On pattern density and sliding block code behavior for the besicovitch and weyl pseudo-distances

Abstract

Initially proposed by Formenti et al. for bi-infinite sequences, the Besicovitch and Weyl pseudo-distances express the viewpoint of an observer moving infinitely far from the grid, rather than staying close as in the product topology. We extend their definition to a more general setting, which includes the usual infinite hypercubic grids, and highlight some noteworthy properties. We use them to measure the "frequency" of occurrences of patterns in configurations, and consider the behavior of sliding block codes when configurations at pseudo-distance zero are identified. One of our aims is to get an alternative characterization of surjectivity for sliding block codes. Mathematics Subject Classification 2000: 37B15, 68Q80. © 2010 Springer-Verlag Berlin Heidelberg.