Inexact agreement

Abstract

An Inexact Agreement protocol alows processors that each have a value approximating $\hat{\nu}$ to compute new values that are closer to each other and close to $\hat{\nu}$. Two fault-tolerant protocols for Inexact Agreement are described. As long as fewer than 1/3 of the processors are faulty, the protocols give the required convergence; they also permit iteration and thus convergence to any desired precision. When between 1/3 and 2/3 of the processors are faulty, the protocols may not converge. However, then processors either detect that too many faults have occurred or the new values computed by processors remain close to each other and to $\hat{\nu}$. In this case, the divergence is bounded. Use of the protocols for clock synchronization in a distributed system is explained.