Reaching Agreement in the Presence of Faults

The problem addressed here concerns a set of isolated processors, some unknown subset of which may be faulty, that communicate only by means of two-party messages. Each nonfaulty processor has a private value of reformation that must be communicated to each other nonfanlty processor. Nonfaulty processors always communicate honestly, whereas faulty processors may lie The problem is to devise an algorithm in which processors communicate their own values and relay values received from others that allows each nonfaulty processor to refer a value for each other processor The value referred for a nonfanlty processor must be that processor's private value, and the value inferred for a faulty one must be consistent wRh the corresponding value inferred by each other nonfanlty processor It is shown that the problem is solvable for, and only for, n> _ 3m + 1, where m IS the number of faulty processors and n is the total number. It is also shown that if faulty processors can refuse to pass on reformation but cannot falsely relay information, the problem is solvable for arbitrary n _> m _> 0. This weaker assumption can be approxunated m practice using cryptographic methods