{"type":"ScholarlyArticle","title":"New Algorithms for #2-SAT and #3-SAT","authors":[{"name":"Junqiang Peng","slug":"junqiang-peng","given":"Junqiang","family":"Peng","affiliation":""},{"name":"Zimo Sheng","slug":"zimo-sheng","given":"Zimo","family":"Sheng","affiliation":""},{"name":"Mingyu Xiao","slug":"mingyu-xiao","given":"Mingyu","family":"Xiao","affiliation":""}],"abstract":"The #2-SAT and #3-SAT problems involve counting the number of satisfying assignments (also called models) for instances of 2-SAT and 3-SAT, respectively. In 2010, Zhou et al. (https://doi.org/10.1609/aaai.v24i1.7537) proposed an O*(1.1892^m)-time algorithm for #2-SAT and an efficient approach for #3-SAT, where m denotes the number of clauses. In this paper, we show that the weighted versions of #2-SAT and #3-SAT can be solved in O*(1.1082^m) and O*(1.4423^m) time, respectively. These results directly apply to the unweighted cases and achieve substantial improvements over the previous results. These advancements are enabled by the introduction of novel reduction rules, a refined analysis of branching operations, and the application of path decompositions on the primal and dual graphs of the formula.","doi":"10.24963/ijcai.2025/297","url":"https://ijcai.org/proceedings/2025/297","pdf":"https://ijcai.org/proceedings/2025/0297.pdf","markdown":"https://ijcai.org/proceedings/2025/297.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/297","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":297,"pages":{"first":2666,"last":2674},"keywords":["Constraint Satisfaction and Optimization: CSO: Satisfiabilty"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}