{"title":"通过两个查询问题的应用证明SAT没有小电路","authors":"L. Fortnow, A. Pavan, Samik Sengupta","doi":"10.1109/CCC.2003.1214433","DOIUrl":null,"url":null,"abstract":"We show that if SAT does not have small circuits, then there must exist a small number of formulas such that every small circuit fails to compute satisfiability correctly on at least one of these formulas. We use this result to show that if P/sup NP[1]/=P/sup NP[2]/, then the polynomial-time hierarchy collapses to S/sub 2//sup P//spl sube//spl Sigma//sub 2//sup p//spl cap//spl Pi//sub 2//sup p/. Even showing that the hierarchy collapsed to /spl Sigma//sub 2//sup p/ remained open.","PeriodicalId":286846,"journal":{"name":"18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.","volume":"49 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2003-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"23","resultStr":"{\"title\":\"Proving SAT does not have small circuits with an application to the two queries problem\",\"authors\":\"L. Fortnow, A. Pavan, Samik Sengupta\",\"doi\":\"10.1109/CCC.2003.1214433\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that if SAT does not have small circuits, then there must exist a small number of formulas such that every small circuit fails to compute satisfiability correctly on at least one of these formulas. We use this result to show that if P/sup NP[1]/=P/sup NP[2]/, then the polynomial-time hierarchy collapses to S/sub 2//sup P//spl sube//spl Sigma//sub 2//sup p//spl cap//spl Pi//sub 2//sup p/. Even showing that the hierarchy collapsed to /spl Sigma//sub 2//sup p/ remained open.\",\"PeriodicalId\":286846,\"journal\":{\"name\":\"18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.\",\"volume\":\"49 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2003-07-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"23\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CCC.2003.1214433\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CCC.2003.1214433","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Proving SAT does not have small circuits with an application to the two queries problem
We show that if SAT does not have small circuits, then there must exist a small number of formulas such that every small circuit fails to compute satisfiability correctly on at least one of these formulas. We use this result to show that if P/sup NP[1]/=P/sup NP[2]/, then the polynomial-time hierarchy collapses to S/sub 2//sup P//spl sube//spl Sigma//sub 2//sup p//spl cap//spl Pi//sub 2//sup p/. Even showing that the hierarchy collapsed to /spl Sigma//sub 2//sup p/ remained open.
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