Engineering an Exact Pseudo-Boolean Model Counter
This addresses a crucial need for efficient techniques in model counting for Pseudo-Boolean formulas, which are more succinct and flexible for real-world problems, representing an incremental advancement in the field.
The paper tackled the problem of model counting for Pseudo-Boolean formulas, which had been relatively overlooked, by proposing PBCount, the first exact model counter for such formulas, and it achieved a result of handling 1513 instances compared to 1013 by the state-of-the-art.
Model counting, a fundamental task in computer science, involves determining the number of satisfying assignments to a Boolean formula, typically represented in conjunctive normal form (CNF). While model counting for CNF formulas has received extensive attention with a broad range of applications, the study of model counting for Pseudo-Boolean (PB) formulas has been relatively overlooked. Pseudo-Boolean formulas, being more succinct than propositional Boolean formulas, offer greater flexibility in representing real-world problems. Consequently, there is a crucial need to investigate efficient techniques for model counting for PB formulas. In this work, we propose the first exact Pseudo-Boolean model counter, PBCount, that relies on knowledge compilation approach via algebraic decision diagrams. Our extensive empirical evaluation shows that PBCount can compute counts for 1513 instances while the current state-of-the-art approach could only handle 1013 instances. Our work opens up several avenues for future work in the context of model counting for PB formulas, such as the development of preprocessing techniques and exploration of approaches other than knowledge compilation.