Sequential densities of rational languages
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915871186747392 |
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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 |
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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 |