{"type":"ScholarlyArticle","title":"A Top-Down Tree Model Counter for Quantified Boolean Formulas","authors":[{"name":"Florent Capelli","slug":"florent-capelli","given":"Florent","family":"Capelli","affiliation":"Univ. Artois , CNRS , Centre de Recherche en Informatique de Lens (CRIL) , F-62300 Lens , France"},{"name":"Jean-Marie Lagniez","slug":"jean-marie-lagniez","given":"Jean-Marie","family":"Lagniez","affiliation":"Univ. Artois , CNRS , Centre de Recherche en Informatique de Lens (CRIL) , F-62300 Lens , France"},{"name":"Andreas Plank","slug":"andreas-plank","given":"Andreas","family":"Plank","affiliation":"Institute for Symbolic Artificial Intelligence , JKU Linz , Austria"},{"name":"Martina Seidl","slug":"martina-seidl","given":"Martina","family":"Seidl","affiliation":"Institute for Symbolic Artificial Intelligence , JKU Linz , Austria"}],"abstract":"This paper addresses the challenge of solution counting for Quantified Boolean Formulas (QBFs), a task distinct from the well-established model counting problem for SAT (\\#SAT). Unlike SAT, where models are straightforward assignments to Boolean  variables, QBF solution counting involves tree models that capture dependencies among variables within different quantifier blocks. We present a comprehensive top-down tree model counter capable of handling diverse satisfiable QBF formulas. Emphasizing the critical role of the branching heuristic, which must consider variables in the correct order according to quantification blocks, we further demonstrate the importance of addressing connected components, free variables, and caching. Experimental results indicate that our proposed approach for counting tree models of QBF formulas is highly efficient in practice, surpassing existing state-of-the-art methods designed for this specific purpose.","doi":"10.24963/ijcai.2024/205","url":"https://ijcai.org/proceedings/2024/205","pdf":"https://ijcai.org/proceedings/2024/0205.pdf","markdown":"https://ijcai.org/proceedings/2024/205.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/205","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":"Constraint Satisfaction and Optimization","track":"Main Track","number":205,"pages":{"first":1853,"last":1861},"keywords":["Constraint Satisfaction and Optimization: CSO: Satisfiabilty","Constraint Satisfaction and Optimization: CSO: Solvers and tools"],"videos":[],"references":[{"position":1,"raw":"[Audemard et al., 2022] Gilles Audemard, Jean-Marie Lagniez, and Marie Miceli. 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