Consistency of Multidimensional Combinatorial Substitutions

  • Timo Jolivet
  • Jarkko Kari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7353)


Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in ℤ d . We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of the way they are glued together in the image by a substitution. Two problems can arise when defining a substitution in such a way: it can fail to be consistent, and the patterns in an image by the substitution might overlap.

We prove that it is undecidable whether a two-dimensional substitution is consistent or overlapping, and we provide practical algorithms to decide these properties in some particular cases.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Timo Jolivet
    • 1
    • 2
  • Jarkko Kari
    • 1
  1. 1.FUNDIM, Department of MathematicsUniversity of TurkuFinland
  2. 2.LIAFAUniversité Paris 7France

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