On interactive proofs with a laconic prover

Authors:
Oded Goldreich;Salil Vadhan;Avi Wigderson
Affiliations:
Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel;Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA;Institute for Advanced Study, Princeton, NJ and Institute for Computer Science, Hebrew University, Jerusalem, Israel
Venue:
Computational Complexity
Year:
2002

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Abstract

We continue the investigation of interactive proofs with bounded communication, as initiated by Goldreich & Håstad (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.