{"title":"梅林-亚瑟游戏的二次模拟","authors":"Thomas Watson","doi":"10.1145/3389399","DOIUrl":null,"url":null,"abstract":"The known proofs of MA ⊆ PP incur a quadratic overhead in the running time. We prove that this quadratic overhead is necessary for black-box simulations; in particular, we obtain an oracle relative to which MA-TIME (t) ⊈ P-TIME (o(t2)). We also show that 2-sided-error Merlin–Arthur games can be simulated by 1-sided-error Arthur–Merlin games with quadratic overhead. We also present a simple, query complexity based proof (provided by Mika Göös) that there is an oracle relative to which MA ⊈ NPBPP (which was previously known to hold by a proof using generics).","PeriodicalId":198744,"journal":{"name":"ACM Transactions on Computation Theory (TOCT)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quadratic Simulations of Merlin–Arthur Games\",\"authors\":\"Thomas Watson\",\"doi\":\"10.1145/3389399\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The known proofs of MA ⊆ PP incur a quadratic overhead in the running time. We prove that this quadratic overhead is necessary for black-box simulations; in particular, we obtain an oracle relative to which MA-TIME (t) ⊈ P-TIME (o(t2)). We also show that 2-sided-error Merlin–Arthur games can be simulated by 1-sided-error Arthur–Merlin games with quadratic overhead. We also present a simple, query complexity based proof (provided by Mika Göös) that there is an oracle relative to which MA ⊈ NPBPP (which was previously known to hold by a proof using generics).\",\"PeriodicalId\":198744,\"journal\":{\"name\":\"ACM Transactions on Computation Theory (TOCT)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-04-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Transactions on Computation Theory (TOCT)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3389399\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Transactions on Computation Theory (TOCT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3389399","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The known proofs of MA ⊆ PP incur a quadratic overhead in the running time. We prove that this quadratic overhead is necessary for black-box simulations; in particular, we obtain an oracle relative to which MA-TIME (t) ⊈ P-TIME (o(t2)). We also show that 2-sided-error Merlin–Arthur games can be simulated by 1-sided-error Arthur–Merlin games with quadratic overhead. We also present a simple, query complexity based proof (provided by Mika Göös) that there is an oracle relative to which MA ⊈ NPBPP (which was previously known to hold by a proof using generics).
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