My Favorite Ten Complexity Theorems of the Past Decade II：我最喜欢的十种复杂性定理在过去的十年中II.ppt

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My Favorite Ten Complexity Theorems of the Past Decade II：我最喜欢的十种复杂性定理在过去的十年中II.ppt

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My Favorite Ten Complexity Theorems of the Past Decade II：我最喜欢的十种复杂性定理在过去的十年中II

My Favorite Ten Complexity Theoremsof the Past Decade II Lance FortnowUniversity of Chicago Madras, December 1994 Invited Talk at FSTTCS ’04 My Favorite Ten Complexity Theorems of the Past Decade Why? Ten years as a complexity theorist. Looking back at the best theorems during that time. Computational complexity theory continually produces great work. Use as springboard to talk about research areas in complexity theory. Let’s recap the favorite theorems from 1985-1994. Favorite Theorems 1985-94Favorite Theorem 1 Bounded-width Branching Programs Equivalent to Boolean Formula Barrington 1989 Favorite Theorems 1985-94Favorite Theorem 2 Parity requires 2?(n1/d) gates for circuits of depth d. H?stad 1989 Favorite Theorems 1985-94Favorite Theorem 3 Clique requires exponentially large monotone circuits. Razborov 1985 Favorite Theorems 1985-94Favorite Theorem 4 Nondeterministic Space is Closed Under Complement Immerman 1988 and Szelepcsényi 1988 Favorite Theorems 1985-94Favorite Theorem 5 Pseudorandom Functions can be constructed from any one-way function. Impagliazzo-Levin-Luby 1989 H?stad-Impagliazzo-Levin-Luby 1999 Favorite Theorems 1985-94Favorite Theorem 6 There are no sparse sets hard for NP via bounded truth-table reductions unless P = NP Ogihara-Watanabe 1991 Favorite Theorems 1985-94Favorite Theorem 7 A pseudorandom generator with seed of length O(s2(n)) that looks random to any algorithm using s(n) space. Nisan 1992 Favorite Theorems 1985-94Favorite Theorem 8 Every language in the polynomial-time hierarchy is reducible to the permanent. Toda 1991 Favorite Theorems 1985-94Favorite Theorem 9 PP is closed under intersection. Beigel-Reingold-Spielman 1994 Favorite Theorems 1985-94Favorite Theorem 10 Every language in NP has a probabilistically checkable proof that can be verified with O(log n) random bits and a constant number of queries. Arora-Lund-Motwani-Sudan-Szegedy 1992 Kyoto, March 2005 Invited Talk at NHC Conference. Twenty years in field. My Favo