{"title":"减少谎言","authors":"L. Adleman, Kenneth L. Manders","doi":"10.1109/SFCS.1979.35","DOIUrl":null,"url":null,"abstract":"All of the reductions currently used in complexity theory (≤p, ≤γ, ≤R) have the property that they are honest. If A ≤ B then whatever machine M reduces A to B is such that: if on input x, M outputs y then x ε A ↔ y ε B. It would appear that this membership preserving property is intrinsic to the notion of reduction. We will see that it is not. We introduce reductions that lie and sometimes produce outputs y ε B when x ? A. We will use these reductions to further clarify the computational complexity of some problems raised by Gauss.","PeriodicalId":311166,"journal":{"name":"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)","volume":"78 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1979-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"25","resultStr":"{\"title\":\"Reductions that lie\",\"authors\":\"L. Adleman, Kenneth L. Manders\",\"doi\":\"10.1109/SFCS.1979.35\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"All of the reductions currently used in complexity theory (≤p, ≤γ, ≤R) have the property that they are honest. If A ≤ B then whatever machine M reduces A to B is such that: if on input x, M outputs y then x ε A ↔ y ε B. It would appear that this membership preserving property is intrinsic to the notion of reduction. We will see that it is not. We introduce reductions that lie and sometimes produce outputs y ε B when x ? A. We will use these reductions to further clarify the computational complexity of some problems raised by Gauss.\",\"PeriodicalId\":311166,\"journal\":{\"name\":\"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)\",\"volume\":\"78 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1979-10-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"25\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1979.35\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"20th Annual Symposium on Foundations of Computer Science (sfcs 1979)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1979.35","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
All of the reductions currently used in complexity theory (≤p, ≤γ, ≤R) have the property that they are honest. If A ≤ B then whatever machine M reduces A to B is such that: if on input x, M outputs y then x ε A ↔ y ε B. It would appear that this membership preserving property is intrinsic to the notion of reduction. We will see that it is not. We introduce reductions that lie and sometimes produce outputs y ε B when x ? A. We will use these reductions to further clarify the computational complexity of some problems raised by Gauss.
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