Valuations, regular expressions, and fractal geometry
Valuations of words and languages are homomorphisms of the free monoid over an alphabet of \(n\) letters, \((\Sigma_n, \cdot, \lambda)\), to the monoid (\((0, \infty),\cdot, 1)\). The author uses formal power series and valuations of languages to derive a characterization of so-called strongly unambiguous regular expressions. Then valuations are extended to the space of one-sided infinite words, \(\Sigma^\omega_n\), and the author's results on valuations of languages are utilized to estimate the Hausdorff dimension of several fractals generated by (infinite) iterated function systems.
strongly unambiguous regular expressions
scientific article; zbMATH DE number 852854
scientific article