20100810, 01:12  #12 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×11×457 Posts 
There are some minor word changes and a ~200word paragraph added before Remark 7.8.

20100810, 01:20  #13 
Oct 2008
n00bville
1011100000_{2} Posts 
LOL  always the same unmannered Silverman behavior. Heise News Service has written that he is quite established in his field so Silverman`s statements have, as always, no serious impact on reality.

20100810, 01:28  #14  
Aug 2006
5,987 Posts 
Quote:
But if you look at his more recent posts, Silverman has softened considerably on the paper. 

20100810, 01:35  #15 
Oct 2008
n00bville
2^{5}·23 Posts 

20100810, 01:43  #16 
Einyen
Dec 2003
Denmark
2·17·101 Posts 
The author Vinay Deolalikar writes that this version is preliminary version and was not meant for the public and final version is coming soon.
http://www.hpl.hp.com/personal/Vinay_Deolalikar/ "BASIC RESEARCH Vinay Deolalikar. P is not equal to NP. 6th August, 2010 (66 pages 10pt, 102 pages 12pt). Manuscript sent on 6th August to several leading researchers in various areas. Confirmations began arriving 8th August early morning. The preliminary version made it to the web without my knowledge. I have made minor updates, here. Please note that the final version of the paper is under preparation, and is to be posted here very shortly. Stay tuned. " 
20100810, 04:53  #17  
"Lucan"
Dec 2006
England
1100101001010_{2} Posts 
Just fancy that...
(As Private Eye magazine would say):
Quote:


20100810, 07:02  #18 
"Gang aft agley"
Sep 2002
2×1,877 Posts 
Some preliminary analysis and organization by Dick Lipton and Ken Regan: http://rjlipton.wordpress.com/2010/0...p%E2%89%A0np/ . This enumerates four possible issues with the proof for ease of discussion.
Last fiddled with by only_human on 20100810 at 07:29 Reason: trimmed a bit 
20100810, 14:54  #19  
"Gang aft agley"
Sep 2002
2×1,877 Posts 
Wiki
http://michaelnielsen.org/polymath1/..._P!%3DNP_paper
Quote:


20100810, 23:19  #20  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}·1,877 Posts 
Quote:
August 10, 2010 9:50 am Serious (unfixable) problem. Vinay uses FO(LFP) as his main tool. However, I think he fails to realize that FO(LFP) , although defined using least fixed point, also contains greatest fixed points. Thus, if \mu x f(y,x) is the formula denoting least fixpont of f(y,x) under x, and \nu x f(y,x) is the formula denoting greatest fixpont of f(y,x0 undex x, then there is this triple negation rule: \neg \mu x \neg f(y, \neg x) = \nu x f(y,x). (See Kozen's paper on axiomatizing MuCalculus, or my paper with Allen Emerson on MuCalculus in FOCS 1991 titled "MuCalcus, Tree Automata and Determinacy", or just original Vardi and Immerman papers). Note that the left hand side is well defined in LFP, as x is under even number of negations from the operator \mu. Now, his whole theory of least fixed point only increasing the size of the structures falls apart. BTW, this is a usual mistake most people new to fixedpoint logics fall prey to. For example, now he has to deal with formulas of the kind \nu x (f(y, x) \and g(y, x)). His section 4.2 deals with just one least fixed point operator. where his idea is correct. But, in the next section 4.3, where he deals with complex fixed point iterations, he is just hand waving, and possibly way off. Given that he does not even mention greatest fixed points leads me to think that this is a huge (unfixable) gap. Charanjit Jutla IBM T.J. Watson 

20100811, 01:14  #21 
"Gang aft agley"
Sep 2002
2×1,877 Posts 
I was fascinated watching the developing evaluation of the paper. A preliminary consensus seems complete. Here is a blog that takes an optimistic view of this new form of peer review: http://cameronneylon.net/blog/p%E2%...fpeerreview/ Perhaps blitzread is a more apt term.
Among my peripatetic browsing about all of this I came across Leslie Valiant's theory of holographic algorithms which exponentially speed up some computations; this was very interesting to me. There is a (mod 7) operation that seems to be part of canceling a large part of the calculations  leaving a simpler system to be counted (and that by some kind of weighing). It reminded me a bit of the AKS method so simplifying a row. 
20100812, 05:11  #22 
Jun 2005
2×7^{2} Posts 

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