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Consistency of Multidimensional Combinatorial Substitutions

Timo Jolivet, Jarkko Kari, Consistency of Multidimensional Combinatorial Substitutions. Theoretical Computer Science 454, 178–188, 2012.

Abstract:

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.

BibTeX entry:

@ARTICLE{jJoKa12a,
  title = {Consistency of Multidimensional Combinatorial Substitutions},
  author = {Jolivet, Timo and Kari, Jarkko},
  journal = {Theoretical Computer Science},
  volume = {454},
  pages = {178–188},
  year = {2012},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

Publication Forum rating of this publication: level 2

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