We show a new connection between the information complexity of one-way communication problems under product distributions and a relaxed notion of list-decodable codes. As a consequence, we obtain a characterization of the information complexity of one-way problems under product distributions for any error rate based on covering numbers. This generalizes ... more >>>

A function $f(x_1, ... , x_d)$, where each input is an integer from 1 to $n$ and output is a real number, is Lipschitz if changing one of the inputs by 1 changes the output by at most 1. In other words, Lipschitz functions are not very sensitive to small ... more >>>

We study local filters for two properties of functions $f:\B^d\to \mathbb{R}$: the Lipschitz property and monotonicity. A local filter with additive error $a$ is a randomized algorithm that is given black-box access to a function $f$ and a query point $x$ in the domain of $f$. Its output is a ... more >>>