On Cellular Automata

Fuente: arXiv

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Détails bibliographiques
Auteurs principaux:	Hamed, Tawfiq, Saleh, Mohammad
Format:	Preprint
Publié:	2025
Sujets:	Group Theory Dynamical Systems
Accès en ligne:	Acceder al recurso
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author	Hamed, Tawfiq Saleh, Mohammad
author_facet	Hamed, Tawfiq Saleh, Mohammad
contents	Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept of $ ϕ$-cellular automata. We establish new theoretical results, including a generalized Uniform Curtis-Hedlund Theorem and linear $ ϕ$-cellular automata. Additionally, we define the covering map for $ ϕ$-cellular automata and investigate its properties. Specifically, we derive results for quotient covers when the universe of the automaton is a circulant graph. This work contributes to the algebraic and topological understanding of cellular automata, paving the way for future exploration of different types of covers and their applications to broader classes of graphs and dynamical systems.
format	Preprint
id	arxiv_https___arxiv_org_abs_2502_19372
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	On Cellular Automata Hamed, Tawfiq Saleh, Mohammad Group Theory Dynamical Systems Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept of $ ϕ$-cellular automata. We establish new theoretical results, including a generalized Uniform Curtis-Hedlund Theorem and linear $ ϕ$-cellular automata. Additionally, we define the covering map for $ ϕ$-cellular automata and investigate its properties. Specifically, we derive results for quotient covers when the universe of the automaton is a circulant graph. This work contributes to the algebraic and topological understanding of cellular automata, paving the way for future exploration of different types of covers and their applications to broader classes of graphs and dynamical systems.
title	On Cellular Automata
topic	Group Theory Dynamical Systems
url	https://arxiv.org/abs/2502.19372

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