PBCounter: weighted model counting on pseudo-boolean formulas

Abstract

In Weighted Model Counting (WMC), we assign weights to literals and compute the sum of the weights of the models of a given propositional formula where the weight of an assignment is the product of the weights of its literals. The current WMC solvers work on Conjunctive Normal Form (CNF) formulas. However, CNF is not a natural representation for human-being in many applications. Motivated by the stronger expressive power of Pseudo-Boolean (PB) formulas than CNF, we propose to perform WMC on PB formulas. Based on a recent dynamic programming algorithm framework called ADDMC for WMC, we implement a weighted PB counting tool \mathsf{P}\mathsf{B}\mathsf{C}\mathsf{o}\mathsf{u}\mathsf{n}\mathsf{t}\mathsf{e}\mathsf{r}. We compare \mathsf{P}\mathsf{B}\mathsf{C}\mathsf{o}\mathsf{u}\mathsf{n}\mathsf{t}\mathsf{e}\mathsf{r} with the state-of-the-art weighted model counters SharpSAT-TD, ExactMC, D4, and ADDMC, where the latter tools work on CNF with encoding methods that convert PB constraints into a CNF formula. The experiments on three domains of benchmarks show that \mathsf{P}\mathsf{B}\mathsf{C}\mathsf{o}\mathsf{u}\mathsf{n}\mathsf{t}\mathsf{e}\mathsf{r} is superior to the model counters on CNF formulas.

Graphical abstract

Keywords

weighted model counting / pseudo-boolean constraint / algebraic decision diagrams / preprocessing techniques

Yong Lai is an associate professor at the College of Computer Science and Technology, Jilin University, China. He received his PhD degree from Jilin University, China. His research interests include knowledge representation and reasoning, neural-symbolic computation, tractable machine learning, and probabilistic graphical model

Zhenghang Xu received a BS degree in Computer Science and Information Technology, Northeast Normal University, China in 2020. Currently, he is pursuing a Master’s degree at the College of Computer Science and Technology, Jilin University, China. His research interests include model counting and algorithm design

Minghao Yin is a professor at the School of Computer Science and Information Technology, Northeast Normal University, China. He received his PhD degree in Computer Software and Theory from Jilin University, China. His research interests include heuristic search, data mining, and combinatorial optimization

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Acknowledgements

This work was supported by NSFC (Grant Nos. 61976050, 61972384), the Jilin Province Science and Technology Department project (Nos. 20240101378JC, 20240602005RC, YDZJ202201ZYTS415), Jilin Education Department Project (No.JJKH20231319KJ). Thanks to the editorial board and reviewers for their valuable comments.

Competing interests

The authors declare that they have no competing interests or financial conflicts to disclose.

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