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arXiv · 2604.11212

Sofic measures

Marie-Pierre Béal·Vincent Jugé·Jean Mairesse·Dominique Perrin
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Abstract

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~$2^{n^2-1}$.

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Marie-Pierre Béal, Vincent Jugé, Jean Mairesse, Dominique Perrin. 2026-04-13. Sofic measures. https://arxiv.org/abs/2604.11212

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