{"type":"ScholarlyArticle","title":"Phase Transitions of Bounded Satisfiability Problems","authors":[{"name":"Delbert D. Bailey","slug":"delbert-d-bailey","given":"Delbert D.","family":"Bailey","affiliation":""},{"name":"Phokion G. Kolaitis","slug":"phokion-g-kolaitis","given":"Phokion G.","family":"Kolaitis","affiliation":""}],"abstract":"We investigate phase transitions for the family of bounded satisfiability problems 3SAT(b), recently introduced by Zhang, that ask: given a 3CNFformula, is there a truth assignment that violates no more than b of its clauses. Zhang's results were experimental and for a fixed number of variables (n = 25), and suggested that the locations of the phase transitions for 3SAT(b) are separated and move significantly as b increases. Analysis of these locations was posed as an open question . We analytically show that the phase transitions of all 3SAT(b) problems must occur within a narrow region, regardless of how large the value of b is. Moreover, our experiments reveal that the phase transitions for these problems occur in a remarkable way. Specifically, unlike 3SAT, the probability curves for 3SAT(b) do not have a quasi-common intersection point about which they rotate as they become steeper with increasing n. Instead, they move rapidly to the left toward the narrow region that the analysis predicts.","doi":null,"url":"https://ijcai.org/proceedings/2003/169","pdf":"https://ijcai.org/proceedings/2003/0169.pdf","markdown":"https://ijcai.org/proceedings/2003/169.md","bibtex":"https://ijcai.org/proceedings/2003/bibtex/169","volume":{"slug":"2003","title":"Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2003","url":"https://ijcai.org/proceedings/2003/","year":2003,"location":"Acapulco, Mexico","dates":"","editors":"Georg Gottlob","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":169,"pages":{"first":1187,"last":1192},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}