Emergent Mind
Unbalancing Sets and an Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits
(1708.02037)
Published Aug 7, 2017
in
cs.CC
Abstract
We prove a lower bound of $\Omega(n2/\log2 n)$ on the size of any syntactically multilinear arithmetic circuit computing some explicit multilinear polynomial $f(x1, \ldots, xn)$. Our approach expands and improves upon a result of Raz, Shpilka and Yehudayoff ([RSY08]), who proved a lower bound of $\Omega(n{4/3}/\log2 n)$ for the same polynomial. Our improvement follows from an asymptotically optimal lower bound for a generalized version of Galvin's problem in extremal set theory.
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