Strongly Exponential Separation between Monotone VP and Monotone VNP

Abstract

We show that there is a sequence of explicit multilinear polynomials P n (x 1 , … ,x n ) ϵ R [x 1 , … ,x n ] with non-negative coefficients that lies in monotone VNP such that any monotone algebraic circuit for P n must have size exp (Ω ( n )) This builds on (and strengthens) a result of Yehudayoff (STOC 2019) who showed a lower bound of exp (Ω(√n)).