Linear Cellular Automata with Multiple State Variables

  • Jarkko Kari
Conference paper

DOI: 10.1007/3-540-46541-3_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1770)
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

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jarkko Kari
    • 1
  1. 1.Department of Computer Science, MLH 14University of IowaUSA

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