A Note on Nonuniform versus Uniform ACC^k Circuits for NE

TL;DR

This paper establishes an equivalence between nonuniform and P^{NE}-uniform ACC^k circuits for the class NE, and discusses similar results for other classes, highlighting the relationship between uniformity and circuit complexity.

Contribution

It proves that NE has nonuniform ACC^k circuits if and only if it has P^{NE}-uniform ACC^k circuits, clarifying the role of uniformity in circuit complexity.

Findings

Equivalence between nonuniform and P^{NE}-uniform ACC^k circuits for NE.

Method to extend results to other circuit and complexity classes.

Insights into the relationship between uniformity and circuit complexity.

Abstract

We note that for each k \in {0,1,2, ...} the following holds: NE has (nonuniform) ACC^k circuits if and only if NE has P^{NE}-uniform ACC^k circuits. And we mention how to get analogous results for other circuit and complexity classes.