Proof Verification and the Hardness of Approximation Problems

@article{Arora1998ProofVA,
title={Proof Verification and the Hardness of Approximation Problems},
author={Sanjeev Arora and Carsten Lund and Rajeev Motwani and Madhu Sudan and Mario Szegedy},
journal={Electronic Colloquium on Computational Complexity (ECCC)},
year={1998},
volume={5}
}

We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probability 1 (i.e., for every choice of its random string). For strings not in the language, the verifier rejects every provided “proof” with probability at least 1/2. Our result builds upon and improves a… CONTINUE READING