We design a nonadaptive algorithm that, given a Boolean function $f\colon \{0,1\}^n \to \{0,1\}$ which is $\alpha$-far from monotone, makes poly$(n, 1/\alpha)$ queries and returns an estimate that, with high probability, is an $\widetilde{O}(\sqrt{n})$-approximation to the distance of $f$ to monotonicity. Furthermore, we show that for any constant $\kappa > ... more >>>

We study a new model of space-bounded computation, the {\it random-query} model. The model is based on a branching-program over input variables $x_1,\ldots,x_n$. In each time step, the branching program gets as an input a random index $i \in \{1,\ldots,n\}$, together with the input variable $x_i$ (rather than querying an ... more >>>

The problem of learning $t$-term DNF formulas (for $t = O(1)$) has been studied extensively in the PAC model since its introduction by Valiant (STOC 1984). A $t$-term DNF can be efficiently learnt using a $t$-term DNF only if $t = 1$ i.e., when it is an AND, while even ... more >>>