# Nonuniform lower bounds for exponential time classes

Contributed Papers Structural Complexity Theory

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## Abstract

Lower bounds for the first levels of the exponential time hierarchy with respect to circuit and advice classes are studied. Using time bounded Kolmogorov complexity, languages are constructed which witness that various exponential time classes are not included in (fixed) polynomial advice classes. We show as well that these languages are not included in small circuit families where the circuits are of a fixed, polynomial size. The results yield optimal bounds (up to relativization) on efficient nonuniform computation.

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© Springer-Verlag Berlin Heidelberg 1995