Vinay Deolalikar is standing by his {\mathsf{P} \neq \mathsf{NP}} claim and proof. He and I have been exchanging e-mails, and as noted in the. Possible fatal flaws in the finite model part of Deolalikar’s proof Neil Immerman is one of the world’s experts on Finite Model Theory. He used. An update on the P not equal to NP proof Timothy Gowers, Gil Kalai, Ken Regan, Terence Tao, and Suresh Venkatasubramanian are some of.

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It seems quite possible, even more likely than not, that AI will be developed. I was wondering if anyone can suggest some introductory references on finite model theory and the concepts discussed in section 3 of the paper.

## Fatal Flaws in Deolalikar’s Proof?

Several of the posts were written jointly with Ken Regan. However, this is so far off topic that anyone who wished to discuss it may contact me via my dated but still functional LinkedIn page, linked to my name.

To establish this claim, Deolalikar employs tools from finite model theory together with some other methods revolving around deo,alikar. The empirical average-case complexity time vs.

Such proof would have to cover all classes of approaches … like continuous global optimization. Excerpted from this comment of Ken Regan.

Statistical physics methods, that are widely believed exact in physics, but so far are not fully rigorous, predict many properties of the solution space. Plus he was using this as an opportunity to push his elaborate theory of Hilbert spaces of entire functions, and he became angry when people successfully simplified the proof by removing hundreds of pages of this material.

This positive correlation holds information. We must keep the tone constructive and supportive—the Group all agrees with this.

Here is my intuition. Deeolalikar completely different kingdom – numerical analysis – I don’t believe such proof could really cover?

Of course, most really strong researchers know just how dangerous it is to operate this way, particularly with notorious problems. So the characterization this paper is attempting does not seem to me to be about the right category of object. Apparently, number of parameters has to do with Gibbs potential representation and Hammersen Clifford theorem.

So if D has lemma of the form:. Deolalimar want to take the opportunity to congratulate the CS and math community for showing on this blog that it is able to conduct n; overall intelligent and polite public discussion about the P vs NP problem.

Can anyone point me to where this is done? If any of you think the likes of Professors Tao and Lipton would be spending their time better — presumably, on your own pet research projects — then convince them of it.

Of course, any new material should be sourced whenever possible, and remain constructive and objectively neutral; in particular, personal subjective opinions or speculations are to be avoided. Moreover, Vinay has not forced anyone to spend their time. If we believe them both to be true, then this is still a non-trivial and potentially viable strategy towards P! Nonetheless, there is increasing consensus that a common ground exists and that it can be fruitful.

### Fatal Flaws in Deolalikar’s Proof? | Gödel’s Lost Letter and P=NP

My guess is that number of parameters is somehow related to complexity of this function. Retrieved 27 August I made slight edits to make the formulas compile into LaTeX. A brief synopsis of the terms discussed can be found here. The high level overview is obviously something like: Indeed, there is quite a few works trying to characterize hard instances of search problems by the structure of their solution spaces. This is what is deolalukar now for k-SAT, when k is deolalioar enough.

Many other important problems, such as some problems in protein structure predictionare also NP -complete; [30] if these problems were efficiently solvable it could spur considerable advances in life sciences and biotechnology.

NP takes the form not EA. By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand deollaikar your continued use of the website is subject to these policies. But they do appear to give an obstacle to the general proof method.

An important unsolved problem in complexity theory is whether deolaliikar graph isomorphism problem is in PNP -complete, or NP -intermediate. Views Read Edit View history. It is entirely possible that there is some as-yet-undiscovered algorithm that determines k-SAT satisfiability simply by syntactic manipulation of the input k-SAT formulas. Gregory Perlman too was a postdoctoral researcher at top American Universities- NYU, Berkeley and Stony Brook and had developed a very good reputation as a serious scholar.

Any proof separating or equating P and NP should give us tremendous insight into computation, far more deplalikar we ever knew before.