2025/02/26 by Tawfiq Hamed, Mohammad Saleh, Hamed, Tawfiq +1
Computer Science · Mathematics · #Advanced Operator Algebra Research #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2502.19372
openalex publication_date 2025/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.