Asynchronous and Fully Self-stabilizing Time-Adaptive Majority Consensus

We study the scenario where a batch of transient faults hits an asynchronous distributed system by corrupting the state of some f nodes. We concentrate on the basic majority consensus problem, where nodes are required to agree on a common output value which is the input value of the majority of them. We give a fully self-stabilizing adaptive algorithm, i.e., the output value stabilizes in O(f) time at all nodes, for any unknown f . Moreover, a state stabilization occurs in time proportional to the (unknown) diameter of the network. Both upper bounds match known lower bounds to within a constant factor. Previous results (stated for a slightly less general problem called “persistent bit”) assumed the synchronous network model, and that f < n/2.