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Graph Isomorphism Is Low for ZPP(NP) and Other Lowness Results

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STACS 2000 (STACS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1770))

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Abstract

We show the following new lowness results for the probabilistic class ZPPNP.

  • The class AM ∩ coAM is low for ZPPNP. As a consequence it follows that Graph Isomorphism and several group-theoretic problems known to be in AM ∩ coAM are low for ZPPNP.

  • The class IP[P/poly], consisting of sets that have interactive proof systems with honest provers in P/poly, is also low for ZPPNP.

We consider lowness properties of nonuniform function classes, namely, NPMV/poly, NPSV/poly, NPMVt/poly, and NPSVt/poly. Specifically, we show that

  • Sets whose characteristic functions are in NPSV/poly and that have program checkers (in the sense of [8]) are low for AM and ZPPNP.

  • Sets whose characteristic functions are in NPMVt/poly are low for Σ p2

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Author information

Authors and Affiliations

  1. Institute of Mathematical Sciences, C.I.T Campus, Chennai, 600113, India

    Vikraman Arvind

  2. Institut für Informatik, Humboldt-Universität zu Berlin, D-10099, Berlin, Germany

    Johannes Köbler

Authors
  1. Vikraman Arvind
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  2. Johannes Köbler
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dept. of Theoretical Computer Science, Universität Dresden, 01062, Dresden, Germany

    Horst Reichel

  2. Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA, 59655, Villeneuve d’ASCQ Cedex, France

    Sophie Tison

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Arvind, V., Köbler, J. (2000). Graph Isomorphism Is Low for ZPP(NP) and Other Lowness Results. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_36

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  • DOI: https://doi.org/10.1007/3-540-46541-3_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67141-1

  • Online ISBN: 978-3-540-46541-6

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