P ≠ NP
August 7th, 2010, 8:21 pm UTC by GregAn email I was recently forwarded (a couple of steps removed) from Vinay Deolalikar from HP Labs:
Dear Fellow Researchers,
I am pleased to announce a proof that P is not equal to NP, which is attached in 10pt and 12pt fonts.
The proof required the piecing together of principles from multiple areas within mathematics. The major effort in constructing this proof was uncovering a chain of conceptual links between various fields and viewing them through a common lens. Second to this were the technical hurdles faced at each stage in the proof.
This work builds upon fundamental contributions many esteemed researchers have made to their fields. In the presentation of this paper, it was my intention to provide the reader with an understanding of the global framework for this proof. Technical and computational details within chapters were minimized as much as possible.
This work was pursued independently of my duties as a HP Labs researcher, and without the knowledge of others. I made several unsuccessful attempts these past two years trying other combinations of ideas before I began this work.
Comments and suggestions for improvements to the paper are highly welcomed.
The paper is about 100 pages, and looks serious (but being a decade away from last thinking about complexity, I am unable to give any more useful evaluation than that). I’ll refrain from posting the paper itself.
Deciding P ≠ NP is a Millennium Prize Problem and I don’t think I’d get much argument to say it is the biggest open problem in computing science.
Update: I see someone else has uploaded the paper. I should point out that in the email thread I got, Stephen Cook said “This appears to be a relatively serious claim to have solved P vs NP.
via gregbaker.ca
Would be stunning if the proof is validated. Although it wont radically alter out day to day as much as a P=NP result would have (Q mass panic since every encryption system out there would be breakable - and vast amounts of computational problems would become soluble!), it's still a big deal.
The synopsis of the proof sounds intuitive though I have no idea on many of the details. I like the idea of interconnectedness at great distance in the solution space causing the breakdown in linear algorithms. Seems like the right kind of idea that might also help people figure out if quantum computing can ever bridge this gap and how it might do so.
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