Lower bounds for monotone arithmetic circuits via communication complexity

Valiant (1980) showed that general arithmetic circuits with negation can be exponentially more powerful than monotone ones. We give the first improvement to this classical result: we construct a family of polynomials Pn in n variables, each of its monomials has non-negative coefficient, such that Pn can be computed by a polynomial-size depth-three formula but every monotone circuit computing it has size 2Ω(n1/4/log(n)).