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Valuations, regular expressions, and fractal geometry

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Valuations — morphisms from (Σ * n ,·,λ) to ((0, ∞), ·, 1) — are a simple generalization of so-called Bernoulli morphisms. In this paper, we show a characterization of strongly unambiguous regular expressions with the help of valuations and formal power series. We apply these algebraic results to the determination of Hausdorff dimensions of fractals described by regular expressions.

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  1. Lehrstuhl Informatik für Ingenieure und Naturwissenschaftler, Universität Karlsruhe TH, D-76128, Karlsruhe, Germany

    Henning Fernau

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  1. Henning Fernau
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Fernau, H. Valuations, regular expressions, and fractal geometry. AAECC 7, 59–75 (1996). https://doi.org/10.1007/BF01613617

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