Linear Cellular Automata with Multiple State Variables
- Cite this paper as:
- Kari J. (2000) Linear Cellular Automata with Multiple State Variables. In: Reichel H., Tison S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg
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.
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