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 >>>

We initiate the study of the tradeoff between the {\em length} of a
probabilistically checkable proof of proximity (PCPP) and the
maximal {\em soundness} that can be guaranteed by a $3$-query
verifier with oracle access to the proof. Our main observation is
that a verifier limited to querying a short ... more >>>