Roei Tell

The quantified derandomization problem of a circuit class $\mathcal{C}$ with a function $B:\mathbb{N}\rightarrow\mathbb{N}$ is the following: Given an input circuit $C\in\mathcal{C}$ over $n$ bits, deterministically distinguish between the case that $C$ accepts all but $B(n)$ of its inputs and the case that $C$ rejects all but $B(n)$ of its inputs. ... more >>>

Valentine Kabanets, Zhenjian Lu

A polynomial threshold function (PTF) is defined as the sign of a polynomial $p\colon\bool^n\to\mathbb{R}$. A PTF circuit is a Boolean circuit whose gates are PTFs. We study the problems of exact and (promise) approximate counting for PTF circuits of constant depth.

Satisfiability (#SAT). We give the first zero-error randomized algorithm ... more >>>

Dean Doron, Dana Moshkovitz, Justin Oh, David Zuckerman

Existing proofs that deduce $\mathbf{BPP}=\mathbf{P}$ from circuit lower bounds convert randomized algorithms into deterministic algorithms with a large polynomial slowdown. We convert randomized algorithms into deterministic ones with little slowdown. Specifically, assuming exponential lower bounds against nondeterministic circuits, we convert any randomized algorithm over inputs of length $n$ running in ... more >>>