Generic Separations and Leaf Languages

In the early nineties of the previous century, leaf languages were introduced as a means for the uniform characterization of many complexity classes, mainly in the range between P (polynomial time) and PSPACE (polynomial space). It was shown that the separability of two complexity classes can be reduced to a combinatorial property of the corresponding dening leaf languages. In the present paper, it is shown that every separation obtained in this way holds for every generic oracle in the sense of Blum and Impagliazzo. We obtain several consequences of this result, regarding, e.g., simultaneous separations and universal oracles, resource-bounded genericity, and type-2 complexity