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Sofic measures
Marie-Pierre Béal, Vincent Jugé, Jean Mairesse, Dominique Perrin · 2026-04-13 · via math.PR updates on arXiv.org

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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