Millions of 5-State n^3 Sequence Generators via Local Mappings

TL;DR

This paper demonstrates how local simulation techniques can generate millions of 5-state cellular automata solutions for real-time sequence generation, significantly improving previous state counts and transitions.

Contribution

It extends local simulation methods to real-time sequence problems, achieving large-scale solutions with fewer states and transitions than prior approaches.

Findings

Generated millions of 5-state solutions for n^3 sequence generation.

Achieved solutions with as few as 58 transitions, improving over previous 74-transition solutions.

Showed potential to apply local mappings to broader classes of problems.

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. In a previous paper, we applied it to the Firing Squad Synchronization Problem. In this paper, we show that the approach is not tied to this problem by applying it to the class of Real-Time Sequence Generation problems. We improve in particular on the generation of n 3 sequence by using local mappings to obtain millions of 5state solution, one of them using 58 transitions. It is based on the solution of Kamikawa and Umeo that uses 6 states and 74 transitions. Then, we explain in which sense even bigger classes of problems can be considered.