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 used 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 (1992) characterized NP as PCP(log n, (loglogn)^O(1)). The authors improve on their result by showing that NP=PCP(logn, 1). The result has the following consequences: (1) MAXSNP-hard problems (e.g. metric TSP, MAX-SAT, MAX-CUT) do not have polynomial time approximation schemes unless P=NP; and (2) for some ε>0 the size of the maximal clique in a graph cannot be approximated within a factor of n^ε unless P=NP