Near-Optimal Self-stabilising Counting and Firing Squads

Abstract

Consider a fully-connected synchronous distributed system of n nodes, where up to f nodes may be faulty and every node starts in an arbitrary initial state. In the synchronous counting problem, all nodes need to eventually agree on a counter that is increased by one modulo some C in each round. In the self-stabilising firing squad problem, the task is to eventually guarantee that all non-faulty nodes have simultaneous responses to external inputs: if a subset of the correct nodes receive an external “go” signal as input, then all correct nodes should agree on a round (in the not-too-distant future) in which to jointly output a “fire” signal. Moreover, no node should generate a “fire” signal without some correct node having previously received a “go” signal as input.