The class $FORMULA[s] \circ \mathcal{G}$ consists of Boolean functions computable by size-$s$ de Morgan formulas whose leaves are any Boolean functions from a class $\mathcal{G}$. We give lower bounds and (SAT, Learning, and PRG) algorithms for $FORMULA[n^{1.99}]\circ \mathcal{G}$, for classes $\mathcal{G}$ of functions with low communication complexity. Let $R^{(k)}(\mathcal{G})$ be ... more >>>
We propose a simple variant of the INW pseudo-random generator, where blocks have varying lengths, and prove it gives the same parameters as the more complicated construction of Armoni's PRG. This shows there is no need for the specialized PRGs of Nisan and Zuckerman and Armoni, and they can be ... more >>>
In this work, we combine the work of Chen et. al and Hoza to obtain a WPRG against regular ROBPs
with seed length $O(\log t \cdot (\log w+\sqrt{\log \frac{1}{\epsilon}}+\log\log t) + \log \frac {1}{\epsilon})$, improving
upon previous construction which also include some additional lower order terms.
