An 8-state minimal time solution to the firing squad synchronization problem

Abstract

This paper presents a description of a general outline for a minimal time solution to the Firing Squad Synchronization Problem, and a solution of this form which is composed of machines with only eight states. The paper then discusses the verification of this minimal time solution by computer simulation, and gives the schema for the mathematical induction proof that the solution works for any length (the full proof is given in ( Balzer, 1966 )). The final part of the paper discusses some efforts to determine the minimal number of states needed for a minimal time solution. No four state minimal time solution exists. A reasonable set of conditions are presented for which no five state minimal time solution exists. Also, various eight state minimal time solutions exists.