On Cellular Automata
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916632081727488 |
|---|---|
| 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 |