{"title":"S/sub 2/ ZPP/sup NP/","authors":"Jin-Yi Cai","doi":"10.1109/SFCS.2001.959938","DOIUrl":null,"url":null,"abstract":"We show that the class Sp2 is a subclass of ZPP . The proof uses universal hashing, approximate counting and witness sampling. As a consequence, a collapse first noticed by Samik Sengupta that the assumption NP has small circuits collapses PH to Sp2 becomes the strongest version to date of the Karp-Lipton Theorem. We also discuss the problem of finding irrefutable proofs for Sp2 in ZPP .","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"S/sub 2/ ZPP/sup NP/\",\"authors\":\"Jin-Yi Cai\",\"doi\":\"10.1109/SFCS.2001.959938\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the class Sp2 is a subclass of ZPP . The proof uses universal hashing, approximate counting and witness sampling. As a consequence, a collapse first noticed by Samik Sengupta that the assumption NP has small circuits collapses PH to Sp2 becomes the strongest version to date of the Karp-Lipton Theorem. We also discuss the problem of finding irrefutable proofs for Sp2 in ZPP .\",\"PeriodicalId\":378126,\"journal\":{\"name\":\"Proceedings 2001 IEEE International Conference on Cluster Computing\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 2001 IEEE International Conference on Cluster Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.2001.959938\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 2001 IEEE International Conference on Cluster Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.2001.959938","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We show that the class Sp2 is a subclass of ZPP . The proof uses universal hashing, approximate counting and witness sampling. As a consequence, a collapse first noticed by Samik Sengupta that the assumption NP has small circuits collapses PH to Sp2 becomes the strongest version to date of the Karp-Lipton Theorem. We also discuss the problem of finding irrefutable proofs for Sp2 in ZPP .
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