On the Interactive Complexity of Graph Reliability

We give an interactive protocol for s \Gamma t RELIABILITY, the well known reliability problem on graphs. Our protocol shows that if IP (f(n)) denotes the class of languages whose interactive complexity is O(f(n)), that is the set of languages which can be accepted by an interactive proof system with O(f(n)) number of rounds, then s \Gamma t RELIABILITY 2 IP (n): This complexity is significantly smaller than what one could get via reduction to QBF, the standard PSPACE-complete language. Another interesting aspect of our protocol is that it includes a general method to deal with rational numbers in interactive proof systems. 1 Introduction The notion of an interactive proof system or interactive protocol was introduced by Goldwasser, Micali and Rackoff [6] and independently by Babai [1]. Intuitively, it is a way by which an infinitely powerful prover can convince using interaction a polynomially powerful probabilistic verifier about the membership of elements in some language..