{"type":"ScholarlyArticle","title":"On the Satisfiability Threshold of Random Community-Structured SAT","authors":[{"name":"Dina Barak-Pelleg","slug":"dina-barak-pelleg","given":"Dina","family":"Barak-Pelleg","affiliation":"Department of Math , Ben-Gurion University of the Negev , Beer Sheva , Israel"},{"name":"Daniel Berend","slug":"daniel-berend","given":"Daniel","family":"Berend","affiliation":"Departments of Math and of Computer Science , Ben-Gurion University of the Negev , Beer Sheva , Israel"}],"abstract":"For both historical and practical reasons, the Boolean satisfiability\r\nproblem (SAT) has become one of central importance in computer science.\r\nOne type of instances arises when the clauses are chosen uniformly\r\nrandomly \\textendash{} random SAT. Here, a major problem, recently\r\nsolved for sufficiently large clause length, is the satisfiability\r\nthreshold conjecture. The value of this threshold is known exactly\r\nonly for clause length $2$, and there has been a lot of research\r\nconcerning its value for arbitrary fixed clause length.\r\n\r\nIn this paper, we endeavor to study the satisfiability threshold for random industrial SAT. There is as yet no generally accepted model of industrial SAT, and we confine ourselves to one of the more common features of industrial SAT: the set of variables consists of a number of disjoint communities,\r\nand clauses tend to consist of variables from the same community. \r\n\r\nOur main result is that the threshold of random community-structured SAT tends\r\nto be smaller than its counterpart for random SAT. Moreover, under\r\nsome conditions, this threshold even vanishes.","doi":"10.24963/ijcai.2018/174","url":"https://ijcai.org/proceedings/2018/174","pdf":"https://ijcai.org/proceedings/2018/0174.pdf","markdown":"https://ijcai.org/proceedings/2018/174.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/174","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Constraints and SAT","track":"Main track","number":174,"pages":{"first":1249,"last":1255},"keywords":["Constraints and SAT: SAT","Constraints and SAT: Constraints and SAT","Constraints and SAT: Constraint Satisfaction"],"videos":[],"references":[{"position":1,"raw":"[Achlioptas and Peres, 2004] Dimitris Achlioptas and Yuval Peres. \"The threshold for random k-SAT is 2 k ln 2 - O(k)\". 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