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

  • Silvio Capobianco
Conference paper

DOI: 10.1007/978-3-642-11266-9_22

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5901)
Cite this paper as:
Capobianco S. (2010) On Pattern Density and Sliding Block Code Behavior for the Besicovitch and Weyl Pseudo-distances. In: van Leeuwen J., Muscholl A., Peleg D., Pokorný J., Rumpe B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg

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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