In this work, we present an abstract framework for some algebraic error-correcting codes with the aim of capturing codes that are list-decodable to capacity, along with their decoding algorithm. In the polynomial ideal framework, a code is specified by some ideals in a polynomial ring, messages are polynomials and their ... more >>>

We study the amortized circuit complexity of boolean functions.

Given a circuit model $\mathcal{F}$ and a boolean function $f : \{0,1\}^n \rightarrow \{0,1\}$, the $\mathcal{F}$-amortized circuit complexity is defined to be the size of the smallest circuit that outputs $m$ copies of $f$ (evaluated on the same input), ... more >>>

We study two notions that refers to asymmetric graphs, which we view as graphs having a unique ordering that can be reconstructed by looking at an unlabeled version of the graph.

A {\em local self-ordering} procedure for a graph $G$ is given oracle access to an arbitrary isomorphic copy of ... more >>>