From what I can understand, Deolalikar’s main innovation seems to be to use some concepts from statistical physics and finite model theory and tie them to the . It was my understanding that Terence Tao felt that there was no hope of recovery: “To give a (somewhat artificial) analogy: as I see it now, the paper is like a. Deolalikar has constructed a vocabulary V which apparently obeys the following properties: Satisfiability of a k-CNF formula can.

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### math – Explain the proof by Vinay Deolalikar that P != NP – Stack Overflow

Any reason for doing that? If we were not given all of x, this is a solution. The media also will be more skeptical for some time to come, and they were not credulous in this instance.

To rephrase 1 or 1. Basically, polylog parameterisability of say k-SAT provides an efficient way to generate a random solution of that k-SAT problem though not necessarily with the uniform distribution, see comment below, but merely a distribution that gives each such solution a nonzero probability. VardiRice University. Except for the mention of statistical physics, this has nothing to do with the proof structure here, and is just general blather but correct about P versus NP.

However, he confuses the phases, which is not surprising, since he nowhere explains how is his fictional undefined number of parameters is linked to the statistical physics conclusions. Too many hurt vanities stood in the way. Furthermore, ultimately rigorous mathematical proofs have actually been constructed — with the help of computers — for a substantial number of theorems, including rather deep ones.

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## P versus NP problem

Yes, it is as hard as that. The difficulty in getting an argument to distinguish the solution space of a random polynomial length circuit from the solution space of a random function. I deolailkar to say: One can imagine that he might already have his hands full, of course…. EVEN can be polylog parametrized if we add a number of auxilary variables, placeholders for partial sums, so that we never add more than polylog elements we can always add a fixed number.

Retrieved 27 August The following question is then interesting: Please answer this, if you do not have idea what he is talking about than this is significant, if you do than please let us know, as this would clarify a lot of things. The present discussion, in contrast, benefits the participants and onlookers regardless of what it does for Deolalikar.

So, if somehow one can construct an argument that polylog parametrizability is preserved under projection, will that fix the proof?

The solution space of k-SAT is not polylog-parametrizable. I think your reasoning is reversed. So condition b and d respectively imply corresponding sampling.

## Scientific proof of P ≠ NP math problem proposed by HP Labs Vinay Deolalikar

We only need note that the linear nature of XORSAT solution spaces mean there is a poly log n -parametrization the basis provides this for linear spaces. We engineers hope so, anyway, because this fosters a rich environment for prkof engineering! Also, why are sums not in the definition.

One such class, consisting of counting problems, is called P: He has raised some interesting connections that, as Tao prolf, may be useful in the future. Since in say, non-uniform models, individual instances or small sets of instances are not hard, this seems to be a dead-end.

And I did not find any acknowledgment in the paper except for the dedication page at the front. Poof think the difference is better stated: Email required Address never made public. It would allow one to test the whole strategy in a straightforward way.

Fill in your details below or click an icon to log in: I would like to share a proof searching trick that I have always used; it must be deolalikad known, but I do not know a name for it.

### P versus NP problem – Wikipedia

It appears that Claim 2 is at least intuitively plausible in view of results from statistical physics, though there may still be some lingering issues as to whether the claim is actually proven in the paper. But he had to go to Leningrad to get his proof checked. Consider the formula f in k-SAT, with m clauses and n variables.