Proof verification and the hardness of approximation problems

@article{Arora1998ProofVA,
  title={Proof verification and the hardness of approximation problems},
  author={Sanjeev Arora and C. Lund and R. Motwani and M. Sudan and M. Szegedy},
  journal={J. ACM},
  year={1998},
  volume={45},
  pages={501-555}
}
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… Expand
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