We study weighted pseudorandom generators (WPRGs) and derandomizations for read-once branching programs (ROBPs), which are key problems towards answering the fundamental open question $\mathbf{BPL} ?{=} \mathbf{L}$.
Denote $n$ and $w$ as the length and the width of a ROBP.
We have the following results.

For standard ROBPs, there exists an ... more >>>

We study extractors computable in uniform $\mathrm{AC}^0$ and uniform $\mathrm{NC}^1$.

For the $\mathrm{AC}^0$ setting, we give a construction such that for every $k \ge n/ \mathrm{poly} \log n, \eps \ge 2^{-\mathrm{poly} \log n}$, it can extract $(1-\gamma)k$ randomness from an $(n, k)$ source for an arbitrary constant ... more >>>