Using \epsilon-bias spaces over F_2 , we show that the Remote Point Problem (RPP), introduced by Alon et al [APY09], has an NC^2 algorithm (achieving the same parameters as [APY09]). We study a generalization of the Remote Point Problem to groups: we replace F_n by G^n for an arbitrary fixed ... more >>>

We prove the existence of a poly(n,m)-time computable
pseudorandom generator which ``1/poly(n,m)-fools'' DNFs with n variables
and m terms, and has seed length O(\log^2 nm \cdot \log\log nm).
Previously, the best pseudorandom generator for depth-2 circuits had seed
length O(\log^3 nm), and was due to Bazzi (FOCS 2007).

It ... more >>>