Proof Verification and Hardness of Approximation Problems

The class PCP(f(n), g(n)) consists of all languages L for which there exists a polynomial-time probabilistic oracle machine that uses O(f(n)) random bits, queries O(g(n)) bits of its oracle and behaves as follows: If x L then there exists an oracle y such that the machine accepts for all random choices but if x L then for every oracle y the machine rejects with high probability. Arora and Safra very recently characterized NP as PCP(log n, (log log n)O(1) ). We improve on their result by showing that NP = PCP(log n, 1). Our result has the following consequences:

• Type: Conference
• Year: 1992
• Where: FOCS
• Authors: Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, Mario Szegedy
• Keywords: FOCS 1992, Machine, Oracle, Polynomial-time Probabilistic Oracle, Theoretical Computer Science