{"title":"论SAT的复杂性","authors":"R. Lipton, Anastasios Viglas","doi":"10.1109/SFFCS.1999.814618","DOIUrl":null,"url":null,"abstract":"We show that non-deterministic time NTIME(n) is not contained in deterministic time n/sup 2-/spl epsiv// and polylogarithmic space, for any /spl epsiv/>0. This implies that (infinitely often), satisfiability cannot be solved in time O(n/sup 2-/spl epsiv//) and polylogarithmic space. A similar result is presented for uniform circuits; a log-space uniform circuit of polylogarithmic width computing satisfiability requires infinitely often almost quadratic size.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"67","resultStr":"{\"title\":\"On the complexity of SAT\",\"authors\":\"R. Lipton, Anastasios Viglas\",\"doi\":\"10.1109/SFFCS.1999.814618\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that non-deterministic time NTIME(n) is not contained in deterministic time n/sup 2-/spl epsiv// and polylogarithmic space, for any /spl epsiv/>0. This implies that (infinitely often), satisfiability cannot be solved in time O(n/sup 2-/spl epsiv//) and polylogarithmic space. A similar result is presented for uniform circuits; a log-space uniform circuit of polylogarithmic width computing satisfiability requires infinitely often almost quadratic size.\",\"PeriodicalId\":385047,\"journal\":{\"name\":\"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"67\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFFCS.1999.814618\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFFCS.1999.814618","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We show that non-deterministic time NTIME(n) is not contained in deterministic time n/sup 2-/spl epsiv// and polylogarithmic space, for any /spl epsiv/>0. This implies that (infinitely often), satisfiability cannot be solved in time O(n/sup 2-/spl epsiv//) and polylogarithmic space. A similar result is presented for uniform circuits; a log-space uniform circuit of polylogarithmic width computing satisfiability requires infinitely often almost quadratic size.
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