Exponential Lower Bounds for Depth 3 Arithmetic Circuits in Algebras of Functions over Finite Fields

Abstract.

A depth 3 arithmetic circuit can be viewed as a sum of products of linear functions. We prove an exponential complexity lower bound on depth 3 arithmetic circuits computing some natural symmetric functions over a finite field F. Also, we study the complexity of the functions f : D ⁿ→F for subsets D⊂F. In particular, we prove an exponential lower bound on the complexity of depth 3 arithmetic circuits computing some explicit functions f:(F ^*)ⁿ→F (in particular, the determinant of a matrix).