On interactive proofs with a laconic prover (extended abstract)

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 L̄ has a constant-round interactive proof of complexity that depends only exponentially on b. This provides the first evidence that for NPcomplete 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 L̄. © 2011 Springer-Verlag Berlin Heidelberg.