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Tilings Robust to Errors

  • Alexis Ballier
  • Bruno Durand
  • Emmanuel Jeandel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6034)

Abstract

We study the error robustness of tilings of the plane. The fundamental question is the following: given a tileset, what happens if we allow a small probability of errors? Are the objects we obtain close to an error-free tiling of the plane?

We prove that tilesets that produce only periodic tilings are robust to errors. For this proof, we use a hierarchical construction of islands of errors (see [6,7]). We also show that another class of tilesets, those that admit countably many tilings is not robust and that there is no computable way to distinguish between these two classes.

Keywords

Turing Machine Local Constraint Periodic Tiling Aperiodic Tiling Wang Tile 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alexis Ballier
    • 1
  • Bruno Durand
    • 1
  • Emmanuel Jeandel
    • 1
  1. 1.Laboratoire d’informatique fondamentale de Marseille (LIF)Aix-Marseille Université, CNRSMarseille Cedex 13France

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