Lower Bounds for Circuits with Few Modular and Symmetric Gates

Arkadev Chattopadhyay, Kristoffer Arnsfelt Hansen

Abstract: We consider constant depth circuits augmented with few modular, or more generally, arbitrary symmetric gates. We prove that circuits augmented with o(log2 n) symmetric gates must have size n \(^{\Omega({\rm log}\ {\it n})}\) to compute a certain (complicated) function in ACC 0.