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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## Deolalikar Responds To Issues About His P≠NP Proof

No efficient integer factorization algorithm is known, and this fact forms the basis of several modern cryptographic systems, such as the RSA algorithm. Being attached to a speculation is not a good guide to research planning.

In real life, even an exponent of 4 or 5 is usually hard to make practical use of. 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.

The division I worked for, Software had quite an emphasis on innovation. I think that c is basically equivalent to the condition that there is a poly-time randomized algorithm that samples a solution with respect to the uniform distribution on the solution poof.

But think about the extremely small possibility of some math-amateur giving the correct proof for some really big problem…Riemann, Goldbach, Collatz, whatever…how easy would it be, to see if such a proof is pure nonsense probably minutes to hours but how tremendous would be its impact, if it would be correct, and how equally tremendous would be the loss, if this yet unknown guy does not dare to publish anything, because professional mathematicians tend to be somewhat uncomfortable and unpleasant when dealing with some semi-professionals work?

Also, I realised that the distributions here were not quite uniform as claimed above; see my comment below. I am planning for the future. We are already giving significant liberties to the author in assuming that such a space does exist, independently of a verifier.

Thousands of other problems seem similar, in that they are fast to check but slow to solve. I suggest that someone in the group email him and ask for his remarks and permission to add them to the wiki.

It seems that a separation proof for two adyacent complexity classes needs abstraction at least from concrete properties or from concrete algorithms. Ryan, The solution set of 2SAT is closed under median closed; take any three solutions to a 2SAT formula and their component wise median will also be a solution.

Perhaps the deolalikaf question is what did we learn from the last few hectic days.

The second is much more difficult. The starting point here is the Immerman-Vardi theorem, which shows that the solution space to P problems can be described using the first-order logic of Propf.

Also, if we have a distribution with polynomial number of parameters, then we can sample it in polynomial number of steps though this is on a circuit level. 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. So condition b deolalikkar d respectively imply corresponding sampling. Let y1,…,yq be binary random variables in a projection-polylog-parameterisation for f, where q-n variables among y1,…,yq are auxiliary ones.

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

And if I am rude, and will not answer, and might happen that I did not transform it, your prospective algorithm will be in trouble. His lack of proper definitions is another red flag. 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.

Applied research should be funded by corporations, and incorporate the basic results from government funded research. Retrieved 1 May It remains to be seen if there is anything to be gained from the current paper, assuming a similar failure — which very strongly seems to be the case. She thinks she has her proof.

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. Intuitively, spaces with property A have a very simple structure. Is anyone trying to prove that P!

Perhaps this event will finally break down that barrier — and I suspect that will be its enduring value to both the Physics and the Industrial Mathematics communities. So it would be for HP Labs Bangalore! 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: I think this explicates the Claim 1 side of things pretty well.

He has raised some interesting connections that, as Tao says, may be useful in the future.

Lang asked Bernard to tell him exactly which properties of the zeta function he had used deolailkar his proof. Over the last few years, several research areas have witnessed important progress through the unexpected collaboration of statistical physicists, computer scientists, and information theorists.

My intuition works the following way: Then, all such languages in P can be expressed in first-order logic with the addition of a suitable least fixed-point combinator. Perhaps he thought that details can be fixed, and his vague ideas here we have more a sketch or a strategy can be made precise.

The attempts by Terry Tao and others to see if the proof strategy will work at all are very honorable indeed. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Formally, a solution space obeys property A if it can be efficiently defined by a special family of LFP formulae, the monadic formulae and there may be additional requirements as well, such as those relating to order.

All possible algorithms working on possible solutions