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Observations on measure and lowness for Δ P2

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Abstract

Assuming thatk≥2 and Δ /P k does not have p-measure 0, it is shown that BP · Δ /P k =Δ /P k . This implies that the following conditions hold if Δ P2 does not have p-measure 0:

  1. (i)

    AM ∩ co-AM is low for Δ P2 . (Thus BPP and the graph isomorphism problem are low for Δ P2 .)

  2. (ii)

    If Δ P2 ≠ PH, then NP does not have polynomial-size circuits.

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Authors and Affiliations

  1. Department of Computer Science, Iowa State University, 50011, Ames, IA, USA

    J. H. Lutz

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  1. J. H. Lutz
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Additional information

This research was supported in part by National Science Foundation Grant CCR-9157382, with matching funds from Rockwell International, Microware Systems Corporation, and Amoco Foundation.

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Lutz, J.H. Observations on measure and lowness for Δ P2 . Theory of Computing Systems 30, 429–442 (1997). https://doi.org/10.1007/BF02679469

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