Dispersers, deterministic amplification, and weak random sources

We show how to simulate any BPP algorithm in polynomial time using a weak random source of min-entropy r/sup /spl gamma// for any /spl gamma/>0. This follows from a more general result about sampling with weak random sources. Our result matches an ...

We construct an explicit disperser for affine sources over $\F_2^n$ with entropy $k=2^{\log^{0.9} n}=n^{o(1)}$. This is a polynomial time computable function $D:\F_2^n \ar \B$ such that for every affine space $V$ of $\F_2^n$ that has dimension at least $...

We show that the size of the smallest depth-two $N$-superconcentrator is $$ \Theta(N\log^2 N/\log\log N). $$ Before this work, optimal bounds were known for all depths except two. For the upper bound, we build superconcentrators by putting together a ...