Abstract
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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Narbel, P. (1993). The boundary of substitution systems. In: Borzyszkowski, A.M., Sokołowski, S. (eds) Mathematical Foundations of Computer Science 1993. MFCS 1993. Lecture Notes in Computer Science, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57182-5_49
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DOI: https://doi.org/10.1007/3-540-57182-5_49
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