On the Complexity of Interactive Proof with Bounded Communication

We investigate the computational complexity of languages which have interactive proof systems of bounded message complexity. In particular, denoting the length of the input by n, we show that If L has an interactive proof in which the total communication is bounded by c(n) bits then L can be recognized by a probabilistic machine in time exponential in O(c(n) + log(n)). If L has a public-coin interactive proof in which the prover sends c(n) bits then L can be recognized by a probabilistic machine in time exponential in O(c(n) log(c(n)) + log(n)). If L has an interactive proof in which the prover sends c(n) bits then L can be recognized by a probabilistic machine with an NP-oracle in time exponential in O(c(n) log(c(n))+ log(n)). Work done while being on a sabbatical leave at LCS, MIT.