Weighted pseudorandom generators (wPRGs) were suggested by Braverman, Cohen, and Garg (STOC, 2018) as a relaxation of pseudorandom generator (PRG) used for derandomization.
We present proofs of several observations regarding wPRGs, where some of these observations are well known.

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In this paper, we give a one-pass quantum streaming algorithm for Max-$k$SAT that uses $\operatorname{polylog}(n)$ space and achieves a $0.7172$-approximation on instances with $n$ variables. In contrast, prior work by Chou, Golovnev, and Velusamy (FOCS 2020) implies that achieving an approximation ratio better than $\sqrt{2}/2 \approx 0.7071$ for Max-$k$SAT requires ... more >>>

We show that several meta-complexity problems are NP-hard under randomized polynomial-time (half-Levin) reductions, and provably cannot be NP-hard under randomized Levin reductions, under the assumptions that
(cryptography): there exists a subexponentially-secure indistinguishability obfuscator in the sense of Barak et al. (JACM 2012), and
(proof complexity): there are no ... more >>>