The boundary of substitution systems

  • Philippe Narbel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)


The global limit set has been introduced in a preceding work as a generalization of the way of generating infinite words by substitution systems, i.e. by iterating a morphism on a finite alphabet. We prove here that the boundary set (the “adherence set”) of a progressive substitution language is equal to its global limit set plus a simple set of words. This allows us to exhibit conditions to conclude that the full boundary is explicitly constructible, rationally codable and uncountable. The equivalence problem for boundaries is also shown decidable for iterated primitive morphisms.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Philippe Narbel
    • 1
  1. 1.Institut Blaise Pascal, Paris 7L.I.T.PParis

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