Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > DETAIL:

### 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
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 $\exp(\tilde{\Omega}(\sqrt{n})).$