Error reduction by parallel repetition-the state of the art
Uriel Feige · 1995
We show that no fixed number of parallel repetitions suffices in order to reduce the error in two-prover one-round proof systems from one constant to another. Our results imply that the recent bounds proven by Ran Raz, showing that the number of rounds that suffice is inversely proportional to the answer length, are nearly best possible. Our proof technique builds upon an idea of Oleg Verbitsky. We use this opportunity to survey the known results on parallel repetition, and to present the proofs of some previously claimed theorems. 1 Introduction A two prover one round proof system [8], MIP(2,1), is a protocol by which two provers jointly try to convince a computationally limited probabilistic verifier that a common input belongs to a prespecified language. The verifier selects a pair of questions at random. Each prover sees only one of the two questions, and sends back an answer. The verifier evaluates a predicate on the common input and the two questions and answers, and accepts or ...