The Dimension and Entropy of Ω-languages
نویسنده
چکیده
In this paper we will explore the properties of the Hausdoff dimension in Cantor space—the space of strings over arbitrary symbols. It turns out that Hausdorff dimension is closely related to topological entropy, and that the two quantities are equal for closed regular ω-languages. We state and prove those results, and then explore the possibility of extending them to context-free ω-languages and other parts of the Chomsky heirarchy.
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