{"type":"ScholarlyArticle","title":"Finding the Hardest Formulas for Resolution (Extended Abstract)","authors":[{"name":"Tomáš Peitl","slug":"tomas-peitl","given":"Tomáš","family":"Peitl","affiliation":""},{"name":"Stefan Szeider","slug":"stefan-szeider","given":"Stefan","family":"Szeider","affiliation":""}],"abstract":"A CNF formula is harder than another CNF formula with the same\r\nnumber of clauses if it requires a longer resolution proof. We introduce\r\nresolution hardness numbers; they give for m=1,2,... the length\r\nof a shortest proof of a hardest formula on m clauses. We compute\r\nthe first ten resolution hardness numbers, along with the\r\ncorresponding hardest formulas.\r\nTo achieve this, we devise a candidate filtering and symmetry breaking\r\nsearch scheme for limiting the number of potential candidates for hardest\r\nformulas, and an efficient SAT encoding for computing a shortest\r\nresolution proof of a given candidate formula.","doi":"10.24963/ijcai.2021/657","url":"https://ijcai.org/proceedings/2021/657","pdf":"https://ijcai.org/proceedings/2021/0657.pdf","markdown":"https://ijcai.org/proceedings/2021/657.md","bibtex":"https://ijcai.org/proceedings/2021/bibtex/657","volume":{"slug":"2021","title":"Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2021","url":"https://ijcai.org/proceedings/2021/","year":2021,"location":"Montreal","dates":"19-27 August 2021","editors":"Prof. Zhi-Hua Zhou","isbn":"978-0-9992411-9-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2021"},"section":"Sister Conferences Best Papers","track":"Sister Conferences Best Papers","number":657,"pages":{"first":4814,"last":4818},"keywords":["Constraints and SAT: Constraint Satisfaction","Constraints and SAT: SAT: Algorithms and Techniques","Constraints and SAT: Constraints: Modeling, Solvers, Applications","Constraints and SAT: SAT: Solvers and Applications"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}