We give a deterministic algorithm for
approximately counting satisfying assignments of a degree-d polynomial threshold function
(PTF).
Given a degree-d input polynomial p(x_1,\dots,x_n) over \mathbb{R}^n
and a parameter \epsilon > 0, our algorithm approximates
\mathbf{P}_{x \sim \{-1,1\}^n}[p(x) \geq 0]
to within an additive \pm \epsilon in time $O_{d,\epsilon}(1)\cdot ... more >>>