Suppose Alice and Bob each start with private randomness and no other input, and they wish to engage in a protocol in which Alice ends up with a set $x\subseteq[n]$ and Bob ends up with a set $y\subseteq[n]$, such that $(x,y)$ is uniformly distributed over all pairs of disjoint sets. ... more >>>

A hitting-set generator (HSG) is a polynomial map $Gen:\mathbb{F}^k \to \mathbb{F}^n$ such that for all $n$-variate polynomials $Q$ of small enough circuit size and degree, if $Q$ is non-zero, then $Q\circ Gen$ is non-zero. In this paper, we give a new construction of such a HSG assuming that we have ... more >>>

We introduce randomized time-bounded Kolmogorov complexity (rKt), a natural extension of Levin's notion of Kolmogorov complexity from 1984. A string w of low rKt complexity can be decompressed from a short representation via a time-bounded algorithm that outputs w with high probability.

This complexity measure gives rise to a ... more >>>