Non-Uniform Cellular Automata: classes, dynamics, and decidability

TL;DR

This paper explores the behavior, classes, and decidability of properties in non-uniform cellular automata, highlighting differences from classical automata and establishing key theoretical results.

Contribution

It introduces a classification framework for non-uniform cellular automata, analyzes their dynamics, and proves decidability of fundamental properties like surjectivity and injectivity.

Findings

Identified key differences and similarities with classical cellular automata.

Proved decidability of surjectivity and injectivity for non-uniform automata.

Studied a strong form of equicontinuity specific to non-uniform automata.

Abstract

The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like surjectivity and injectivity is also established. The final part studies a strong form of equicontinuity property specially suited for non-uniform cellular automata.