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 >>>

We prove new exponential monotone circuit lower bounds for detecting perfect matchings. We show that $\exp(\widetilde{\Omega}(n^{1/2}))$ gates are required to detect bipartite perfect matchings in $n$-vertex graphs. Our lower bounds are based on a new spread matching lemma.

more >>>