# On Interactive Proofs with a Laconic Prover

Oded Goldreich, Salil Vadhan, and Avi Wigderson

### 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 $\bar L$ 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 $\bar L$.

### Versions

• Automata, Languages, and Programming - 28th International Colloquium, vol. 2076 of Lecture Notes for Computer Science, pp. 334-345, Crete, Greece, July 7-11, 2001. Springer-Verlag.
• Electronic Colloquium on Computational Complexity TR01-046, July 2, 2001.
• Computational Complexity 11, pages 1-53, 2002.  [postscript][pdf][official CC page]

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