Enumeration Classes Defined by Circuits

TL;DR

This paper introduces a new framework using Boolean circuits to classify enumeration problems by complexity, enabling formal comparisons of problems previously only known to be in DelayP.

Contribution

It defines low complexity classes based on circuit enumerators and applies them to categorize well-known enumeration problems, clarifying their relative complexities.

Findings

Classifies enumeration problems within a new circuit-based framework

Locates graph theory, Gray code, and SAT problems within these classes

Provides a formal method to compare complexities of enumeration problems

Abstract

We refine the complexity landscape for enumeration problems by introducing very low classes defined by using Boolean circuits as enumerators. We locate well-known enumeration problems, e.g., from graph theory, Gray code enumeration, and propositional satisfiability in our classes. In this way we obtain a framework to distinguish between the complexity of different problems known to be in $\mathbf{DelayP}$, for which a formal way of comparison was not possible to this day.