Brief Announcement: Accurate Byzantine Agreement with Feedback

The Byzantine Agreement (BA) problem requires non-faulty processes to agree on a common value. In many applications, it is important that the processes agree on the correct value. In this paper, we present a problem called Accurate Byzantine Agreement with Feedback (ABAF) in which all processes receive common feedback from the environment indicating if the value they agreed upon was correct or not (accuracy). We present an algorithm that solves the ABAF problem based on a standard solution to the BA problem and a multiplicative method to maintain and update process weights indicative of how often they are correct. We make guarantees on the accuracy of the algorithm based on assumptions on the accuracy of the processes and the proportion of faulty and non-faulty processes in the system. For each iteration, if the weight of accurate processes is at least 3/4 the weight of the non-faulty processes, the algorithm always decides on the correct value. When the non-faulty processes are accurate with probability greater than 1/2, the algorithm decides on the correct value with very high probability after some initial number of mistakes. In fact, among n processes, if there exists even one process which is accurate for all iterations, the algorithm is wrong only O(log n) times for any large number of iterations of the algorithm.