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 $\bar L$ 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 $\bar L$.
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Goldreich, O., Vadhan, S. & Wigderson, A. On interactive proofs with a laconic prover. comput. complex. 11, 1–53 (2002). https://doi.org/10.1007/s00037-002-0169-0
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DOI: https://doi.org/10.1007/s00037-002-0169-0
Keywords.
- Interactive proof systems
- Arthur-Merlin games
- NP
- sampling protocols
- statistical zero-knowledge
- game theory