Kunz languages for numerical semigroups are context sensitive
This provides a formal language classification for numerical semigroups, relevant to mathematicians studying semigroup theory and formal languages.
The paper establishes a correspondence between numerical semigroups of depth n and Kunz languages, proving that for depth >2 these languages are context-sensitive but not regular, whereas depth 2 yields a regular language.
There is a one-to-one and onto correspondence between the class of numerical semigroups of depth $n$, where $n$ is an integer, and a certain language over the alphabet $\{1,\ldots,n\}$ which we call a Kunz language of depth $n$. The Kunz language associated with the numerical semigroups of depth $2$ is the regular language $\{1,2\}^*2\{1,2\}^*$. We prove that Kunz languages associated with numerical semigroups of larger depth are context-sensitive but not regular.