Enumerating models of DNF faster: breaking the dependency on the 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.