Verifier Non-Locality in Interactive Proofs
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In multi-prover interactive proofs, the verifier interrogates the provers and attempts to steal their knowledge. Other than that, the verifier's role has not been studied. Augmentation of the provers with non-local resources results in classes of languages that may not be NEXP. We have discovered that the verifier plays a much more important role than previously thought. Simply put, the verifier has the capability of providing non-local resources for the provers intrinsically. Therefore, standard MIPs may already contain protocols equivalent to one in which the prover is augmented non-locally. Existing MIPs' proofs of soundness implicitly depend on the fact that the verifier is not a non-local resource provider. The verifier's non-locality is a new unused tool and liability for protocol design and analysis. Great care should have been taken when claiming that ZKMIP=MIP and MIP = NEXP. For the former case, we show specific issues with existing protocols and revisit the proof of this statement. For the latter case, we exhibit doubts that we do not fully resolve. To do this, we define a new model of multi-prover interactive proofs which we call "correlational confinement form".
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