Assume that Alice has a binary string $x$ and Bob a binary string $y$, both of length $n$. Their goal is to output 0, if $x$ and $y$ are at least $L$-close in Hamming distance, and output 1, if $x$ and $y$ are at least $U$-far in Hamming distance, where ... more >>>

We introduce the concept of a randomness steward, a tool for saving random bits when executing a randomized estimation algorithm $\mathrm{Est}$ on many adaptively chosen inputs. For each execution, the chosen input to $\mathrm{Est}$ remains hidden from the steward, but the steward chooses the randomness of $\mathrm{Est}$ and, crucially, is ... more >>>

In this paper we study the identity testing problem of \emph{arithmetic read-once formulas} (ROF) and some related models. A read-once formula is formula (a circuit whose underlying graph is a tree) in which the
operations are $\set{+,\times}$ and such that every input variable labels at most one leaf. We obtain ... more >>>