An emerging theory of "linear-algebraic pseudorandomness" aims to understand the linear-algebraic analogs of fundamental Boolean pseudorandom objects where the rank of subspaces plays the role of the size of subsets. In this work, we study and highlight the interrelationships between several such algebraic objects such as subspace designs, dimension ... more >>>

We give an explicit hitting set of size $\text{poly}(n,d,r)$ for the class of $n$-variate degree-$d$ polynomials whose partial derivative space is bounded by $r$, over any field $\mathbb{F}$ of characteristic zero. In particular, this yields a polynomial sized hitting set for the class of depth-$3$ powering circuits.

The main ... more >>>