Replication Predicates for Dependent-Failure Algorithms

To establish lower bounds on the amount of replication, there is a common partition argument used to construct indistinguishable executions such that one violates some property of interest. This violation leads to the conclusion that the lower bound on process replication is of the form n > bkt/bc, where t is the maximum number of process failures in any of these executions and k, b are positive integers. In this paper, we show how this argument can be extended to give bounds on replication when failures are dependent. We express these bounds in terms of our model of cores and survivors sets using set properties instead of predicates of the form n > bkt/bc. We give two different properties that express the same requirement for k > 1 and b = 1. One property comes directly from the argument, and the other is more useful when designing an algorithm that takes advantage of dependent failures. We also consider a somewhat unusual replication bound of n > b3t/2c that arises in the Leader Election problem for synchronous receive-omission failures. We generalize the replication bound for dependent failures, and develop an algorithm that shows that this generalized replication bound is tight.