computational complexity

, Volume 11, Issue 1–2, pp 1–53 | Cite as

On interactive proofs with a laconic prover

  • Oded GoldreichEmail author
  • Salil Vadhan
  • Avi Wigderson
Original Article


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 $\bar L$.


Interactive proof systems Arthur-Merlin games NP sampling protocols statistical zero-knowledge game theory 

Mathematics Subject Classification (2000).

68Q05 68Q10 68Q15 91A05 


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Copyright information

© Birkhäuser-Verlag 2002

Authors and Affiliations

  1. 1.Department of Computer Science and Applied MathematicsWeizmann Institute of ScienceRehovotIsrael
  2. 2.Division of Engineering and Applied SciencesHarvard UniversityCambridgeUSA
  3. 3.Institute for Advanced StudyPrincetonUSA

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