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Baire Category and Nowhere Differentiability for Feasible Real Functions

  • Josef M. Breutzmann
  • David W. Juedes
  • Jack H. Lutz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2223)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Josef M. Breutzmann
    • 1
  • David W. Juedes
    • 2
  • Jack H. Lutz
    • 3
  1. 1.Dept. Math/CS/PhysicsWartburg CollegeWaverlyUSA
  2. 2.School of EE & CSOhio UniversityAthensUSA
  3. 3.Dept. of Comp. Sci.Iowa State UniversityAmesUSA

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