✦ LIBER ✦
Baire category and nowhere differentiability for feasible real functions
✍ Scribed by Josef M. Breutzmann; David W. Juedes; Jack H. Lutz
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 257 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0044-3050
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✦ Synopsis
Abstract
A notion of resource‐bounded Baire category is developed for the class P~C[0,1]~ of all polynomial‐time computable real‐valued functions on the unit interval. The meager subsets of P~C[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 in P~C[0,1]~ is nowhere differentiable. This is a complexity‐theoretic extension of the analogous classical result that Banach proved for the class C[0, 1] in 1931. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)