A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits

We construct an explicit polynomial f(x1, . . . , xn), with coefficients in {0, 1}, such that the size of any syntactically multilinear arithmetic circuit computing f is at least Ω(n4/3/ log2 n). The lower bound holds over any field.

• Type: Conference
• Year: 2007
• Where: FOCS
• Authors: Ran Raz, Amir Shpilka, Amir Yehudayoff
• Keywords: Explicit Polynomial, FOCS 2007, Lower Bound, Multilinear Arithmetic Circuit, Theoretical Computer Science