Proving properties of interactive proofs by a generalized counting technique

Abstract

The problem of proving membership in languages accepted by interactive proof protocols is reduced to the problem of estimating the number of leaves in certain trees. Using this reduction, we present a direct proof that every language accepted by an interactive protocol whithin g(n) rounds is also accepted by an Arthur Merlin game within ⌈$\text{g(n)}\text{2}$⌉ rounds. This unifies the proofs of the two main positive results on the IP Hierarchy, namely: that private coin tossing can be replaced by public coin tossing, and that the numer of interactions can be reduced by a constant factor.