Boolean Differential Operators

TL;DR

This paper explores four combinatorial interpretations of Boolean differential operators, providing explicit matrix representations for each, thereby enhancing understanding of their algebraic structure.

Contribution

It introduces four new combinatorial interpretations of Boolean differential operators and derives explicit matrix representations for each interpretation.

Findings

Four combinatorial interpretations of Boolean differential operators identified

Explicit matrix representations derived for each interpretation

Enhanced understanding of the algebraic structure of Boolean differential operators

Abstract

We consider four combinatorial interpretations for the algebra of Boolean differential operators. We show that each interpretation yields an explicit matrix representation for Boolean differential operators.