{"title":"NP-P中的稀疏集:EXPTIME与NEXPTIME","authors":"J. Hartmanis, N. Immerman, V. Sewelson","doi":"10.1016/S0019-9958(85)80004-8","DOIUrl":null,"url":null,"abstract":"<div><p>This paper investigates the structural properties of sets in <em>NP-P</em> and shows that the computational difficulty of lower density sets in <em>NP</em> depends explicitly on the relations between higher deterministic and nondeterministic time-bounded complexity classes. The paper exploits the recently discovered <em>upward separation</em> method, which shows for example that there exist sparse sets in <em>NP-P</em> if and only if <em>EXPTIME ≠ NEXPTIME</em>. In addition, the paper uses relativization techniques to determine logical possibilities, limitations of these proof techniques, and exhibits one of the first natural structural differences between relativized <em>NP</em> and <em>CoNP</em>.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1985-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(85)80004-8","citationCount":"0","resultStr":"{\"title\":\"Sparse sets in NP-P: EXPTIME versus NEXPTIME\",\"authors\":\"J. Hartmanis, N. Immerman, V. Sewelson\",\"doi\":\"10.1016/S0019-9958(85)80004-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper investigates the structural properties of sets in <em>NP-P</em> and shows that the computational difficulty of lower density sets in <em>NP</em> depends explicitly on the relations between higher deterministic and nondeterministic time-bounded complexity classes. The paper exploits the recently discovered <em>upward separation</em> method, which shows for example that there exist sparse sets in <em>NP-P</em> if and only if <em>EXPTIME ≠ NEXPTIME</em>. In addition, the paper uses relativization techniques to determine logical possibilities, limitations of these proof techniques, and exhibits one of the first natural structural differences between relativized <em>NP</em> and <em>CoNP</em>.</p></div>\",\"PeriodicalId\":38164,\"journal\":{\"name\":\"信息与控制\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1985-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0019-9958(85)80004-8\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"信息与控制\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019995885800048\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995885800048","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
This paper investigates the structural properties of sets in NP-P and shows that the computational difficulty of lower density sets in NP depends explicitly on the relations between higher deterministic and nondeterministic time-bounded complexity classes. The paper exploits the recently discovered upward separation method, which shows for example that there exist sparse sets in NP-P if and only if EXPTIME ≠ NEXPTIME. In addition, the paper uses relativization techniques to determine logical possibilities, limitations of these proof techniques, and exhibits one of the first natural structural differences between relativized NP and CoNP.
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