Valuation Entropy of ω-Languages & IFS

Valuations --- morphisms from (\Sigma ; \Delta; e) to ((0; 1); \Delta; 1) --- are a simple generalization of Bernoulli morphisms (distributions, measures) as introduced in [4,6]. 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 (especially in Euclidean spaces) especially defined via regular ω-languages. In this way, we can sharpen and generalize theorems formulated in earlier papers [1,2,10,11,19,27]