Lower Bounds and Separations for Constant Depth Multilinear Circuits

We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multilinear, if the polynomial computed by each of its gates is multilinear). We also prove a super-polynomial separation between the size of product-depth1 d and product-depth d + 1 multilinear circuits (where d is constant). That is, there exists a polynomial f such that

• Type: Conference
• Year: 2008
• Where: COCO
• Authors: Ran Raz, Amir Yehudayoff
• Keywords: Algorithms, COCO 2008, Exponential Lower Bound, Multilinear Arithmetic Circuits, Multilinear Circuit