Randomness-efficient oblivious sampling

Abstract

We introduce a natural notion of obliviousness of a sampling procedure, and construct a randomness-efficient oblivious sampler. Our sampler uses (equation presented) We apply this sampling procedure to reduce the randomness required to halve the number of rounds of interaction in an Arthur Merlin proof system. Given a 2g(n) round AM proof for L in which Arthur sends l(n) coins per round and Merlin responds with a q(n) bit string, we construct a g(n) round AM proof for L in which Arthur sends O(l+ (q + log g) • log l) coins per round and Merlin responds with a poly(n) bit string.