Observations on measure and lowness for Δ2P

Extended abstract
  • Jack H. Lutz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)


Assuming that k≥2 and Δ k P does not have p-measure 0, it is shown that BP · Δ k P k P . This implies that the following conditions hold if Δ 2 P does not have p-measure 0.
  1. (i)

    AM ∩ co-AM is low for Δ 2 P . (Thus BPP and the graph isomorphism problem are low for Δ> 2 P .)

  2. (ii)

    If Δ 2 P ≠ PH, then NP does not have polynomial-size circuits.



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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Jack H. Lutz
    • 1
  1. 1.Department of Computer ScienceIowa State UniversityAmes

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