{"title":"On reductions of NP sets to sparse sets","authors":"S. Homer, L. Longpré","doi":"10.1109/SCT.1991.160246","DOIUrl":null,"url":null,"abstract":"M. Ogiwara and O. Watanabe (1990) showed that if SAT is bounded truth-table reducible to a sparse set, then P=NP. In the present work, the authors simplify their proof, strengthen the result, and use it to obtain several new results. Among the new results are the following: applications of the main theorem to log-truth-table and log-Turing reductions of NP sets to sparse sets; generalizations of the main theorem which yield results similar to the main result at arbitrary levels of the polynomial hierarchy; and the construction of an oracle relative to which P not=NP but there are NP-complete sets which are f(n)-tt-reducible to a tally set, for any f(n) in Omega (log n).<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"55","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SCT.1991.160246","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 55
Abstract
M. Ogiwara and O. Watanabe (1990) showed that if SAT is bounded truth-table reducible to a sparse set, then P=NP. In the present work, the authors simplify their proof, strengthen the result, and use it to obtain several new results. Among the new results are the following: applications of the main theorem to log-truth-table and log-Turing reductions of NP sets to sparse sets; generalizations of the main theorem which yield results similar to the main result at arbitrary levels of the polynomial hierarchy; and the construction of an oracle relative to which P not=NP but there are NP-complete sets which are f(n)-tt-reducible to a tally set, for any f(n) in Omega (log n).<>
M. Ogiwara和O. Watanabe(1990)证明了如果SAT是可约为稀疏集的有界真值表，则P=NP。在本工作中，作者简化了他们的证明，加强了结果，并利用它得到了几个新的结果。这些新结果包括:主要定理在NP集的对数真值表和对数图灵约简中的应用;主要定理的推广，其结果与多项式层次的任意层次上的主要结果相似;以及P不=NP的oracle的构造，但存在NP完备集，f(n)-tt-可约为一个计数集，对于(log n)中的任意f(n)
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