The Frobenius problem for homomorphic embeddings of languages into the integers

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Abstract

Let S be a map from a language Lto the integers satisfying S(vw) =S(v) +S(w)for all v, w ∈L. The classical Frobenius problem asks whether the complement of S(L)in the natural numbers will be infinite or finite, and in the latter case the value of the largest element in this complement. This is also known as the ‘coin-problem’, and Lis the full language consisting of all words over a finite alphabet. We solve the Frobenius problem for the golden mean language, any Sturmian language and the Thue–Morse language. We also consider two-dimensional embeddings.



Original languageEnglish
Pages (from-to)73-79
Number of pages7
JournalTheoretical Computer Science
Volume732
DOIs
Publication statusPublished - 2018

Keywords

  • Frobenius problem
  • Golden mean language
  • Paperfolding morphism
  • Sturmian language
  • Thue–Morse language

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