We extend the recent work of Reis and Rothvoss on sparsifying sums of $\ell_1$ norms to the more general task of sparsifying (Minkowski) sums of centrally symmetric, convex sets. As our main result, we prove that for any $\varepsilon > 0$ and centrally symmetric, convex sets $C_1, \ldots, C_m\subseteq\mathbb R^n$ ... more >>>

A branching program is a labeled directed graph that, on each input $x$, induces an $s$-$t$ connectivity instance. Nondeterministic branching programs (NBPs) accept an input if there exists an accepting path, whereas parity branching programs ($\oplus$BPs) accept if the number of accepting paths is odd. Wigderson (Structure in Complexity Theory ... more >>>

We study pseudorandom bit generators for Boolean linear sums modulo a fixed
integer $M$. A distribution $X\in\{0,1\}^n$ $\varepsilon$-fools these tests if, for
every $a\in\mathbb{Z}_M^n$, the distribution of
\[
\sum_{i=1}^n a_iX_i \pmod M
\]
is $\varepsilon$-close in statistical distance to the corresponding distribution
under independent uniform bits.

Lovett, Reingold, Trevisan, ... more >>>