Byzantine Fireflies

This paper addresses the problem of synchronous beeping, as addressed by swarms of fireflies. We present Byzantine-resilient algorithms ensuring that the correct processes eventually beep synchronously despite a subset of nodes beeping asynchronously. We assume that $$n > 2f$$n is the number of processes and f is the number of Byzantine processes and that the initial state of the processes can be arbitrary self-stabilization. We distinguish the cases where the beeping period is known, unknown or approximately known. We also consider the situation where the processes can produce light continuously.