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Baire Category and Nowhere Differentiability for Feasible Real Functions

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Algorithms and Computation (ISAAC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2223))

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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.

This research was supported in part by National Science Foundation Grants 9157382, 9610461, and 9988483.

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Author information

Authors and Affiliations

  1. Dept. Math/CS/Physics, Wartburg College, 50677, Waverly, IA, USA

    Josef M. Breutzmann

  2. School of EE & CS, Ohio University, 45701, Athens, OH, USA

    David W. Juedes

  3. Dept. of Comp. Sci., Iowa State University, 50011, Ames, IA, USA

    Jack H. Lutz

Authors
  1. Josef M. Breutzmann
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  2. David W. Juedes
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  3. Jack H. Lutz
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Editor information

Editors and Affiliations

  1. Basser Department of Computer Science, University of Sydney, Madsen Building F09, 2006, Sydney, NSW, Australia

    Peter Eades

  2. Department of Computer Science, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    Tadao Takaoka

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© 2001 Springer-Verlag Berlin Heidelberg

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Breutzmann, J.M., Juedes, D.W., Lutz, J.H. (2001). Baire Category and Nowhere Differentiability for Feasible Real Functions. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_20

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  • DOI: https://doi.org/10.1007/3-540-45678-3_20

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