{"title":"One-Way Functions and the Berman-Hartmanis Conjecture","authors":"Manindra Agrawal, O. Watanabe","doi":"10.1109/CCC.2009.17","DOIUrl":null,"url":null,"abstract":"The Berman-Hartmanis conjecture states that all NP-complete sets are P-isomorphic each other. On this conjecture, we first improve the previous result of Agrawal and show that all NP-complete sets are P/poly-time computable 1,li-reducible to each other based on the assumption that there exist regular one-way functions that cannot be inverted by randomized polynomial-time algorithms. Secondly, we show that, besides the above assumption, if all one-way functions have some easy part to invert, then all NP-complete sets are P/poly-isomorphic to each other.","PeriodicalId":158572,"journal":{"name":"2009 24th Annual IEEE Conference on Computational Complexity","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 24th Annual IEEE Conference on Computational Complexity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CCC.2009.17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 10
Abstract
The Berman-Hartmanis conjecture states that all NP-complete sets are P-isomorphic each other. On this conjecture, we first improve the previous result of Agrawal and show that all NP-complete sets are P/poly-time computable 1,li-reducible to each other based on the assumption that there exist regular one-way functions that cannot be inverted by randomized polynomial-time algorithms. Secondly, we show that, besides the above assumption, if all one-way functions have some easy part to invert, then all NP-complete sets are P/poly-isomorphic to each other.
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