Probabilistic checking of proofs; a new characterization of NP

S. Arora, S. Safra
1992 Proceedings., 33rd Annual Symposium on Foundations of Computer Science  
We give a new characterization of NP: the class NP contains exactly those languages L for which membership proofs (a proof that an input x is in L) can be verified probabilistically in polynomial time using logarithmic number of random bits and by reading sublogarithmic 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.
doi:10.1109/sfcs.1992.267824 dblp:conf/focs/AroraS92 fatcat:l656u6jahzbg5dt4x64obgignm