Surjunctivity for cellular automata in Besicovitch spaces
arXiv:0705.0670
Abstract
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.
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