{"title":"用并行求解csp约束简洁证明系统","authors":"Jason Li, R. O'Donnell","doi":"10.1145/3087556.3087557","DOIUrl":null,"url":null,"abstract":"We show that the basic semidefinite programming relaxation value of any constraint satisfaction problem can be computed in NC; that is, in parallel polylogarithmic time and polynomial work. As a complexity-theoretic consequence we get that \\MIPone[k,c,s] \\subseteq \\PSPACE provided s/c \\leq (.62-o(1))k/2^k, resolving a question of Austrin, H\\aa stad, and Pass. Here \\MIPone[k,c,s] is the class of languages decidable with completeness c and soundness s by an interactive proof system with k provers, each constrained to communicate just 1 bit.","PeriodicalId":162994,"journal":{"name":"Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures","volume":"103 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Bounding Laconic Proof Systems by Solving CSPs in Parallel\",\"authors\":\"Jason Li, R. O'Donnell\",\"doi\":\"10.1145/3087556.3087557\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the basic semidefinite programming relaxation value of any constraint satisfaction problem can be computed in NC; that is, in parallel polylogarithmic time and polynomial work. As a complexity-theoretic consequence we get that \\\\MIPone[k,c,s] \\\\subseteq \\\\PSPACE provided s/c \\\\leq (.62-o(1))k/2^k, resolving a question of Austrin, H\\\\aa stad, and Pass. Here \\\\MIPone[k,c,s] is the class of languages decidable with completeness c and soundness s by an interactive proof system with k provers, each constrained to communicate just 1 bit.\",\"PeriodicalId\":162994,\"journal\":{\"name\":\"Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures\",\"volume\":\"103 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3087556.3087557\",\"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 29th ACM Symposium on Parallelism in Algorithms and Architectures","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3087556.3087557","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bounding Laconic Proof Systems by Solving CSPs in Parallel
We show that the basic semidefinite programming relaxation value of any constraint satisfaction problem can be computed in NC; that is, in parallel polylogarithmic time and polynomial work. As a complexity-theoretic consequence we get that \MIPone[k,c,s] \subseteq \PSPACE provided s/c \leq (.62-o(1))k/2^k, resolving a question of Austrin, H\aa stad, and Pass. Here \MIPone[k,c,s] is the class of languages decidable with completeness c and soundness s by an interactive proof system with k provers, each constrained to communicate just 1 bit.
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