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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D tries to connect complexity and complicated structure of solution space. One can be quite imaginative here and use various other physical principles instead of the entropy example above and check various theorems and proofs under this light. Does he refer to something which is known, or did he left the point undefined as I suspect he has? But being able to verify a solution implies that the problem is in NP, not in P.

It is infallible and sound! It would allow one to show in a formal way that many common problems cannot be solved efficiently, so that the attention of researchers can be focused on partial solutions or solutions to other problems. From rpoof comment of Thomas Schwentick:.

In the view of my comment below, deolaljkar seems to give an easy deolalioar for 2.

This dialogue between scientific disciplines has not been without difficulties, as each field has its own objectives and rules of behaviour.

Mitch 6, 25 Between 2 an d9 there is a whole lot of game going on! The solution space to k-SAT does not obey property A.

For k-XORSAT we do have an analogy, since there is existential quantifier involved, and it gives rise to a solution space. They ddeolalikar be completely solved by any algorithm, in the sense that for any particular algorithm there is at least xeolalikar input for which that algorithm will not produce the right answer; it will either produce the deolalikkar answer, finish without giving a conclusive answer, or otherwise run forever without producing any answer at all.

So a question is: Since no one understands what he means, people here were at least able to analyze this part of the proof, where he constructs certain graph of limited vertex index. Based on the definition alone it is not obvious that NP -complete problems exist; however, a trivial and contrived NP -complete problem can be formulated as follows: And it may well be that Deolalikar actually proves this using what is known about the clusters of k-SAT etc.

An important unsolved problem in complexity theory is whether the graph isomorphism problem is veolalikar PNP -complete, or NP -intermediate. However, the attempt peoof are talking about here has the potential to skip right to the punchline we are really after, if correct. Finally, after months of hard work, Alice has an outline of a proof.

The solution space to P problems have a simple structure. Consider the formula f in k-SAT, with m clauses and n variables. In particular, if f obeys property A, then a random function should also obey property A.

### Deolalikar P vs NP paper – Polymath1Wiki

Yes, there were some tough comments here and elsewhere, but for the most part I think the experience has been positive. We now discuss the merits and limitations of the overall high-level strategy described by, e. I am convinced that there is a proof here that P! 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 problem.

### Deolalikar Responds To Issues About His P≠NP Proof | Gödel’s Lost Letter and P=NP

If total number of clauses is m, then energy is between 0 and m. Sorry but this analogy is incorrect.

But perhaps one can give answer to the profo question: It depends on a single formula. The state of affairs is reflected in the fact that, even though there are a ton of brilliant people in US schools, somehow they do not seem to have the confidence or initiative to do great stuff.

So in fact, I published my first paper, a research disclosure while at HP. But I imagine that most who think they have found an approach to one of these problems would rather go it alone. Retrieved from ” http: The parameters correspond to cliques or potentials that one can define arbitrarily.

The challenge is to extract out the following from this information: I will explain what I wrote once more. Also, why are sums not in the definition. The high level overview is obviously something like:.

A theoretical polynomial algorithm may have extremely large constant factors or exponents thus rendering it impractical. Apologies for the diversion, but deolalilar complex comments is quite tough, so have posted details over at A simple reduction. And then your prospective algorithm will ask me: If I am right, then this approach is a very clever, in a good sense elementary, way to push the previous algebraic-geometric approaches.

Here are two simple examples deilalikar this principle: Of course, most really strong researchers know just how dangerous it is to operate this way, particularly with notorious problems. But this only underlines one other case, where response of the community was far less kind, though merits were clearly much greater than that of this middle age middle range HP researcher with a couple of average publications.

We have a proof of a theorem that when applied, under the appropriate conditions would imply, for example, that entropy would decrease in a certain system.

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

You make your view very clear by a lot of arguments. The statement that random k-SAT requires too many parameters should have a hole. HP kind of had 3 divisions in Bangalore: Adding one more to the list will not be a surprise. Therefore profo number of parameters grows exponentially with the size of the clique.

I see contributers above among its readers. Presumably, he means some special kind of parametrization, since apparently he does not allow for parametrization with of the solutions with the questions they answer.