On the Induction Operation for Shift Subspaces and Cellular Automata as Presentations of Dynamical Systems
Abstract
We consider continuous, translationcommuting transformations of compact, translationinvariant families of mappingsfrom finitely generated groups into finite alphabets. It is wellknown that such transformations and spaces can be described "locally" via families of patterns and finitary functions; such descriptions can be reused on groups larger than the original, usually defining nonisomorphic structures. We show how some of the properties of the "induced" entities can be deduced from those of the original ones, and vice versa; then, we show how to "simulate" the smaller structure into the larger one, and obtain a characterization in terms of group actions for the dynamical systems admitting of presentations via structures as such. Special attention is given to the class of sofic shifts.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.3841
 Bibcode:
 2007arXiv0711.3841C
 Keywords:

 Mathematics  Dynamical Systems;
 37B15;
 68Q80
 EPrint:
 20 pages, no figures. Presented at LATA 2008. Extended version, submitted to Information and Computation