IFS and Control Languages

Abstract Valuations — morphisms from (σ *, ·, e ) to ((0, ∞), ·, 1) —are a generalization of Bernoulli morphisms introduced in [7]. Here, we show how to generalize the notion of entropy (of a language) in order to obtain new formulae to determine the Hausdorff dimension of fractal sets (also in Euclidean spaces) especially defined via regular Ω-languages. In this way, we can sharpen and generalize earlier results [1, 10, 11, 20, 29].

Authors

• Henning Fernau
• Ludwig Staiger

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