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

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SOFSEM 2010: Theory and Practice of Computer Science (SOFSEM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

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Authors and Affiliations

  1. Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618, Tallinn, Estonia

    Silvio Capobianco

Authors
  1. Silvio Capobianco
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Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584 CH, Utrecht, The Netherlands

    Jan van Leeuwen

  2. LaBRI, Universit Bordeaux, 351 cours de la Libration, 1F-33405, Talence Cedex, France

    Anca Muscholl

  3. Department of Computer Science & Applied Mathematics, Weizmann Institute, Faculty of Mathematics and Computer Science, 76100, Rehovot, Israel

    David Peleg

  4. Department of Software Engineering Faculty of Mathematics and Physics Malostranské nám, Charles University, 25 11800, Prague 1, Czech Republic

    Jaroslav Pokorný

  5. Software Engineering, Department of Computer Science, RWTH Aachen University, 3, Ahornstrae 55, D-52074, Aachen, Germany

    Bernhard Rumpe

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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. https://doi.org/10.1007/978-3-642-11266-9_22

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  • DOI: https://doi.org/10.1007/978-3-642-11266-9_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11265-2

  • Online ISBN: 978-3-642-11266-9

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