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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His lack of proper definitions is another red flag. There are powerful tools nl today that enable to create such proofs, for example Deollaikar or HOL-light or Coq. It is only the point 4 that had claims that were clear enough to be analyzed, so for this reason, clear flaws have been found there and it is not a single flaw, but several problems.

Is the proof correct? The problem of deciding the truth of a statement in Presburger arithmetic requires even more time. But they do appear to give an obstacle to the general proof method.

Vinay can perhaps use his technology to prove a much weaker separation result, but one that is wide open. These algorithms were sought long before the concept of NP -completeness was even defined Karp’s 21 NP -complete problemsamong the first found, were all well-known existing problems at the time they were shown to be NP -complete.

To phrase it another way, consider the following excerpt from the paper describing part of the strategy Page 92, third draft:. Even the latter has not been formalized, it is no more than a hunch. The locality issue has been brought up elsewhere too, and looks to be quite an important point. I dont think my approach has some similarity with that work.

For example, the arithmetic formula is just the tree The same happens with boolean formulas. I think you exaggerate a bit. Or can it be fixed? However, there should be also a computational model-independent way to determine this number of parameters, as he claims this number is exponential for k-SAT in hard phase.

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

The 1RSB threshold is at average degree 4, there is a rigorous link between necessary local Markov chain sampling time and reconstruction on trees. A proof of the non-existence of such an algorithm is obviously much harder, which is why I assume most of the attempted proofs are long sequences of math statements instead of algorithms we could check by running.

I have followed Terence Tao ‘s blog and Tim Gowersboth of whom have reservations, but Deolalikar is sticking with his assertions and was supposedly preparing an updated response to the critics. Since the process evolving deolapikar this blog may be interesting as a social phenomenon independently of the mathematical contentsit seems important to track the publicity following from it, as is well done on in the Media section of the wiki. The cost of this is, on balance, considerable enough to be of some concern.

Could someone please provide a Physics-of-SAT for Dummies explanation of 1 clustering, 2 condensation, 3 dsolalikar However to have a monadic LFP, he has to change his structure from singletons to k-tuples, BUT this changes the Gaifman graph a lot it becomes of diameter at pn 2 so that you cannot apply Gaifman locality usefully anymore. I am also not telling anyone what they should or should not work on.

At each stage, the successor distance is doubled, so in stages we have the whole ordering. It is unclear if this leads to anywhere, but it is still interesting provided 2.

Also, your comments seem to be out of context, so it makes me deokalikar if you are just trying to market your book. She has not checked all the details, but she is quite excited about the potential. Sign up or log in Sign up using Google. The following is a lightly edited excerpt from a comment of Russell Impagliazzo:.

## Fatal Flaws in Deolalikar’s Proof?

I am eagerly deolalikxr the outcome of this, but to jump to conclusions and call this proof trash is completely disrespectful and immature. While these suggestions may be laudable in their own right, I doubt that they will do much to prevent the problem of a proof that is unlikely to work being nevertheless being taken seriously by a large number of people.

There are a number of mining software available. On the other hand, the fact that many serious people invest time on thinking about the ideas illustrated in the paper although these are not new ideasmight be a good thing overall.

The problem I worked on is still open. Yesterday I tried to supply a simple one based on his ideas as a strawman to focus the objections on some concrete target, but it looked like failing for reasons other than the ones intended. There is existential quantifier deloalikar instances which give positive answer are the solutions.

You are commenting using your Facebook account. And it is not as if one could enforce some sort of rule that badly written solutions to famous problems will not be read; if n attempt looks serious enough, people may well have to grit their teeth and plow through the bad exposition anyway, to settle the matter.

Let deolaalikar explain in more detail. In the case of 2, a large number of very strong o computer scientists and interested mathematicians are rightly compelled to pretty much drop whatever they are doing and look at this seriously NOW — or, in some xeolalikar, be compelled to make public statements as to why they are not dropping whatever they are doing to look at this seriously.

Suggestion Two The next two suggestions are due to Ken Regan. Second, without everyone being required to support and present their work carefully and rigorously, there is a bias in the review process whereby some researchers i.

I think this shifting trick of yours and Jeremiah preserves the P-nature or lack thereof of the unrestricted SAT problem, but not for the restricted SAT problem in which some of the literals are already fixed. Note that “average case behaviour” here refers to the structure of the solution space, as opposed to the difficulty of solving a random instance of the problem.

So we have an argument about Sat which it is claimed separates P and NP, but we can inject Sat into a proper subset of itself to which that argument fails to apply.

Create a free website or blog at WordPress. I do not think that this is wasted time. Finally, I realized that it is not possible to keep up the hectic pace of the last few days for much longer.

But that definitely does not imply that each stage of the induction is order independent. By reading the whole discussion, at a very high level, all separation proofs that are based on concrete definitions n; algorithms and concrete definitions of properties of problems seems like trying to lift up a heavy body while standing on it.

Blogs have brought together TCS community and crafted a coherent response to the proof and done the job. Also, the class PP is directly related to the geometry of the solution space: