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Observations on measure and lowness for Δ P2

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1046))

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Abstract

Assuming that k≥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.

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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Authors and Affiliations

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

    Jack H. Lutz

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  1. Jack H. Lutz
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Claude Puech Rüdiger Reischuk

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© 1996 Springer-Verlag Berlin Heidelberg

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Lutz, J.H. (1996). Observations on measure and lowness for Δ P2 . In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_8

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  • DOI: https://doi.org/10.1007/3-540-60922-9_8

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  • Print ISBN: 978-3-540-60922-3

  • Online ISBN: 978-3-540-49723-3

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