🤖 AI Summary
This work addresses the inefficiency of query operations—such as uniform sampling, direct access, and model enumeration—on propositional formulas in conjunctive normal form (CNF) after compilation into deterministic decomposable negation normal form (d-DNNF). To overcome this limitation, the authors propose a preprocessing technique that preserves only the model count rather than full logical equivalence. Applied prior to CNF-to-d-DNNF compilation, this method optimizes the input formula while retaining essential preprocessing information to accelerate downstream queries. The study presents the first systematic evaluation of model-count-preserving preprocessors, demonstrating their ability to substantially enhance the performance of diverse query tasks on d-DNNF representations, thereby surpassing the constraints of traditional equivalence-preserving preprocessing. Extensive experiments across multiple benchmark domains confirm the approach’s efficiency and robustness.
📝 Abstract
In this paper, we investigate preprocessing techniques aimed at improving the efficiency of accessing models of propositional formulas represented in conjunctive normal form (CNF). We focus on three fundamental tasks: uniform sampling, direct model access, and model enumeration. Our analysis reveals that most state-of-the-art preprocessors, when they do not preserve formula equivalence, are generally unsuitable for these tasks. In contrast, we demonstrate that preprocessors which preserve model counts can be effectively leveraged, provided relevant preprocessing information is maintained. To validate our approach, we perform extensive experiments on a diverse suite of benchmarks from multiple domains. The experimental results show that our preprocessing methods are both efficient and robust, yielding significant performance improvements for model access queries when CNF formulas are compiled into d-DNNF representations.