Valuations of Languages, with Applications to Fractal Geometry

But even the very hairs of your head are all numbered. Fear not therefore: ye are of more value than many sparrows. shows that valuations are useful not only within the theory of codes, but also when dealing with ambiguity, especially in contextfree grammars, or for deening outer measures on the space of !-words which are of some importance to the theory of fractals. These connections yield new formulae to determine the Hausdorr dimension of fractal sets (especially in Euclidean spaces) deened via formal languages. The class of fractals describable with contextfree languages strictly includes that of MRFS-fractals introduced in 58, 18]. Some of the results of this paper also appear as part of the author's PhD thesis 36] and in 30, 31].