Polymorphisms and Circuit Complexity

Abstract

We present a framework for studying circuit complexity that is inspired by techniques that are used for analyzing the complexity of CSPs. We prove that the circuit complexity of a Boolean function $f$ is characterized by the partial polymorphisms of $f$'s truth table. Moreover, the non-deterministic circuit complexity of $f$ is characterized by the polymorphisms of $f$'s truth table.

Updated notation and fixed some typos