{"type":"ScholarlyArticle","title":"Combining the k-CNF and XOR Phase-Transitions","authors":[{"name":"Jeffrey M. Dudek","slug":"jeffrey-m-dudek","given":"Jeffrey M.","family":"Dudek","affiliation":""},{"name":"Kuldeep S. Meel","slug":"kuldeep-s-meel","given":"Kuldeep S.","family":"Meel","affiliation":""},{"name":"Moshe Y. Vardi","slug":"moshe-y-vardi","given":"Moshe Y.","family":"Vardi","affiliation":""}],"abstract":"The runtime performance of modern SAT solvers on random k-CNF formulas is deeply connected with the 'phase-transition' phenomenon seen empirically in the satisfiability of random k-CNF formulas. Recent universal hashing-based approaches to sampling and counting crucially depend on the runtime performance of SAT solvers on formulas expressed as the conjunction of both k-CNF and XOR constraints (known as k-CNF-XOR formulas), but the behavior of random k-CNF-XOR formulas is unexplored in prior work. In this paper, we present the first study of the satisfiability of random k-CNF-XOR formulas. We show empirical evidence of a surprising phase-transition that follows a linear trade-off between k-CNF and XOR constraints. Furthermore, we prove that a phase-transition for k-CNF-XOR formulas exists for k = 2 and (when the number of k-CNF constraints is small) for k > 2.","doi":null,"url":"https://ijcai.org/proceedings/2016/109","pdf":"https://ijcai.org/proceedings/2016/0109.pdf","markdown":"https://ijcai.org/proceedings/2016/109.md","bibtex":"https://ijcai.org/proceedings/2016/bibtex/109","volume":{"slug":"2016","title":"Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2016","url":"https://ijcai.org/proceedings/2016/","year":2016,"location":"New York, NY, USA","dates":"9–15 July 2016","editors":"Subbarao Kambhampati","isbn":"978-1-57735-770-4; 978-1-57735-771-1","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":109,"pages":{"first":727,"last":733},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}