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Topological entropy of formal languages

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Abstract

We introduce the notion of topological entropy of a formal language as the topological entropy of the minimal topological automaton accepting it. Using a characterization of this notion in terms of approximations of the Myhill–Nerode congruence relation, we are able to compute the topological entropies of certain example languages. Those examples suggest that the notion of a “simple” formal language coincides with the language having zero entropy.

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Acknowledgments

We would like to express our sincere gratitude towards the anonymous reviewer for numerous valuable suggestions that significantly improved the presentation of the paper.

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Correspondence to Daniel Borchmann.

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Communicated by Benjamin Steinberg.

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Schneider, F.M., Borchmann, D. Topological entropy of formal languages. Semigroup Forum 94, 556–581 (2017). https://doi.org/10.1007/s00233-016-9782-0

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