On the dynamics of cellular automata induced from a prefix code

In this paper we study some general dynamical properties of the class of one-dimensional permutation cellular automata induced by maximal finite prefix codes defined on the one-sided full shift AN. Then we define families of codes every member of which induces an onto permutation cellular automaton F, and we investigate some properties of the (topological) dynamical system (AN,F) such as positive expansiveness, entropy and periodic points. We also define and study a special case of permutation cellular automata, namely, elector automata, which are canonically constructed from codes, and provide classes of cellular automata which attain their limit sets in finite time, and other families without that property.