{"title":"A pseudorandom oracle characterization of BPP","authors":"J. H. Lutz","doi":"10.1109/SCT.1991.160261","DOIUrl":null,"url":null,"abstract":"It is known from work of C.H. Bennett and J. Gill (1981) and K. Ambos-Spies (1986) that the following conditions are equivalent: (i) L in BPP; (ii); for almost all oracles A, l in P/sup A/. It is shown here that the following conditions are also equivalent to (i) and (ii): (iii) the set of oracles A for which L in P/sup A/ has pspace-measure 1; (iv) for every pspace-random oracle A, L in P/sup A/. It follows from this characterization that almost every A in DSPACE (2/sup poly/) is polynomial-time hard for BPP. Succinctly, the main content of the proof is that pseudorandom generators exist relative to every pseudorandom oracle.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"35 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"21","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SCT.1991.160261","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 21
Abstract
It is known from work of C.H. Bennett and J. Gill (1981) and K. Ambos-Spies (1986) that the following conditions are equivalent: (i) L in BPP; (ii); for almost all oracles A, l in P/sup A/. It is shown here that the following conditions are also equivalent to (i) and (ii): (iii) the set of oracles A for which L in P/sup A/ has pspace-measure 1; (iv) for every pspace-random oracle A, L in P/sup A/. It follows from this characterization that almost every A in DSPACE (2/sup poly/) is polynomial-time hard for BPP. Succinctly, the main content of the proof is that pseudorandom generators exist relative to every pseudorandom oracle.<>
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