The dimension of a formal language

A connection is established between formal language theory and mathematical analysis by associating the symbols of strings of a language with the digits of expansions of points in the unit interval. A language is made to correspond to a particular subset of the unit interval, and the dimension of a language is defined as the Hausdorff dimension of this subset. It is shown that the dimension of a language is less than or equal to its channel capacity, and it is shown that a statement involving the dimension of a language can be added to a list of criteria developed by Brainerd and Knode (1972) for determining that a language is not recognizable by a finite automaton