Valuations ---~morphisms from $(\Si\stern,\cdot,\lW)$
to $((0,\infty),\cdot,1)$~--- are a generalization of
Bernoulli morphisms introduced in Eilenberg (1974).
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 $\omega$-languages.  
In this way, we can sharpen and generalize earlier results of 
Bandt (1989), Mauldin and Williams (1988) and ourselves (1993-1996).