We study \emph{entropy flattening}: Given a circuit $\mathcal{C}_X$ implicitly describing an $n$-bit source $X$ (namely, $X$ is the output of $\mathcal{C}_X$ on a uniform random input), construct another circuit $\mathcal{C}_Y$ describing a source $Y$ such that (1) source $Y$ is nearly \emph{flat} (uniform on its support), and (2) the Shannon ... more >>>

We consider several closely related variants of PAC-learning in which false-positive and false-negative errors are treated differently. In these models we seek to guarantee a given, low rate of false-positive errors and as few false-negative errors as possible given that we meet the false-positive constraint. Bshouty and Burroughs first observed ... more >>>

Resolution over linear equations (introduced in [RT08]) emerged recently as an important object of study. This refutation system, denoted Res(lin$_R$), operates with disjunction of linear equations over a ring $R$. On the one hand, the system captures a natural ``minimal'' extension of resolution in which efficient counting can be achieved; ... more >>>