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IFS and control languages

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

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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].

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Author information

Authors and Affiliations

  1. Wilhelm-Schickhard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076, Tübingen, Germany

    Henning Fernau

  2. Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, Kurt-Mothes-Str. 1, D-06120, Halle, Germany

    Ludwig Staiger

Authors
  1. Henning Fernau
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  2. Ludwig Staiger
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Editor information

Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Fernau, H., Staiger, L. (1998). IFS and control languages. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055825

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  • DOI: https://doi.org/10.1007/BFb0055825

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  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

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