Breaking the log-squared barrier in pseudorandom generator constructions for read-once branching programs, namely, achieving seed length $o(\log^2 n)$ for length-$n$ programs, has remained a longstanding open problem since Nisan's seminal construction.

We show that breaking this barrier, even achieving seed length $O(\log^{3/2} n)$ (for, say, constant width), would follow from ... 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.

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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 >>>