We prove a lower estimate on the increase in entropy when two copies of a conditional random variable $X | Y$, with $X$ supported on $\mathbb{Z}_q=\{0,1,\dots,q-1\}$ for prime $q$, are summed modulo $q$. Specifically, given two i.i.d. copies $(X_1,Y_1)$ and $(X_2,Y_2)$ of a pair of random variables $(X,Y)$, with $X$ ... more >>>

The Minimum Circuit Size Problem (MCSP) is: given the truth table of a Boolean function $f$ and a size parameter $k$, is the circuit complexity of $f$ at most $k$? This is the definitive problem of circuit synthesis, and it has been studied since the 1950s. Unlike many problems of ... more >>>

The VP versus VNP question, introduced by Valiant, is probably the most important open question in algebraic complexity theory. Thanks to completeness results, a variant of this question, VBP versus VNP, can be succinctly restated as asking whether the permanent of a generic matrix can be written as a determinant ... more >>>