Abstract
We study the dynamics of cellular automata, and more specifically their transitivity and expansivity, when the set of configurations is endowed with a shift-invariant (pseudo-)distance. We first give an original proof of the non-transitivity of cellular automata when the set of configurations is endowed with the Besicovitch pseudo-distance. We then show that the Besicovitch pseudo-distance induces a distance on the set of shift-invariant measures and on the whole space of measures, and we prove that in these spaces also, cellular automata cannot be expansive nor transitive.
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Bienvenu, L., Sablik, M. (2007). The Dynamics of Cellular Automata in Shift-Invariant Topologies. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_11
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DOI: https://doi.org/10.1007/978-3-540-73208-2_11
Publisher Name: Springer, Berlin, Heidelberg
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