Results on resource-bounded measure
We construct an oracle relative to which NP has p-measure 0 but Dp has measure 1 in EXP. This gives a strong relativized negative answer to a question posed by Lutz [Lut96]. Secondly, we give strong evidence that BPP is small. We show that BPP has p-measure 0 unless EXP=MA and thus the polynomial-time hierarchy collapses. This contrasts with the work of Regan et. al. [RSC95], where it is shown that P/poly does not have p-measure 0 if exponentially strong pseudorandom generators exist.
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