Linear cellular automata with multiple state variables

Abstract

We investigate a finite state analog of subband coding, based on linear Cellular Automata with multiple state variables. We show that such a CA is injective (surjective) if and only if the determinant of its transition matrix is an injective (surjective, respectively) single variable automaton.We prove that in the one-dimensional case every injective automaton can be factored into a sequence of elementary automata, defined by elementary transition matrices. Finally, we investigate the factoring problem in higher dimensional spaces.