Suwei Yang

Suwei Yang, Kuldeep S. Meel

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.

Suwei Yang, Kuldeep S. Meel

Model counting is a fundamental task that involves determining the number of satisfying assignments to a logical formula, typically in conjunctive normal form (CNF). While CNF model counting has received extensive attention over recent decades, interest in Pseudo-Boolean (PB) model counting is just emerging partly due to the greater flexibility of PB formulas. As such, we observed feature gaps in existing PB counters such as a lack of support for projected and incremental settings, which could hinder adoption. In this work, our main contribution is the introduction of the PB model counter PBCount2, the first exact PB model counter with support for projected and incremental model counting. Our counter, PBCount2, uses our Least Occurrence Weighted Min Degree (LOW-MD) computation ordering heuristic to support projected model counting and a cache mechanism to enable incremental model counting. In our evaluations, PBCount2 completed at least 1.40x the number of benchmarks of competing methods for projected model counting and at least 1.18x of competing methods in incremental model counting.