The Frobenius problem for homomorphic embeddings of languages into the integers

Dekking, F.M.

doi:10.1016/j.tcs.2018.04.023

The Frobenius problem for homomorphic embeddings of languages into the integers

Title

The Frobenius problem for homomorphic embeddings of languages into the integers

Author

Dekking, F.M. (TU Delft Applied Probability)

Date

2018

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.

Subject

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

To reference this document use:

http://resolver.tudelft.nl/uuid:28fc3854-d96e-48d3-bbd9-d4bf9530db90

DOI

https://doi.org/10.1016/j.tcs.2018.04.023

Embargo date

2020-05-30

ISSN

0304-3975

Source

Theoretical Computer Science, 732, 73-79