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Logspace verifiers, NC, and NP

Extended abstract
  • Satyanarayana V. Lokam
  • Meena Mahajan
  • V. Vinay
Session 3A
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1004)

Abstract

We explore the connection between public-coin interactive proof systems with logspace verifiers and \(\mathcal{N}\mathcal{C}\)using two different approaches. In the first approach, we describe an interactive proof system for accepting any language in \(\mathcal{N}\mathcal{C}\)after a logspace reduction, where the verifier is logspace-bounded and the protocol requires polylog time. These results are proved by describing \(\mathcal{N}\mathcal{C}\)computations as computations over arithmetic circuits using maximum and average gates, and then translating the arithmetic circuits into interactive proof systems in a natural way. In the second approach, we give a characterization of \(\mathcal{N}\mathcal{C}\)in terms of interactive proof systems where the verifier is logspace-bounded and runs in polylog time. The equivalent interactive proof systems work with error-correcting encodings of inputs, using the polylogarithmically checkable codes introduced in the context of transparent proofs.

We also characterize \(\mathcal{N}\mathcal{C}\)and \(\mathcal{P}\mathcal{S}\mathcal{P}\mathcal{A}\mathcal{C}\mathcal{E}\)via public-coin interactive proof systems where the verifier is logspace-bounded, but has restricted access to auxiliary storage.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Satyanarayana V. Lokam
    • 1
  • Meena Mahajan
    • 2
  • V. Vinay
    • 3
  1. 1.Department of Computer ScienceThe University of ChicagoChicagoUSA
  2. 2.C.I.T. CampusThe Institute of Mathematical SciencesMadrasIndia
  3. 3.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia

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