An Optimal Self-Stabilizing Firing Squad

Abstract: Consider a fully connected network where up to $t$ processes may crash, and all processes start in an arbitrary memory state. The self-stabilizing firing squad problem consists of eventually guaranteeing simultaneous response to an external input. This is modeled by requiring that the non-crashed processes "fire" simultaneously if some correct process received an external "GO" input, and that they only fire as a response to some process receiving such an input. This paper presents FireAlg, the first self-stabilizing firing squad algorithm. The FireAlg algorithm is optimal in two respects: (a) Once the algorithm is in a safe state, it fires in response to a GO input as fast as any other algorithm does, and (b) Starting from an arbitrary state, it converges to a safe state as fast as any other algorithm does.