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On helping and interactive proof systems

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Algorithms and Computation (ISAAC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 834))

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Abstract

We investigate the complexity of honest provers in interactive proof systems. This corresponds precisely to the complexity of oracles helping the computation of robust probabilistic oracle machines. We obtain upper bounds for languages in FewEXP and for sparse sets in NP. Further, interactive protocols with provers that are reducible to sets of low information content are considered. Specifically, if the verifier communicates only with provers in P/poly, then the accepted language is low for ∑ p2 . In the case that the provers are polynomial-time reducible to log*-sparse sets or to sets in strong-P/log then the protocol can be simulated by the verifier even without the help of provers. As a consequence we obtain new collapse results under the assumption that intractable sets reduce to sets with low information content.

Part of the work was done while visiting Universität Ulm. Supported in part by an Alexander von Humboldt research fellowship.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Institute of Mathematical Sciences, Madras, India

    V. Arvind

  2. Theoretische Informatik, Universität Ulm, D-89069, Ulm, Germany

    J. Köbler & R. Schuler

Authors
  1. V. Arvind
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  2. J. Köbler
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  3. R. Schuler
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Ding-Zhu Du Xiang-Sun Zhang

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© 1994 Springer-Verlag Berlin Heidelberg

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Arvind, V., Köbler, J., Schuler, R. (1994). On helping and interactive proof systems. In: Du, DZ., Zhang, XS. (eds) Algorithms and Computation. ISAAC 1994. Lecture Notes in Computer Science, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58325-4_175

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  • DOI: https://doi.org/10.1007/3-540-58325-4_175

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58325-7

  • Online ISBN: 978-3-540-48653-4

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