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FOCS
2008
IEEE

Almost-Natural Proofs

14 years 1 months ago
Almost-Natural Proofs
Razborov and Rudich have shown that so-called natural proofs are not useful for separating P from NP unless hard pseudorandom number generators do not exist. This famous result is widely regarded as a serious barrier to proving strong lower bounds in circuit complexity theory. By definition, a natural combinatorial property satisfies two conditions, constructivity and largeness. Our main result is that if the largeness condition is weakened slightly, then not only does the Razborov–Rudich proof break down, but such “almost-natural” (and useful) properties provably exist. Specifically, under the same pseudorandomness assumption that Razborov and Rudich make, a simple, explicit property that we call discrimination suffices to separate P/poly from NP; discrimination is nearly linear-time computable and almost large, having density 2−q(n) where q is a quasi-polynomial function. (This is a slightly stronger result than the one announced in the FOCS 2008 extended of this paper.) ...
Timothy Y. Chow
Added 29 May 2010
Updated 29 May 2010
Type Conference
Year 2008
Where FOCS
Authors Timothy Y. Chow
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