{"title":"大k的可满足性猜想的证明","authors":"Jian Ding, A. Sly, Nike Sun","doi":"10.1145/2746539.2746619","DOIUrl":null,"url":null,"abstract":"We establish the satisfiability threshold for random k-SAT for all k ≥ k0. That is, there exists a limiting density αs(k) such that a random k-SAT formula of clause density α is with high probability satisfiable for α < αs, and unsatisfiable for α > αs. The satisfiability threshold αs is given explicitly by the one-step replica symmetry breaking (1SRB) prediction from statistical physics. We believe that our methods may apply to a range of random constraint satisfaction problems in the 1RSB class.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"73 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2014-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"176","resultStr":"{\"title\":\"Proof of the Satisfiability Conjecture for Large k\",\"authors\":\"Jian Ding, A. Sly, Nike Sun\",\"doi\":\"10.1145/2746539.2746619\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish the satisfiability threshold for random k-SAT for all k ≥ k0. That is, there exists a limiting density αs(k) such that a random k-SAT formula of clause density α is with high probability satisfiable for α < αs, and unsatisfiable for α > αs. The satisfiability threshold αs is given explicitly by the one-step replica symmetry breaking (1SRB) prediction from statistical physics. We believe that our methods may apply to a range of random constraint satisfaction problems in the 1RSB class.\",\"PeriodicalId\":20566,\"journal\":{\"name\":\"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing\",\"volume\":\"73 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"176\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2746539.2746619\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2746539.2746619","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Proof of the Satisfiability Conjecture for Large k
We establish the satisfiability threshold for random k-SAT for all k ≥ k0. That is, there exists a limiting density αs(k) such that a random k-SAT formula of clause density α is with high probability satisfiable for α < αs, and unsatisfiable for α > αs. The satisfiability threshold αs is given explicitly by the one-step replica symmetry breaking (1SRB) prediction from statistical physics. We believe that our methods may apply to a range of random constraint satisfaction problems in the 1RSB class.
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