Part 3. Mathematical models

About two spectral dimensions of the thin languages

P. S. Dergach


Abstract: The article is devoted to the class $\mathbb{T}$ of thin languages - regular languages with no more then linear growth function. For such languages it is introduced the concept of two dimensions - $dim$ and $Dim$. The paper describes all possible values of this quantities. More over, we obtain all possible values of the pairs $(dimP, DimP )$, where $P \in \mathbb{T}$.

Keywords: spectrum, thin language, dimension, growth function.