OK, a little extra, and speaking very informally ...
I've skimmed the first couple of pages, and in essence he seems to be setting up to show that a circuit that's sufficiently complex to solve the clique problem will have to have an exponential number of components. That would imply that any algorithm to solve "Clique" would be exponential, hence super-polynomial, hence not in "P".
Problem is, others have proven that there are technical barriers to this approach, and I see no hint of the author explicitly saying why his approach avoids these problems.
For more about this concern, see points 1, 4, and 6 in this very accessible post:
The PowerPoint talk "Has There Been Progress on the P vs. NP Question?" lunk to at the end of that post (before the comments) is a very good, accessible overview and is an excellent starting point to highlight what you need to follow up on.
Wikipedia's section on why the proof of P=NP or P!=NP is likely to be hard is also useful reading:
I've skimmed the first couple of pages, and in essence he seems to be setting up to show that a circuit that's sufficiently complex to solve the clique problem will have to have an exponential number of components. That would imply that any algorithm to solve "Clique" would be exponential, hence super-polynomial, hence not in "P".
Problem is, others have proven that there are technical barriers to this approach, and I see no hint of the author explicitly saying why his approach avoids these problems.
For more about this concern, see points 1, 4, and 6 in this very accessible post:
http://www.scottaaronson.com/blog/?p=458
The PowerPoint talk "Has There Been Progress on the P vs. NP Question?" lunk to at the end of that post (before the comments) is a very good, accessible overview and is an excellent starting point to highlight what you need to follow up on.
Wikipedia's section on why the proof of P=NP or P!=NP is likely to be hard is also useful reading:
http://en.wikipedia.org/wiki/P_versus_NP_problem#Results_abo...