The derandomization of MA, the probabilistic version of NP, is a long standing open question. In this work, we connect this problem to a variant of another major problem: the quantum PCP conjecture. Our connection goes through the surprising quantum characterization of MA by Bravyi and Terhal. They proved the ... more >>>

The class of model checking for first-order formulas on sparse graphs has a complete problem with respect to fine-grained reductions, Orthogonal Vectors (OV) [GIKW17]. This paper studies extensions of this class or more lenient parameterizations. We consider classes obtained by allowing function symbols;
first-order on ordered structures; adding various notions ... more >>>

Polynomial factoring has famous practical algorithms over fields-- finite, rational \& $p$-adic. However, modulo prime powers it gets hard as there is non-unique factorization and a combinatorial blowup ensues. For example, $x^2+p \bmod p^2$ is irreducible, but $x^2+px \bmod p^2$ has exponentially many factors! We present the first randomized poly($\deg ... more >>>