Strongly Exponential Separation Between Monotone VP and Monotone VNP

Srikanth Srinivasan

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arXiv · 1903.01630

Strongly Exponential Separation Between Monotone VP and Monotone VNP

Srikanth Srinivasan

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Abstract

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 $\exp(\Omega(n)).$ This builds on (and strengthens) a result of Yehudayoff (2018) who showed a lower bound of $\exp(\tilde{\Omega}(\sqrt{n})).$

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Srikanth Srinivasan. 2019-03-05. Strongly Exponential Separation Between Monotone VP and Monotone VNP. https://arxiv.org/abs/1903.01630

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