Enumerating models of DNF faster: breaking the dependency on the formula size

TL;DR

This paper develops new enumeration algorithms for DNF models that achieve delay depending on model size rather than formula size, including constant, quadratic, and sublinear delays for specific subclasses.

Contribution

It introduces algorithms with delays independent of the formula size for certain DNF subclasses and analyzes average delay to improve enumeration efficiency.

Findings

Constant delay for k-DNF with fixed k

Quadratic delay for monotone formulas

Sublinear average delay in formula size

Abstract

In this article, we study the problem of enumerating the models of DNF formulas. The aim is to provide enumeration algorithms with a delay that depends polynomially on the size of each model and not on the size of the formula, which can be exponentially larger. We succeed for two subclasses of DNF formulas: we provide a constant delay algorithm for $k$-DNF with fixed $k$ by an appropriate amortization method and we give a quadratic delay algorithm for monotone formulas. We then focus on the \emph{average delay} of enumeration algorithms and show how to obtain a sublinear delay in the formula size.