We show that the known list-decoding algorithms for univariate multiplicity and folded Reed-Solomon (FRS) codes can be made to run in nearly-linear time. This yields, to the best of our knowledge, the first known family of codes that can be decoded (and encoded) in nearly linear time, even as they ... more >>>

A fundamental problem in circuit complexity is to find explicit functions that require large depth to compute. When considering the natural DeMorgan basis of $\{\text{OR},\text{AND}\}$, where negations incur no cost, the best known depth lower bounds for an explicit function in NP have the form $(3-o(1))\log_2 n$, established by H{\aa}stad ... more >>>

The notion of the derandomized square of two graphs, denoted as $G \circ H$, was introduced by Rozenman and Vadhan as they rederived Reingold's Theorem, $\mathbf{SL} = \mathbf{L}$. This pseudorandom primitive, closely related to the Zig-Zag product, plays a crucial role in recent advancements on space-bounded derandomization. For this and ... more >>>