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In Hrubeš' Algebraic Monotone Calculus AMC a DNF tautology $A$ is proved by a monotone arithmetic circuit computing $\chi(A)-\epsilon\cdot\chi(1)$ for some $\epsilon>0$, where $\chi(A)$ is the set-multilinear polynomial whose coefficient at $\mathbf x^{\sigma}$ counts the terms of $A$ satisfied by $\sigma$, and $\chi(1)=\prod_{i\le n}(x_i^0+x_i^1)$. Proof size is circuit size, and ... more >>>
For infinitely many rates $R \in (0,1)$, we show that full-length Reed-Solomon codes over fields of low characteristic can contain super-polynomially many codewords in a Hamming ball of radius just exceeding the Johnson radius. Over prime fields, we exhibit full-length Reed-Solomon codes of constant rate $R$ with polynomially many codewords ... more >>>
A quadratic source is a random variable $X\sim\mathbb{F}_2^n$ generated by applying $n$ quadratics to a hidden uniform string. Previously, the best-known explicit extractor for this model required min-entropy roughly $k=n-\sqrt{\log n}$. In this paper, we give an explicit construction for min-entropy $k=\mathrm{polylog}(n)$. Even for the special case of $2$-local sources, ... more >>>
