Exploring Millions of 6-State FSSP Solutions: the Formal Notion of Local CA Simulation

TL;DR

This paper demonstrates that millions of minimal 6-state solutions to the Firing Squad Synchronization Problem can be generated efficiently using local cellular automaton simulations on a single computer, expanding the known solution space.

Contribution

It introduces a method to generate numerous solutions from existing ones via local simulation, significantly increasing the known solutions for the problem.

Findings

Millions of solutions generated from existing ones

Local simulation enables efficient exploration of solution space

Single computer suffices for large-scale solution generation

Abstract

In this paper, we come back on the notion of local simulation allowing to transform a cellular automaton into a closely related one with different local encoding of information. This notion is used to explore solutions of the Firing Squad Synchronization Problem that are minimal both in time (2n -- 2 for n cells) and, up to current knowledge, also in states (6 states). While only one such solution was proposed by Mazoyer since 1987, 718 new solutions have been generated by Clergue, Verel and Formenti in 2018 with a cluster of machines. We show here that, starting from existing solutions, it is possible to generate millions of such solutions using local simulations using a single common personal computer.