Faulty Processors Research Articles

A lower bound for the time to assure interactive consistency

Abstract : The problem of 'assuring interactive consistency' is defined in (PSL). It is assumed that there are n isolated processors, of which at most m are faulty. The processors can communicate by means of two-party messages, using a medium which is reliable and of negligible delay. The sender of a message is always identifiable by the receiver. Each processor p has a private value sigma(p). The problem is to devise an algorithm that will allow each processor p to compute a value for each processor r, such that (a) if p and r are nonfaulty then p computes r's private value sigma(r), and (b) all the nonfaulty processors compute the same value for each processor r. It is shown in (PSL) that if n 3m + 1, then there is no algorithm which assures interactive consistency. On the other hand, if n or = 3m + 1, then an algorithm does exist. The algorithm presented in (PSL) uses m + 1 rounds of communication, and thus can be said to require 'time' m + 1. An obvious question is whether fewer rounds of communication suffice to solve the problem. In 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. (Author)

The Byzantine generals strike again

Can unanimity be achieved in an unreliable distributed system? This problem was named the “Byzantine Generals Problem” by L. Lamport, R. Shostak, and M. Pease (Technical Report 54, Computer Science Laboratory, SRI International, March 1980). The results obtained in the present paper prove that unanimity is achievable in any distributed system if and only if the number of faulty processors in the system is: (1) less than one-third of the total number of processors; and (2) less than one-half of the connectivity of the system's network. In cases where unanimity is achievable, algorithms for obtaining it are given. This result forms a complete characterization of networks in the light of the Byzantine Problem.

Centralized, automated chemical-delivery system.

The authors describe the design of a dispensing system which supplies chemicals to ten widely dispersed film processors from centralized bulk-storage feed tanks. Features include a safety circuit which disables a faulty processor in the event of pump malfunction and centralized monitoring of the developer-tank temperature for each processor.

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 information that must be communicated to each other nonfaulty 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 infer a value for each other processor. The value inferred for a nonfaulty processor must be that processor's private value, and the value inferred for a faulty one must be consistent with the corresponding value inferred by each other nonfaulty processor. It is shown that the problem is solvable for, and only for, n ≥ 3 m + 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 information but cannot falsely relay information, the problem is solvable for arbitrary n ≥ m ≥ 0. This weaker assumption can be approximated in practice using cryptographic methods.