The Evolution Homomorphism and Permutation Actions on Group Generated Cellular Automata

In this paper cellular automata generated over group alphabets are examined. For abelian groups and numerous local update rules, time evolution is additive and properties such as reversibility of systems can be examined using algebraic techniques. In particular, a necessary and sufficient condition for the reversibility of a finite one-dimensional cellular automata generated over a finite cyclic group using a 2-rule is provided. Finally, evolutions that respect permutations of the cellular configurations are introduced and examined.