Live data from Hacker News

P ≠ NP

scribd.com

41–50 of 233 posts

Re: P ≠ NP

#41
Several points on the question of whether the proof is likely to be correct:

* As far as I know this paper wasn't circulated for informal peer review before being made public; I heard no talk on the grapevine. (Edit: apparently it was circulated and someone other than the author made it public.)

* Therefore a proper assessment is going to take a while. Until then we can only speculate :-)

* While the crank attempts at P =? NP are statistically much more common (http://news.ycombinator.com/item?id=347295), this isn't one of them. The author is a legit computer scientist: http://www.hpl.hp.com/personal/Vinay_Deolalikar/

* On the other hand he hasn't published much on complexity theory and isn't known in that community. Which is weird but not necessarily a red flag.

* Looking at his papers, it's possible he's been working on this for about 5+ years -- he has two threads of research, basic and industrial, and the former line of publications dried up around 2004.

* On the other hand I don't think anyone knew he was working on this. The only known serious effort was by Ketan Mulmuley at U Chicago.

* It has been known that the straightforward combinatorial approaches to P =? NP aren't going to work, and therefore something out of left field was required (http://web.cs.wpi.edu/~gsarkozy/3133/p78-fortnow.pdf). Mulmuley's plan of attack involved algebraic geometry.

* This paper uses statistical physics. This approach doesn't seem to have been talked about much in the community; I found only one blog comment http://rjlipton.wordpress.com/2009/04/27/how-to-solve-pnp/#c... which mentions the survey propagation algorithm. (Deolalikar's paper also talks about it tangentially.)

* If the statistical physics method used here is powerful enough to resolve P != NP, then there's a good chance it is powerful enough to have led to many smaller results before the author was able to nail the big one. It's a little weird we haven't heard anything about that earlier.

* Finally, since the author is using physics-based methods, there's the possibility that he is using something that's a "theorem" in physics even though it is technically only a conjecture and hasn't actually been proven. Physicists are notorious for brushing technicalities under the rug. It would be very unlikely that the author didn't realize that, but still worth mentioning.

* If that is indeed what happened here, but the rest of the proof holds up, then we would be left with a reduction from P != NP to a physics conjecture, which could be very interesting but not ground breaking.

Conclusion: overall, it certainly looks superficially legit. But in non peer reviewed solutions of open problems there's always a high chance that there's a bug, which might or might not be fixable. Even Andrew Wiles's first attempt at FLT had one. So I wouldn't get too excited yet.

Re: P ≠ NP

#43
post #16
post #4

WOW. Assuming this isn't a hoax, and the proof holds up, this is front-page news kind of big deal. As I recall, this has way more real-world practical usage than the Fermats Last Theorem proof. Read the "Consequences of Proof" section in the Wikipedia article here: http://en.wikipedia.org/wiki/P_versus_NP_problem [edit] The responses below are correct. Proving P=NP means the world gets turned upside down. P != NP is…

a) Complicated academic proofs take (and should take) months if not years to verify, and will only be "front-page news" after verification. This is hardly the first unverified proof of the [edit: possible (in)]equality of P and NP. b) The practical consequences of P=NP are immense. The practical consequences of P≠NP are that we can stop looking for computational unicorns and fairies. We have for some time thought tha…

> This is hardly the first unverified proof of the equality of P and NP.

in 'a' above didn't you mean to write 'inequality of P and NP' ?

Re: P ≠ NP

#44
post #3

102 pages via one of the most annoying PDF readers on the planet? No thanks. There are good, free, PDF readers for every major operating system and for every major mobile device. I wish people would just link directly to PDFs.

I wish people would just link directly to PDFs.

Agreed, and the benefit of doing that is you get a Scribd link come up on HN too :-)

Re: P ≠ NP

#45
post #37

The paper's origin was that the author mailed a copy for review to some very high-level folks in the field (Cook, Mazirani, Sipser, etc). Here's the mail: Date: Fri, 6 Aug 2010 21:28:39 +0000 Subject: Proof announcement: P is not equal to NP Dear Fellow Researchers, I am pleased to announce a proof that P is not equal to NP, which is attached in 10pt and 12pt fonts. The proof required the piecing together of principl…

If this proof is up for review, that would mean there could be errors in it, right?

As another commenter mentioned, it will likely take months or even years to verify.

Re: P ≠ NP

#46

Earlier quoted context omitted.

I hear this statement frequently when P = NP is discussed, but as someone not involved in computer science I have a hard time understanding it. Could you explain what some of those consequences be? Does P = NP really need to be proved to achieve those practical consequences? Can't it just be assumed to be true and then see what the result is?

Intuitively: NP questions take a long time to answer. P questions take much less time. The statement "P = NP" means that any NP question can be transformed into a P question. Answering the P question gives you an answer to the NP question. So, if P = NP, then we can answer questions that we thought were slow, much more quickly than we would have thought possible. Proving P = NP would (presumably) give you that method…

Yeah, the common complaint against "P=NP would break cryptography" is "but what if the polynomial algorithm for (say) SAT is n^10000?". That is not very likely, in my opinion. Even though "polynomial" is not equivalent to "efficient", in practice all problems that have a polynomial algorithm also have an efficient algorithm.

Re: P ≠ NP

#47
post #37

The paper's origin was that the author mailed a copy for review to some very high-level folks in the field (Cook, Mazirani, Sipser, etc). Here's the mail: Date: Fri, 6 Aug 2010 21:28:39 +0000 Subject: Proof announcement: P is not equal to NP Dear Fellow Researchers, I am pleased to announce a proof that P is not equal to NP, which is attached in 10pt and 12pt fonts. The proof required the piecing together of principl…

I'm curious - how do you know this mail was sent to the aforementioned people in complexity theory?

Re: P ≠ NP

#49

Several points on the question of whether the proof is likely to be correct: * As far as I know this paper wasn't circulated for informal peer review before being made public; I heard no talk on the grapevine. (Edit: apparently it was circulated and someone other than the author made it public.) * Therefore a proper assessment is going to take a while. Until then we can only speculate :-) * While the crank attempts a…

Thanks. I think you nailed just about every one of my concerns about this paper. I've only read the introduction, but if the rest of the paper can deliver what the first 16 pages promise, it looks like a winner to me. I suspect that if there's some problem hidden somewhere, it's a case of showing that some property or another of k-SAT holds almost always in the limit, but not being able to show that any specific instance of k-SAT has that property. And, if that's the case, it's probably a symptom of relying on one of those physics "theorems" you've mentioned. Color me cautiously optimistic, here.

Re: P ≠ NP

#50
post #40

I skimmed through the synopsis but this philosophical statement baffles me (although obviously it is unrelated to the validity or invalidity of the proof): "The implications of [P ?= NP] on the general philosophical question of [..] whether human creativity can be automated, would be profound." How so? If P!=NP, that is obeyed by the brain as much as by computers and whatever trick our brains does to be creative desp…

While I agree P != NP doesn't say anything about human creativity, but the reason it can't be automated is, I think, different: creativity is closely tied to libido and biological evolution, which in turn can't be simulated in machines in full.
Post reply on HN