Understanding the average-case complexity of $\mathrm{NP}$ is a central goal in complexity theory and cryptography. A necessary milestone is to understand the corresponding average-case versus worst-case question for the polynomial hierarchy ($\mathrm{PH}$). In a celebrated result, Hirahara [Hir21] proved that if every distributional problem in $\mathrm{PH}$ is easy on average, ... more >>>

Catalytic computation involves the study of Turing machines that are provided an additional catalytic tape (with arbitrary content) that the machine may use while ensuring that the tape contents are restored at the end of the computation. Although it is known that catalytic log-space machines are at least as powerful ... more >>>

We revisit the problem of constructing explicit pseudorandom generators which output $n$ bits that look random to $n$-variate degree-$d$ polynomials modulo $m$. We give new generators with seed length $2^{O(dm^2)} \log(n/\varepsilon)$, which is optimal for any fixed $m$ and $d$. Along the way, we prove new Fourier growth bounds for ... more >>>