Topological properties of cellular automata on trees

Published 14 Aug 2012 in cs.FL, cs.CC, cs.DM, and nlin.CG | (1208.2766v1)

Abstract: We prove that there do not exist positively expansive cellular automata defined on the full k-ary tree shift (for k>=2). Moreover, we investigate some topological properties of these automata and their relationships, namely permutivity, surjectivity, preinjectivity, right-closingness and openness.

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