{"type":"ScholarlyArticle","title":"SAT Encodings for Pseudo-Boolean Constraints Together With At-Most-One Constraints (Extended Abstract)","authors":[{"name":"Miquel Bofill","slug":"miquel-bofill","given":"Miquel","family":"Bofill","affiliation":"Universitat de Girona , Girona , Spain"},{"name":"Jordi Coll","slug":"jordi-coll","given":"Jordi","family":"Coll","affiliation":"Institut d'Investigació en Intel•ligència Artificial ( IIIA-CSIC) , Bellaterra , Spain"},{"name":"Peter Nightingale","slug":"peter-nightingale","given":"Peter","family":"Nightingale","affiliation":"University of York , York , United Kingdom"},{"name":"Josep Suy","slug":"josep-suy","given":"Josep","family":"Suy","affiliation":"Universitat de Girona , Girona , Spain"},{"name":"Felix Ulrich-Oltean","slug":"felix-ulrich-oltean","given":"Felix","family":"Ulrich-Oltean","affiliation":"University of York , York , United Kingdom"},{"name":"Mateu Villaret","slug":"mateu-villaret","given":"Mateu","family":"Villaret","affiliation":"Universitat de Girona , Girona , Spain"}],"abstract":"When solving a combinatorial problem using propositional satisfiability (SAT), the encoding of the constraints  is of vital importance. \r\nPseudo-Boolean (PB) constraints  appear frequently in a wide variety of problems. When PB constraints occur together with at-most-one (AMO) constraints over the same variables, they can be combined into PB(AMO) constraints. \r\nIn this paper we present new encodings  for PB(AMO) constraints. \r\nOur experiments show that these encodings  can be substantially smaller than those of PB constraints and allow many more instances to be solved within a time limit. \r\nWe also observed that there is no single overall winner among the considered encodings, but efficiency of each encoding may depend on PB(AMO) characteristics such as the magnitude of coefficient values.","doi":"10.24963/ijcai.2023/769","url":"https://ijcai.org/proceedings/2023/769","pdf":"https://ijcai.org/proceedings/2023/0769.pdf","markdown":"https://ijcai.org/proceedings/2023/769.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/769","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Journal Track","track":"Journal Track","number":769,"pages":{"first":6853,"last":6857},"keywords":["Constraint Satisfaction and Optimization: CSO: Modeling","Constraint Satisfaction and Optimization: CSO: Satisfiabilty","Constraint Satisfaction and Optimization: CSO: Constraint satisfaction"],"videos":[],"references":[{"position":1,"raw":"[Abío et al., 2012] Ignasi Abío, Robert Nieuwenhuis, Albert Oliveras, Enric Rodríguez-Carbonell, and Valentin Mayer- Eichberger. 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