Investigating the Power of Circuits with $MOD_6$ Gates

TL;DR

This paper explores the computational capabilities of Boolean circuits equipped with MOD_6 gates, analyzing their complexity and algebraic properties to understand their power and limitations.

Contribution

It introduces a formal framework for studying MOD_6 circuits and connects their computational power to algebraic models, providing foundational insights.

Findings

MOD_6 circuits have unique algebraic properties

Standard complexity notions are applied to MOD_6 circuits

Results establish relationships between circuit models and algebraic structures

Abstract

We consider the power of Boolean circuits with MOD$_{6}$ gates. First, we introduce a few basic notions of computational complexity, and describe the standard models with which we study the complexity of problems. We then define the model of Boolean circuits, equate a restricted class of circuits with an algebraic model, and present some results from working with this algebra.