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Pseudorandom Generators, Measure Theory, and Natural Proofs
, 1995
"... We prove that if strong pseudorandom number generators exist, then the class of languages that have polynomialsized circuits (P/poly) is not measurable within exponential time, in terms of the resourcebounded measure theory of Lutz. We prove our result by showing that if P/poly has measure zero in ..."
Abstract

Cited by 32 (4 self)
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We prove that if strong pseudorandom number generators exist, then the class of languages that have polynomialsized circuits (P/poly) is not measurable within exponential time, in terms of the resourcebounded measure theory of Lutz. We prove our result by showing that if P/poly has measure zero in exponential time, then there is a natural proof against P/poly, in the terminology of Razborov and Rudich [25]. We also provide a partial converse of this result.
The density of weakly complete problems under adaptive reductions
 SIAM Journal on Computing
"... Given a real number <1, every language that is weakly P n =2;Thard for E or weakly P n;Thard for E2 is shown to be exponentially dense. This simultaneously strengthens results of Lutz and Mayordomo(1994) and Fu(1995). 1 ..."
Abstract

Cited by 5 (1 self)
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Given a real number <1, every language that is weakly P n =2;Thard for E or weakly P n;Thard for E2 is shown to be exponentially dense. This simultaneously strengthens results of Lutz and Mayordomo(1994) and Fu(1995). 1