{"type":"ScholarlyArticle","title":"Minimization for Generalized Boolean Formulas","authors":[{"name":"Edith Hemaspaandra","slug":"edith-hemaspaandra","given":"Edith","family":"Hemaspaandra","affiliation":""},{"name":"Henning Schnoor","slug":"henning-schnoor","given":"Henning","family":"Schnoor","affiliation":""}],"abstract":"The minimization problem for propositional formulas is an important optimization problem in the second level of the polynomial hierarchy. In general, the problem is Sigma-2-complete under Turing reductions, but restricted versions are tractable. We study the complexity of minimization for formulas in two established frameworks for restricted propositional logic: The Post framework allowing arbitrarily nested formulas over a set of Boolean connectors, and the constraint setting, allowing generalizations of CNF formulas. In the Post case, we obtain a dichotomy result: Minimization is solvable in polynomial time or coNP-hard. This result also applies to Boolean circuits. For CNF formulas, we obtain new minimization algorithms for a large class of formulas, and give strong evidence that we have covered all polynomial-time cases.","doi":"10.5591/978-1-57735-516-8/IJCAI11-102","url":"https://ijcai.org/proceedings/2011/102","pdf":"https://ijcai.org/proceedings/2011/0102.pdf","markdown":"https://ijcai.org/proceedings/2011/102.md","bibtex":"https://ijcai.org/proceedings/2011/bibtex/102","volume":{"slug":"2011","title":"Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2011","url":"https://ijcai.org/proceedings/2011/","year":2011,"location":"Barcelona, Catalonia, Spain","dates":"16–22 July 2011","editors":"Toby Walsh","isbn":"978-1-57735-512-0; 978-1-57735-513-7; 978-1-57735-514-4; 978-1-57735-515-1; 978-1-57735-516-8","publisher":"AAAI Press/International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":102,"pages":{"first":566,"last":570},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}