Abstract
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in ℤd. 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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Jolivet, T., Kari, J. (2012). Consistency of Multidimensional Combinatorial Substitutions. In: Hirsch, E.A., Karhumäki, J., Lepistö, A., Prilutskii, M. (eds) Computer Science – Theory and Applications. CSR 2012. Lecture Notes in Computer Science, vol 7353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30642-6_20
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DOI: https://doi.org/10.1007/978-3-642-30642-6_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30641-9
Online ISBN: 978-3-642-30642-6
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