Tuesday, May 15, 2007

This year's Godel Prize

The 2007 Godel Prize goes to Alexander Razborov and Steven Rudich for their paper, "Natural Proofs" (JCSS Vol 55. No. 1, 1997).

I'd like to think that Godel himself would have approved of this particular award, given the mind-bending nature of the Razborov-Rudich result. To use Scott Aaronson's loose formulation, their result can be summarized as
The reason P != NP is so difficult to prove is that P != NP
Computational Complexity (is it the Lance-blog, or the Bill-blog, or a Lance-post in the Bill-blog, or a Lance-post in the Bill-blog-that-used-to-be-Lance's-blog?), and In Theory have detailed explanations of the RR result, and do a far better job than I can do here.

To put it in perspective, the Razborov-Rudich result is a "meta-result": it says that no proofs of a certain kind (the so-called natural proofs) can be used to prove P != NP, unless other hardness assumptions break to begin with. Another example of a meta-result is the (older) result by Baker, Gill and Solovay that the P=NP question does not relativize (i.e cannot be proved using methods that hold under the application of oracles).

Razborov-Rudich really put a shaft in methods for separating P and NP (see this pessimistic post by Lance). If only all the P vs NP cranks actually tried examining proofs like this before wasting all those valuable bits on comp.theory ;)

(HT: [LB, UB] and Process Algebra Diary).
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