Leveraging Decision-DNNF Compilation for Enumerating Disjoint Partial Models

The All-Solution Satisfiability Problem (AllSAT) extends SAT by requiring the identification of all possible solutions for a propositional formula. In practice, enumerating all complete models is often infeasible, making the identification of partial models essential for generating a concise representation of the solution set. Deterministic Decomposable Negation Normal Form (d-DNNF) serves as a language for representation known to offer polynomial-time algorithms for model enumeration. Specifically, when a propositional formula is encoded in d-DNNF, it enables iterative model enumeration with polynomial delay between models. However, despite the existence of theoretical algorithms for this purpose, no available implementations are currently accessible. Furthermore, these theoretical approaches are nearly impractical as they solely yield complete models. We introduce a novel algorithm that maintains a polynomial delay between partial models while significantly enhancing efficiency compared to baseline approaches. Furthermore, through experimental validation, we demonstrate the superiority of compiling a CNF formula Σ into a d-DNNF formula Σ′ and subsequently enumerating models of Σ′ over existing state-of-the-art methodologies for CNF partial model enumeration.