The Truth System: Can a System of Lying Processes Stabilize?

Abstract

We introduce a new abstract system, called the truth system. In the truth system, a process deduces a true value, with high probability, from an incoming stream of both true and false values, where the probability that a value in the incoming stream is true is at least 0.6. At each instant, the receiving process maintains at most one candidate of the true value, and eventually the process reaches the conclusion that its candidate value equals, with high probability, the true value. In this paper, we present three versions of the truth system, discuss their properties, and show how to choose their parameters so that their probability of error is small, i.e. about 10^− 6. The third version, called the stable system, is the most valuable. We employ the stable system as a building block in a stabilizing unidirectional token ring of n processes. When n is small, i.e. about 100 or less, the stable system can be considered error-free and we argue that the resulting token ring is stabilizing with high probability. We simulate the token ring, when n is at most 100, and observe that the ring always stabilizes even though each process lies about its state 40% of the time.