A lower bound for the time to assure interactive consistency

Abstract

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)