On Pattern Density and Sliding Block Code Behavior for the Besicovitch and Weyl Pseudo-distances

  • Silvio Capobianco
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5901)

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.

Keywords

Pattern pseudo-distance sliding block code 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Silvio Capobianco
    • 1
  1. 1.Institute of Cybernetics at Tallinn University of TechnologyTallinnEstonia

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