Unbalancing Sets and an Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits

Noga Alon, Mrinal Kumar, Ben Lee Volk, Marc Herbstritt
2018 Computational Complexity Conference  
We prove a lower bound of Ω(n 2 / log 2 n) on the size of any syntactically multilinear arithmetic circuit computing some explicit multilinear polynomial f (x 1 , . . . , x n ). Our approach expands and improves upon a result of Raz, Shpilka and Yehudayoff ([31]), who proved a lower bound of Ω(n 4/3 / log 2 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.
doi:10.4230/lipics.ccc.2018.11 dblp:conf/coco/AlonKV18 fatcat:75gqziq4ejfjxmrc3p7k4zbohi