We continue the investigation of interactive proofs with bounded communication, as initiated by Goldreich and Hastad (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 {em 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 (eg when b = 1 , or when we have perfect completeness), we get significantly better upper bounds on the complexity of L .
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