Abstract. A consensus protocol enables a system of n asynchronous processes, some of which are faulty, to reach agreement. There are two kinds of faulty processes: fail-stop processes that can only die and malicious processes that can also send false messages. The class of asynchronous systems with fair schedulers is defined, and consensus protocols that terminate with probability I for these systems are investigated. With fail-stop processes, it is shown that r(n + 1)/21 correct processes are necessary and sufficient to reach agreement. In the malicious case, it is shown that r(2n + 1)/31 correct processes are necessary and sufficient to reach agreement. This is contrasted with an earlier result, stating that there is no consensus protocol for the fail-stop case that always terminates within a bounded number of steps, even if only one process can fail. The possibility of reliable broadcast (Byzantine Agreement) in asynchronous systems is also investigated. Asynchronous Byzantine Agreement is defined, and it is shown that I(2n + 1)/31 correct processes are necessary and sufficient to achieve it.

Agreement problems involve a system of processes, some of which may be faulty. A fundamental problem of fault-tolerant distributed computing is for the reliable processes to reach a consensus. We survey the considerable literature on this problem that has developed over the past few years and give an informal overview of the major theoretical results in the area.

Byzantine Agreement involves a system of n processes, of which some t may be faulty. The problem is for the correct processes to agree on a binary value sent by a transmitter that may itself be one of the n processes. If the transmitter sends the same value to each process, then all correct processes must agree on that value, but in any case, they must agree on some value. An explicit solution not using authentication for n = 3t + 1 processes is given, using. 2t + 3 rounds and 0 ( t 3 l og t) message bits. This solution is easily extended to the general case of n>, 3t + 1 to give a solution using 2t + 3 rounds and O(nt + t3 log t) message bits.

this paper, we answer this question in the negative. That is, we show that any algorithm which assures interactive consistency in the presence of m faulty processors requires at least m + 1 rounds of communication