Model counting is a fundamental problem in many practical applications, including query evaluation in probabilistic databases and failure-probability estimation of networks. In this work, we focus on a variant of this problem where the underlying formula is expressed in the Disjunctive Normal Form (DNF), also known as #DNF. This problem has been shown to be #P-complete, making it often intractable to solve exactly. Much research has therefore focused on obtaining approximate solutions, particularly in the form of $(\varepsilon, \delta)$ approximations. The primary contribution of this paper is a new approach, called pepin, an approximate #DNF counter that significantly outperforms prior state-of-the-art approaches. Our work is based on the recent breakthrough in the context of the union of sets in the streaming model. We demonstrate the effectiveness of our approach through extensive experiments and show that it provides an affirmative answer to the challenge of efficiently computing #DNF.

翻译：模型计数是许多实际应用中的基础问题，包括概率数据库中的查询评估和网络故障概率估计。在本研究中，我们重点关注该问题的一个变体，其中底层公式以析取范式（DNF）表示，也称为#DNF问题。该问题已被证明是#P完全问题，因此精确求解通常不可行。大量研究因而聚焦于获得近似解，特别是以$(\varepsilon, \delta)$近似的形式。本文的主要贡献是提出了一种名为pepin的新方法，这是一种近似#DNF计数器，其性能显著优于现有最先进方法。我们的工作基于流模型中集合并集问题的最新突破性进展。通过大量实验，我们证明了该方法的有效性，并表明它为高效计算#DNF的挑战提供了肯定性答案。