Abstract
We study the ergodic behavior of linear cellular automata over Zm. The main contribution of this paper is an easy-to-check necessary and sufficient condition for a linear cellular automaton over Zm to be ergodic. We prove that, for general cellular automata, ergodicity is equivalent to topological chaos (transitivity and sensitivity to initial conditions). Finally we prove that linear CA over Zp with p prime have dense periodic orbits.
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© 1997 Springer-Verlag Berlin Heidelberg
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Cattaneo, G., Formenti, E., Manzini, G., Margara, L. (1997). On ergodic linear cellular automata over Zm . In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023478
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DOI: https://doi.org/10.1007/BFb0023478
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