Functional Lower Bounds for Arithmetic Circuits and Connections to Boolean Circuit Complexity

摘要

We say that a circuit C over a field F {functionally} computes a polynomial P in F[x_1, x_2, ..., x_n] if for every x in {0,1}^n we have that C(x) = P(x). This is in contrast to syntactically computing P, when C = P as formal polynomials. In this paper, w