{"type":"ScholarlyArticle","title":"On Irrelevant Literals in Pseudo-Boolean Constraint Learning","authors":[{"name":"Daniel Le Berre","slug":"daniel-le-berre","given":"Daniel","family":"Le Berre","affiliation":"Université d'Artois , Lens , France; CRIL , CNRS UMR 8188 , Lens , France"},{"name":"Pierre Marquis","slug":"pierre-marquis","given":"Pierre","family":"Marquis","affiliation":"Université d'Artois , Lens , France; CRIL , CNRS UMR 8188 , Lens , France; Institut Universitaire de France {leberre ,"},{"name":"Stefan Mengel","slug":"stefan-mengel","given":"Stefan","family":"Mengel","affiliation":"CRIL , CNRS UMR 8188 , Lens , France; Université d'Artois , Lens , France"},{"name":"Romain Wallon","slug":"romain-wallon","given":"Romain","family":"Wallon","affiliation":"Université d'Artois , Lens , France; CRIL , CNRS UMR 8188 , Lens , France"}],"abstract":"Learning pseudo-Boolean (PB) constraints in PB solvers exploiting cutting planes based inference is not as well understood as clause learning in conflict-driven clause learning solvers.\r\nIn this paper, we show that PB constraints derived using cutting planes may contain irrelevant literals, i.e., literals whose assigned values (whatever they are) never change the truth value of the constraint.\r\nSuch literals may lead to infer constraints that are weaker than they should be, impacting the size of the proof built by the solver, and thus also affecting its performance.\r\nThis suggests that current implementations of PB solvers based on cutting planes should be reconsidered to prevent the generation of irrelevant literals.\r\nIndeed, detecting and removing irrelevant literals is too expensive in practice to be considered as an option (the associated problem is NP-hard).","doi":"10.24963/ijcai.2020/160","url":"https://ijcai.org/proceedings/2020/160","pdf":"https://ijcai.org/proceedings/2020/0160.pdf","markdown":"https://ijcai.org/proceedings/2020/160.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/160","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Constraints and SAT","track":"Main track","number":160,"pages":{"first":1148,"last":1154},"keywords":["Constraints and SAT: SAT: Algorithms and Techniques","Constraints and SAT: SAT: : Solvers and Applications"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24736/file_24736.m3u8","length_sec":254,"provider":"hls"}],"references":[{"position":1,"raw":"[Benhamou and Sais, 1994] Belaid Benhamou and Lakhdar Sais. 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