2007/05/04 by Silvio Capobianco, Capobianco, Silvio
Computer Science · Mathematics · #37B15 (Primary) 68Q80 (Secondary) #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:37B15 #msc:68Q80 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0705.0670
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
openalex publication_date 2007/05/04 · arxiv created 2008/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.