{"type":"ScholarlyArticle","title":"Compilation and Fast Model Counting beyond CNF","authors":[{"name":"Alexis de Colnet","slug":"alexis-de-colnet","given":"Alexis","family":"de Colnet","affiliation":"Algorithms and Complexity Group , TU Wien , Vienna , Austria"},{"name":"Stefan Szeider","slug":"stefan-szeider","given":"Stefan","family":"Szeider","affiliation":"Algorithms and Complexity Group , TU Wien , Vienna , Austria"},{"name":"Tianwei Zhang","slug":"tianwei-zhang","given":"Tianwei","family":"Zhang","affiliation":"Algorithms and Complexity Group , TU Wien , Vienna , Austria"}],"abstract":"Circuits in deterministic decomposable negation normal form (d-DNNF)  are representations of Boolean functions that enable linear-time model counting. This paper strengthens our theoretical knowledge of what classes of functions can be efficiently transformed, or compiled, into d-DNNF. Our main contribution is the fixed-parameter tractable (FPT) compilation of conjunctions of specific constraints parameterized by incidence treewidth. This subsumes the known result for CNF. The constraints in question are all functions representable by constant-width ordered binary decision diagrams (OBDDs) for all variable orderings. For instance, this includes parity constraints and cardinality constraints with constant threshold. The running time of the FPT compilation is singly exponential in the incidence treewidth but hides large constants in the exponent. To balance that, we give a more efficient FPT algorithm for model counting that applies to a sub-family of the constraints and does not require compilation.","doi":"10.24963/ijcai.2024/367","url":"https://ijcai.org/proceedings/2024/367","pdf":"https://ijcai.org/proceedings/2024/0367.pdf","markdown":"https://ijcai.org/proceedings/2024/367.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/367","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Knowledge Representation and Reasoning","track":"Main Track","number":367,"pages":{"first":3315,"last":3323},"keywords":["Knowledge Representation and Reasoning: KRR: Knowledge compilation"],"videos":[],"references":[{"position":1,"raw":"[Amarilli et al., 2020] Antoine Amarilli, Florent Capelli, Mikaël Monet, and Pierre Senellart. 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