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The Rational Index: A Complexity Measure for Languages

With every language L we associate an increasing function called its rational index. We obtain this function by comparing L with rational languages of increasing complexity.We show that the rational indices of two languages related by a rational transduction are polynomially related. From this, we can define new rational cones of languages in terms of rational indices.We then focus our attention on the rational index of context-free languages and raise several questions closely related to the open problems concerning the subcones of the family of context-free languages.