Given a finite group $G$ by its multiplication table as input, we give a deterministic polynomial-time construction of a directed Cayley graph on $G$ with $O(\log |G|)$ generators, which has a rapid mixing property and a constant spectral expansion.\\

We prove a similar result in the undirected case, and ... more >>>

We consider the following problem that arises in outsourced storage: a user stores her data $x$ on a remote server but wants to audit the server at some later point to make sure it actually did store $x$. The goal is to design a (randomized) verification protocol that has the ... more >>>

Affine-invariant properties are an abstract class of properties that generalize some
central algebraic ones, such as linearity and low-degree-ness, that have been
studied extensively in the context of property testing. Affine invariant properties
consider functions mapping a big field $\mathbb{F}_{q^n}$ to the subfield $\mathbb{F}_q$ and include all
properties that form ... more >>>