ASYNCHRONOUS APPROXIMATE AGREEMENT

This paper examines the Approximate Agreement Problem in an asynchronous failure-by-omission system with deterministic protocols. We give a simple algorithm, and prove that the algorithm is optimal by considering the power of the ''adversary'' scheduler to disrupt processors' views. We show that the adversary need not cause any omissions to achieve its purpose, and therefore no algorithm can do better than simply to operate round-by-round, as our does. We extend these results to asynchronous crash-failure systems. The resulting understanding of the adversary should be applicable to other problems in asynchronous failure-by-omission or crash-failure-systems. (C) 1994 Academic Press, Inc.