Implementing Computations in Automaton (Semi)groups

TL;DR

This paper explores computational aspects of automaton (semi)groups, introducing new implementation methods, comparing them with existing techniques, and proposing conjectures based on extensive experimental results.

Contribution

It presents novel implementation approaches for automaton (semi)groups and offers new conjectures on their order based on experimental data.

Findings

New implementation methods for automaton (semi)groups

Comparison results showing performance differences

Proposed conjectures on the order of finite automaton (semi)groups

Abstract

We consider the growth, order, and finiteness problems for automaton (semi)groups. We propose new implementations and compare them with the existing ones. As a result of extensive experimentations, we propose some conjectures on the order of finite automaton (semi)groups.