Solitons in 3-State Mealy Automata

TL;DR

This paper explores the classification of 3-state automata over a 2-letter alphabet, aiming to identify automata that exhibit soliton-like behavior similar to box-ball systems, which are known for their integrability.

Contribution

The paper introduces a framework for classifying 3-state automata based on features inspired by box-ball systems, advancing understanding of automata with soliton solutions.

Findings

Identification of classes of automata with soliton properties

Framework for classifying automata similar to BBS

Insights into integrable automata structures

Abstract

Box--ball systems (BBS) are integrable systems with soliton solutions and other good properties. We will search for automata that belong to the same class as BBS automata by introducing some classes of automata through the features of BBS automaton. In particular, we would like to classify 3-state automata over a 2-letter alphabet.