Sofic measures
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917402965442560 |
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| author | Béal, Marie-Pierre Jugé, Vincent Mairesse, Jean Perrin, Dominique |
| author_facet | Béal, Marie-Pierre Jugé, Vincent Mairesse, Jean Perrin, Dominique |
| contents | Sofic measures, also known as hidden Markov measures, have been extensively studied. In this paper, we survey some equivalent definitions of this notion and improve a bound for deciding whether a sofic measure is~$k$-step Markov. We prove that if an invariant sofic measure with a linear representation of dimension~$n$ is a~$k$-step Markov chain, then~$k$ can be chosen at most equal to~$2^{n^2-1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11212 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sofic measures Béal, Marie-Pierre Jugé, Vincent Mairesse, Jean Perrin, Dominique Probability Dynamical Systems Sofic measures, also known as hidden Markov measures, have been extensively studied. In this paper, we survey some equivalent definitions of this notion and improve a bound for deciding whether a sofic measure is~$k$-step Markov. We prove that if an invariant sofic measure with a linear representation of dimension~$n$ is a~$k$-step Markov chain, then~$k$ can be chosen at most equal to~$2^{n^2-1}$. |
| title | Sofic measures |
| topic | Probability Dynamical Systems |
| url | https://arxiv.org/abs/2604.11212 |