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### Revision(s):

Revision #1 to TR19-032 | 31st July 2020 08:15

#### Strongly Exponential Separation Between Monotone VP and Monotone VNP

Revision #1
Authors: Srikanth Srinivasan
Accepted on: 31st July 2020 08:15
Downloads: 38
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 $\exp(\tilde{\Omega}(\sqrt{n})).$

Changes to previous version:

Added references to results of Kuznetsov, Kasim-Zade, Gashkov and Sergeev. Also added more detailed proof outline. Some typos/small errors corrected.

### Paper:

TR19-032 | 4th March 2019 18:21

#### Strongly Exponential Separation Between Monotone VP and Monotone VNP

TR19-032
Authors: Srikanth Srinivasan
Publication: 5th March 2019 10:51
Downloads: 440
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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