Abstract

A notion of resource‐bounded Baire category is developed for the classPC[0,1]of all polynomial‐time computable real‐valued functions on the unit interval. The meager subsets ofPC[0,1]are characterized in terms of resource‐bounded Banach‐Mazur games. This characterization is used to prove that, in the sense of Baire category, almost every function inPC[0,1]is nowhere differentiable. This is a complexity‐theoretic extension of the analogous classical result that Banach proved for the classC[0, 1] in 1931. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)