Interactive Proof Systems

We show a rough equivalence between alternating time-space complexity and a public-coin interactive proof system with the veriier having a polynomial related time-space complexity. Special cases include All of NC has interactive proofs with a log-space polynomial-time public-coin veriier vastly improving the best previous lower bound of LOGCFL for this model 7]. All languages in P have interactive proofs with a polynomial-time public-coin veriier using o(log 2 n) space. All exponential-time languages have interactive proof systems with public-coin polynomial-space exponential-time veriiers. To achieve better bounds, we show how to reduce a k-tape alternating Turing machine to a 1-tape alternating Turing machine with only a constant factor increase in time and space.