A Minimal Time Solution to the Firing Squad Synchronization Problem with Von Neumann Neighborhood of Extent 2

Abstract

Cellular automata provide a simple environment in which to study global behaviors. One example of a problem that utilizes cellular automata is the Firing Squad Synchronization Problem, first proposed in 1957. This paper provides an overview of the standard Firing Squad Synchronization Problem and a commonly used technique in solving it. This paper also provides a statement of a new extension of the Standard Firing Squad Synchronization Problem to a different neighborhood definition - a Von Neumann neighborhood of extent 2. An 8 state 651 rule minimal time solution to the extended problem is described, presented and proven, along with Python code used in running simulations of the solution.