{"type":"ScholarlyArticle","title":"On Minimum Representations of Matched Formulas (Extended Abstract)","authors":[{"name":"Ondřej Čepek","slug":"ondrej-cepek","given":"Ondřej","family":"Čepek","affiliation":"Department of Theoretical Computer Science and Mathematical Logic , Charles University in Prague , Faculty of Mathematics and Physics , Czech Republic"},{"name":"Štefan Gurský","slug":"stefan-gursky","given":"Štefan","family":"Gurský","affiliation":"Department of Theoretical Computer Science and Mathematical Logic , Charles University in Prague , Faculty of Mathematics and Physics , Czech Republic"},{"name":"Petr Kučera","slug":"petr-kucera","given":"Petr","family":"Kučera","affiliation":"Department of Theoretical Computer Science and Mathematical Logic , Charles University in Prague , Faculty of Mathematics and Physics , Czech Republic"}],"abstract":"A Boolean formula in conjunctive normal form (CNF) is called matched if the system of sets of variables which appear in individual clauses has a system of distinct representatives. We present here two results for matched CNFs: The first result is a shorter and simpler proof of the fact that Boolean minimization remains complete for the second level of polynomial hierarchy even if the input is restricted to matched CNFs. The second result is structural --- we show that  if a Boolean function f admits a representation by a matched CNF then every clause minimum CNF representation of f is matched.","doi":"10.24963/ijcai.2017/706","url":"https://ijcai.org/proceedings/2017/706","pdf":"https://ijcai.org/proceedings/2017/0706.pdf","markdown":"https://ijcai.org/proceedings/2017/706.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/706","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Journal track","track":"Journal track","number":706,"pages":{"first":4980,"last":4984},"keywords":["Constraints and Satisfiability: Constraint Optimisation","Constraints and Satisfiability: Satisfiability"],"videos":[],"references":[{"position":1,"raw":"[Aharoni and Linial, 1986] Ron Aharoni and Nathan Linial. 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