For a universal constant $\alpha > 0$, we prove size lower bounds of $2^{\alpha N}$ for computing an explicit monotone function in NP in the following models of computation: monotone formulas, monotone switching networks, monotone span programs, and monotone comparator circuits, where $N$ is the number of variables of the ... more >>>

In "An Almost Cubic Lower Bound for $\sum\prod\sum$ circuits in VP", [BLS16] present an infinite family of polynomials, $\{P_n\}_{n \in \mathbb{Z}^+}$, with $P_n$
on $N = \Theta(n polylog(n))$
variables with degree $N$ being in VP such that every
$\sum\prod\sum$ circuit computing $P_n$ is of size $\Omega\big(\frac{N^3}{2^{\sqrt{\log N}}}\big)$.
We ... more >>>

The advent of data science has spurred interest in estimating properties of discrete distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most attention, with each property estimated using a different technique and often intricate analysis tools.

Motivated by the ... more >>>