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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Think of the difference as winning at chess from starting position, and winning at every winnable position. It does not capture P. I just did a brief check of the typos collected on profo wiki for the second draft, and unfortunately they are mostly still present in the third draft.

On the other side, and in comparison, the attention this guy is getting is far from what it is worth. For example, it is possible that SAT requires exponential time in the worst case, but that almost all randomly selected instances of it are efficiently solvable. If you would like a non-hand-waving comment, here goes. So, the manuscript might lack the pure math rigor.

Scientific proof of “P ≠ NP” math problem proposed by HP Labs’ Vinay Deolalikar

One should always try both directions of every problem. Actually, you need a pseudorandom generator that builds for each n a pseudorandom circuit, and then the R x,y predicate asks for a whatever function in n x if there is a whatever function in n long y for which the output of the circuit is 1.

Then again, we do not know what is his number of parameters, and what are distributions that he parametrizes. Mr Lipton, i would like to comment on the principle of proof you stated above.

The languages in the polynomial hierarchyPHcorrespond to all of second-order logic. The high level is always of first importance, because it is next to impossible to construct a fully detailed proof of something interesting without a good understanding at the high level. It is plausible that this function is pseudorandom enough that it is indistinguishable from a random function [math]g: Also, one other source of objection was the model theory aspect, and especially the detailed critique provided by Steven Lindell see the wiki.


Several of the posts were written jointly with Ken Regan. In fact, I see 2 as less problematic. It is seriously harmful to the TCS community in many ways.

P versus NP problem – Wikipedia

It seems only harder to prove tight polynomial lower bounds on polynomial-time solvable problems. To begin with, let us use a simple notion of solution space, namely the space of all x for which the problem Q x has an affirmative answer but note that this is not the notion of solution space used in Deolalikar’s paper.

Polynomial hierarchy Exponential hierarchy Grzegorczyk hierarchy Arithmetical hierarchy Boolean hierarchy. There are many details in the various chapters. Oxford Lecture Series in Mathematics and its Applications. But this is not enough yet to establish Claim 1, because crucial properties such as monadicity are lacking; without such properties imposed, the solution spaces could in fact be quite complicated.

As for polylog parametrizalibility, I think what we may consider include the following. In general, following your 1. Define the following function of T a real parameter, temperature in stat. The problem of deciding the truth of a statement deolxlikar Presburger arithmetic requires even more time. No algorithm for any NP -complete problem is known to run in polynomial time. Personal tools Log in. This seems too sparse to have real use. For example, assuming three variables X,Y, and Z.

But they do appear pgoof give an obstacle to the general proof method.

For instance, the Boolean rpoof problem is NP -complete by the Cook—Levin theoremso any instance of any problem in NP can be transformed mechanically into an instance of the Boolean satisfiability problem in polynomial time. AI warfare is the most likely resolution of Fermi’s paradox.


Here, precise statements are missing. But a huge sub-class of prolf called “NP-complete” would be doomed. If you need education on the prevalence of string theorists as a political rather than academic bloc in universities, ISBN I think we all should thank you, Richard, for your enthusiasm in updating this blog, and your providing food for thought and a space for discussion.

However, this is not polylog parametrization if l is not of order polylog n.

The former has not been read, revised, and understood by many people over years of hard thought, while the latter has. That suggests a pragmatical line of inquiry that is very deolalika for engineers: We are interested in number of satisfied equations. Istvan, there is nothing fishy going on.

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

If there is an algorithm say a Turing machineor a computer program with unbounded memory that can produce the correct answer for drolalikar input string of length n in at most cn k steps, where k and c are constants independent of the input string, then we say that the problem can be solved in polynomial time and we prlof it in the class P.

If you actually work on the canonical structure, then you require the multiple arity relations that can take us from a tuple to its individual elements and back again. In particular, if f obeys property A, then a random function should also obey property A. Deolalikaar 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.

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