{"title":"NP-硬集是指数密集的，除非coNP C NP/poly","authors":"H. Buhrman, J. M. Hitchcock","doi":"10.1109/CCC.2008.21","DOIUrl":null,"url":null,"abstract":"We show that hard sets S for NP must have exponential density, i.e. |S=n| ges 2nepsi for some isin > 0 and infinitely many n, unless coNP sube NP/poly and the polynomial-time hierarchy collapses. This result holds for Turing reductions that make n1-isin queries. In addition we study the instance complexity o/NP- hard problems and show that hard sets also have an exponential amount of instances that have instance complexity n for some sigma > 0. This result also holds for Turing reductions that make n1-isin queries.","PeriodicalId":338061,"journal":{"name":"2008 23rd Annual IEEE Conference on Computational Complexity","volume":"70 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"32","resultStr":"{\"title\":\"NP-Hard Sets Are Exponentially Dense Unless coNP C NP/poly\",\"authors\":\"H. Buhrman, J. M. Hitchcock\",\"doi\":\"10.1109/CCC.2008.21\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that hard sets S for NP must have exponential density, i.e. |S=n| ges 2nepsi for some isin > 0 and infinitely many n, unless coNP sube NP/poly and the polynomial-time hierarchy collapses. This result holds for Turing reductions that make n1-isin queries. In addition we study the instance complexity o/NP- hard problems and show that hard sets also have an exponential amount of instances that have instance complexity n for some sigma > 0. This result also holds for Turing reductions that make n1-isin queries.\",\"PeriodicalId\":338061,\"journal\":{\"name\":\"2008 23rd Annual IEEE Conference on Computational Complexity\",\"volume\":\"70 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"32\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2008 23rd Annual IEEE Conference on Computational Complexity\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CCC.2008.21\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2008 23rd Annual IEEE Conference on Computational Complexity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CCC.2008.21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
NP-Hard Sets Are Exponentially Dense Unless coNP C NP/poly
We show that hard sets S for NP must have exponential density, i.e. |S=n| ges 2nepsi for some isin > 0 and infinitely many n, unless coNP sube NP/poly and the polynomial-time hierarchy collapses. This result holds for Turing reductions that make n1-isin queries. In addition we study the instance complexity o/NP- hard problems and show that hard sets also have an exponential amount of instances that have instance complexity n for some sigma > 0. This result also holds for Turing reductions that make n1-isin queries.
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