Catalytic computation involves the study of Turing machines that are provided an additional catalytic tape (with arbitrary content) that the machine may use while ensuring that the tape contents are restored at the end of the computation. Although it is known that catalytic log-space machines are at least as powerful ... 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 >>>