The celebrated Ore-DeMillo-Lipton-Schwartz-Zippel (ODLSZ) lemma asserts that $n$-variate non-zero polynomial functions of degree $d$ over a field $\mathbb{F}$, are non-zero over any ``grid'' (points of the form $S^n$ for finite subset $S \subseteq \mathbb{F}$) with probability at least $\max\{|S|^{-d/(|S|-1)},1-d/|S|\}$ over the choice of random point from the grid. In particular, ... more >>>

We study low-degree testing for group-valued functions over a Boolean slice. Specifically given a degree parameter $d$ and oracle access to a function $f:\{0,1\}^n_{n/2} \to G$ where $\{0,1\}^n_k$ denotes the set of vectors in $\{0,1\}^n$ of Hamming weight $k$ and $G$ is an Abelian group (not necessarily finite), the low-degree ... more >>>