-NP.htm)

There’s nothing to make this attempt more worthy of interest than the other
99, as far as I know.

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quchen
Which makes me wonder: how do you filter these? In physics it's common
practice to ignore papers about Perpetuum Mobiles (excuse the probably
incorrect plural), but here we have a topic that is somewhat easy to write
good and bad about while still having very high relevance.

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j2kun
Here's two lists of ways to filter. They're heuristics, but they work well.

One for general mathematical proofs:
[http://www.scottaaronson.com/blog/?p=304](http://www.scottaaronson.com/blog/?p=304)

One specific to P != NP:
[http://www.scottaaronson.com/blog/?p=458](http://www.scottaaronson.com/blog/?p=458)

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Sniffnoy
Two notes on these:

1\. On the first one, note also numbers 11 and 12 Scott mentions in the
comments.

2\. The second is not always so specific to P vs. NP (and indeed has some
overlap with the first -- #1 on the second list is a stricter version of #3
from the first). #3 and #4 for instance could be applied to lots of hard open
problems, #6 to really any hard open problem, and #5 is basically fully
general.

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Aardwolf
A proof that P=NP without an accompanying program that solves SAT or another
NP problem in polynomial time does not count to me :)

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raverbashing
I agree

And let me say, I don't even care about a paper. Sure, it's useful, but it
shouldn't be the focus.

A simple implementation that solves _any_ of the NP problems in polynomial
time is a much better proof than any article.

(of course, those that prove P != NP can't do that, still)

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aeurielesn
I beg to disagree with both of you.

You are kinda disrespecting the important of theoretic research, and a big
part of any field of interest on research.

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raverbashing
Oh the theoretical aspect is important.

But applying it is important as well. Of course, most quantum computing
algorithms have not had a chance of being implemented; it's not always
possible

Or, as Knuth put it "Beware of bugs in the above code; I have only proved it
correct, not tried it."

But if someone comes up with a paper showing a new algorithm but doesn't come
up with an implementation of it when it would be straightforward to do so, I
begin to doubt this person.

Most other fields don't have the luxury of easy testing.

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skykooler
This was already posted here. It is fatally flawed in that, although the
theoretical computing time is polynomial, the memory required grows
exponentially.

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jmpe
Memory growth is not a consideration in the academic proof, Turing machine
tape is infinite in both directions.

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taejo
Turing machines have may have infinite memory, but they can also only write
one step per cell. So a polynomial-time TM can't use superpolynomial memory.

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mion
The best intuition I've read that P = NP can't possibly turn out to be true,
is that if it were, you could write a piece of music as easily as you could
appreciate it.

Also, I can't imagine the answer to something as fundamental as this coming
out of a hacky solution. There's probably a more elegant, natural way to prove
it. And by natural I mean maybe they should start looking outside Turing's
theory.

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hansbo
I've read that one too, but I don't particularly like it. P=NP implies only
that all problems which can be verified in polynomial time can also be solved
in polynomial time, not necessarily that it can be solved as quickly, nor that
it can be solved easily.

Perhaps writing a piece of music is also done in polynomial time, but it
requires more training (more advanced algorithm)? Or, perhaps, the time
complexity is x^3 for writing, instead of x for appreciating.

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mion
Agreed, it is bit sensationalist. But what if someone proves it and then we
realize that even though it can be done in polynomial time, there's some other
constraint (like "x^N but N has to be super big") that renders the result
impractical?

I think once someone proves it, it will be obvious in hindsight as a lot of
people are just ignoring the isomorphisms in nature.

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pfortuny
I would wait until the paper has no more corrections made at least for a whole
non-summer month. Well, it looks like there were no corrections in October but
maybe he took his vacation then?

Give it some more time, I suggest.

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DanWaterworth
Can anyone comment on how credible this is. It seems to have been submitted
many times.

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this_user
Every once in a while some publishes a paper that seeks to prove that N equals
NP, but so far none were conclusive. Given that track record and the fact that
the all existing evidence points to N unequal NP, I would be very cautious
with this paper.

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petercooper
But only when N is 1 or P is 0.

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jnazario
seems like a solid argument to me for peer reviewed publications.

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simgidacav
Even if this content is quite old, the idea of linking it here in those days
is quite clever. Just tell me how many of you did not immediately think "Oh
crap, my RSA is doomed!".

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Houshalter
Cryptography? Really? Wouldn't this mean you could create absurdly intelligent
AIs and solve pretty much any optimization problem?

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doughj3
How did this go from being #3 on the front page of Hacker News to non-existent
even two or three pages back?

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elwell
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