We prove that the sum of $d$ small-bias generators $L
: \F^s \to \F^n$ fools degree-$d$ polynomials in $n$
variables over a prime field $\F$, for any fixed
degree $d$ and field $\F$, including $\F = \F_2 =
{0,1}$.

Our result improves on both the work by Bogdanov and
Viola ... more >>>

We revisit the connection between boosting algorithms and hard-core set constructions discovered by Klivans and Servedio. We present a boosting algorithm with a certain smoothness property that is necessary for hard-core set constructions: the distributions it generates do not put too much weight on any single example. We then use ... more >>>

Hardness amplification is the fundamental task of
converting a $\delta$-hard function $f : {0,1}^n ->
{0,1}$ into a $(1/2-\eps)$-hard function $Amp(f)$,
where $f$ is $\gamma$-hard if small circuits fail to
compute $f$ on at least a $\gamma$ fraction of the
inputs. Typically, $\eps,\delta$ are small (and
$\delta=2^{-k}$ captures the case ... more >>>