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Valuations, regular expressions, and fractal geometry

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

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  • DOI: https://doi.org/10.1007/BF01613617

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