Strongly Exponential Separation Between Monotone VP and Monotone VNP
We show that there is a sequence of explicit multilinear polynomials P_n(x_1,...,x_n)∈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 (Ω(n)). This builds on (and strengthens) a result of Yehudayoff (2018) who showed a lower bound of (Ω̃(√(n))).
READ FULL TEXT