Synchronizing the Squad with (Almost) Arbitrary Cut Ratio

Abstract

In this paper, we design a solution to the generalized firing squad problem where the splittings can be chosen to happen at any ratio greater than two thirds. This is in the same spirit as the (non-generalized) solutions of Mazoyer except that we do not use signal speeds but the concept of fields to achieve this goal. Signals and speeds do appear visually as an effect of the spatio-temporal structure of the cellular automaton. However, not being setup by design allows the solution to automatically extends to more generalized settings. Moreover, the conceptual design of the solution is separated from the state space optimization that is only handle afterward. The finiteness of state space is also sketched.