Near-Optimal Bootstrapping of Hitting Sets for Algebraic Models

The Polynomial Identity Lemma (also called the "Schwartz-Zippel lemma") states that any nonzero polynomial f (x(1), ... , x(n)) of degree at most s will evaluate to a nonzero value at some point on any grid S-n subset of F-n with |S| > s. Thus, there is an explicit hitting set for all n-variate degree -s, size -s algebraic circuits of size (s + 1)(n).