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Results on resource-bounded measure

  • Harry Buhrman
  • Stephen Fenner
  • Lance Fortnow
Session 3: Computational Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1256)

Abstract

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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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Harry Buhrman
    • 1
  • Stephen Fenner
    • 2
  • Lance Fortnow
    • 3
  1. 1.Centrum voor Wiskunde en InformaticaGermany
  2. 2.University of Southern MaineUSA
  3. 3.CWI & The University of ChicagoUSA

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