A generalization of cellular automata over groups

Let G be a group and let A finite set with at least two elements. cellular automaton (CA) over AG is function τ:AG→AG defined via memory S⊆G local μ:AS→A. The goal of this paper to introduce the definition generalized (GCA) τ:AG→AH, where H another arbitrary group, homomorphism ϕ:H→G. Our preserves essence CA, as we prove analogous versions three key results in theory CA: Curtis-Hedlund Theorem for GCA, Composition Invertibility GCA. When = H, that invertible GCA isomorphic semidirect product Aut(G)op CA. Finally, apply our study automorphisms monoid CA(G;A) consisting all CA . In particular, show every ϕ∈Aut(G) defines an automorphism conjugation by ϕ, that, when abelian, Aut(G) embedded outer CA(G;A).Communicated Pedro Garcia-Sanchez