Strongly Exponential Separation Between Monotone VP and Monotone VNP

We show that there is a sequence of explicit multilinear polynomials $P_n(x_1,\ldots,x_n)\in \mathbb{R}[x_1,\ldots,x_n]$ 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 (2018) who showed a lower bound of $\exp(\tildeΩ(\sqrt{n})).$

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