We establish new correlation bounds and pseudorandom generators for a collection of computation models. These models are all natural generalizations of structured low-degree $F_2$-polynomials that we did not have correlation bounds for before. In particular:

1. We construct a PRG for width-2 $poly(n)$-length branching programs which read $d$ bits ... more >>>

A secret-sharing scheme allows the distribution of a secret $s$ among $n$ parties, such that only certain predefined “authorized” sets of parties can reconstruct the secret, while all other “unauthorized” sets learn nothing about $s$. The collection of authorized/unauthorized sets is defined by a monotone function $f: \{0,1\}^n \rightarrow \{0,1\}$. ... more >>>