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Paper:

TR19-032 | 4th March 2019 18:21

Strongly Exponential Separation Between Monotone VP and Monotone VNP

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TR19-032
Authors: Srikanth Srinivasan
Publication: 5th March 2019 10:51
Downloads: 128
Keywords: 


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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