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Surjunctivity for cellular automata in Besicovitch spaces

Published 2007-05-04, updated 2008-06-16Version 3

The Besicovitch pseudodistance measures the relative size of the set of points where two functions take different values; the quotient space modulo the induced equivalence relation is endowed with a natural metric. We study the behavior of cellular automata in the new topology and show that, under suitable additional hypotheses, they retain certain properties possessed in the usual product topology; in particular, that injectivity still implies surjectivity.

Comments: 9 pages, no figures, LaTeX. Shortened, some definition changed, proof of main lemma changed accordingly. Almost as submitted to Journal of Cellular Automata for special issue dedicated to Automata 2007 conference proceedings. Exceptions: one major error corrected in definition of surjunctivity; adapted for use of the article document class

Categories: math.DS

Subjects: 37B15, 68Q80

Keywords: cellular automata, besicovitch spaces, surjunctivity, besicovitch pseudodistance measures, usual product topology

Tags: conference paper

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