Probabilistic checking of proofs: a new characterization of NP

We give a new characterization of NP: the class NP contains exactly those languages <italic>L</italic> for which membership proofs (a proof that an input <italic>x</italic> is in <italic>L</italic>) can be verified probabilistically in polynomial time using <italic>logarithmic</italic> number of random bits and by reading <italic>sublogarithmic</italic> number of bits from the proof. We discuss implications of this characterization; specifically, we show that approximating Clique and Independent Set, even in a very weak sense, is NP-hard.

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