On the Complexity of Space Bounded Interactive Proofs (Extended Abstract)

We prove two results on interactive proof systems with 2-way probabilistic finite state verifiers. The first is a lower bound on the power of such proof systems, if they are not required to halt with high probability on rejected inputs: we show that they can accept any recursively enumerable language. The second is an upper bound on the power of interactive proof systems that halt with high probability on all inputs: any language they accept is in ATIME(22 O(n) ). Our results generalize to other space bounds. The proof techniques we develop have other interesting applications. The proof method for the lower bound also shows that the emptiness problem for 1-way probabilistic finite state machines is undecidable. In proving the upper bound, we obtain some results of independent interest on the rate of convergence of time-varying Markov chains and of non-Markov chains, called feedback chains, to their halting states.