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On Interactive Proofs with a Laconic Prover

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Automata, Languages and Programming (ICALP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

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Abstract

We continue the investigation of interactive proofs with bounded communication, as initiated by Goldreich and Håstad (IPL 1998). Let L be a language that has an interactive proof in which the prover sends few (say b) bits to the verifier. We prove that the complement L has a constant-round interactive proof of complexity that depends only exponentially on b. This provides the first evidence that for NP- complete languages, we cannot expect interactive provers to be much more “laconic” than the standard NP proof.

When the proof system is further restricted (e.g., when b = 1, or when we have perfect completeness), we get significantly better upper bounds on the complexity of L.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel

    Oded Goldreich

  2. Division of Engineering & Applied Sciences, Harvard University, Cambridge, MA

    Salil Vadhan

  3. School of Mathematics, Institute for Advanced Study, Princeton, NJ

    Avi Wigderson

Authors
  1. Oded Goldreich
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  2. Salil Vadhan
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  3. Avi Wigderson
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Goldreich, O., Vadhan, S., Wigderson, A. (2001). On Interactive Proofs with a Laconic Prover. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_28

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  • DOI: https://doi.org/10.1007/3-540-48224-5_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

  • eBook Packages: Springer Book Archive

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