A 4-state solution to the Firing Squad Synchronization Problem based on hybrid rule 60 and 102 cellular automata

TL;DR

This paper introduces a new 4-state hybrid cellular automaton solution combining rule 60 and 102 to efficiently solve the Firing Squad Synchronization Problem on finite lines with two generals, achieving minimal synchronization time.

Contribution

It presents the first 4-state hybrid rule CA approach for FSSP that is simpler, faster, and time-optimal for lines of length 2^n with two generals.

Findings

Achieves minimal synchronization time of (n-1) steps.

Provides a hybrid rule transition table for 4-state CA.

Outperforms previous linear CA solutions in simplicity and speed.

Abstract

In this paper, we present a 4-state solution to the Firing Squad Synchronization Problem (FSSP) based on hybrid rule 60/102 Cellular Automata(CA). This solution solves the problem on the line of length 2^n with two generals. Previous work on FSSP for 4-state systems focused mostly on linear cellular automata, where synchronizes an infinite number of lines but not all possible lines. We give time-optimal solutions to synchronize an infinite number of lines by rule 60 and rule 102 respectively, and construct a hybrid rule 60 and 102 states transition table. Compared to the known solutions of cellular automata, the hybrid CA way is simpler and faster, the minimal time is (n-1) step.