Finite Dynamical Systems, Linear Automata, and Finite Fields

TL;DR

This paper explores the relationship between finite fields and finite dynamical systems, providing insights into linear systems and addressing open problems in the field.

Contribution

It introduces a novel connection between finite fields and finite dynamical systems, enhancing understanding of linear systems and their properties.

Findings

Established a link between finite fields and finite dynamical systems.

Provided new methods to analyze linear systems using finite field theory.

Addressed specific open problems in finite dynamical systems.

Abstract

We establish a connection between finite fields and finite dynamical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.