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 >>>

We give an algorithm that with high probability properly learns random monotone t(n)-term
DNF under the uniform distribution on the Boolean cube {0, 1}^n. For any polynomially bounded function t(n) <= poly(n) the algorithm runs in time poly(n, 1/eps) and with high probability outputs an eps accurate monotone DNF ... more >>>

This paper addresses the problem of testing whether a Boolean-valued function f is a halfspace, i.e. a function of the form f(x)=sgn(w &#8901; x - &#952;). We consider halfspaces over the continuous domain R^n (endowed with the standard multivariate Gaussian distribution) as well as halfspaces over the Boolean cube {-1,1}^n ... more >>>