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FOCS

2008

IEEE

2008

IEEE

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.) ...

Added |
29 May 2010 |

Updated |
29 May 2010 |

Type |
Conference |

Year |
2008 |

Where |
FOCS |

Authors |
Timothy Y. Chow |

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