Sequential densities of rational languages

Fuente: arXiv
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Main Authors: Gorman, Alexi Block, Perrin, Dominique
Format: Preprint
Published: 2026
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author Gorman, Alexi Block
Perrin, Dominique
author_facet Gorman, Alexi Block
Perrin, Dominique
contents We introduce the notion of density of a rational language with respect to a sequence of probability measures. We prove that if $(μ_n)$ is a sequence of Bernoulli measures converging to a positive Bernoulli measure $\overlineμ$, the sequential density is the ordinary density with respect to $\overlineμ$. We also prove that if $(μ_n)$ is a sequence of invariant probability measures converging in the strong sense to an invariant probability measure $\overlineμ$, then the sequential density of every rational language exists for this sequence.
format Preprint
id arxiv_https___arxiv_org_abs_2603_17188
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Sequential densities of rational languages
Gorman, Alexi Block
Perrin, Dominique
Dynamical Systems
Formal Languages and Automata Theory
We introduce the notion of density of a rational language with respect to a sequence of probability measures. We prove that if $(μ_n)$ is a sequence of Bernoulli measures converging to a positive Bernoulli measure $\overlineμ$, the sequential density is the ordinary density with respect to $\overlineμ$. We also prove that if $(μ_n)$ is a sequence of invariant probability measures converging in the strong sense to an invariant probability measure $\overlineμ$, then the sequential density of every rational language exists for this sequence.
title Sequential densities of rational languages
topic Dynamical Systems
Formal Languages and Automata Theory
url https://arxiv.org/abs/2603.17188