Strongly Exponential Separation Between Monotone VP and Monotone VNP

03/05/2019

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by   Srikanth Srinivasan, et al.

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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))).