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On the Computational Complexity of Positive Linear Functionals on \(\mathcal{C}[0;1]\)

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Mathematical Aspects of Computer and Information Sciences (MACIS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9582))

Abstract

The Lebesgue integration has been related to polynomial counting complexity in several ways, even when restricted to smooth functions. We prove analogue results for the integration operator associated with the Cantor measure as well as a more general second-order \({{\mathbf {\mathsf{{\#P}}}}} \)-hardness criterion for such operators. We also give a simple criterion for relative polynomial time complexity and obtain a better understanding of the complexity of integration operators using the Lebesgue decomposition theorem.

Supported in part by the Marie Curie International Research Staff Exchange Scheme Fellowship 294962 within the 7th European Community Framework Programme and by the German Research Foundation (DFG) with project Zi 1009/4-1. A SHORT version of this work was presented at CCA 2015.

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Authors and Affiliations

  1. Department of Mathematics, TU Darmstadt, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    Hugo Férée & Martin Ziegler

  2. Université de Lorraine, LORIA, UMR 7503, 54506, Vandœuvre-lès-Nancy, France

    Hugo Férée

  3. Inria, 54600, Villers-lès-Nancy, France

    Hugo Férée

  4. CNRS, LORIA, UMR 7503, 54506, Vandœuvre-lès-Nancy, France

    Hugo Férée

  5. KAIST, School of Computing, 291 Daehak-ro, 34141, Daejeon, Republic of Korea

    Martin Ziegler

Authors
  1. Hugo Férée
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  2. Martin Ziegler
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Corresponding author

Correspondence to Martin Ziegler .

Editor information

Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Hamburg University of Technology, Hamburg, Germany

    Siegfried M. Rump

  3. New York University, New York, New York, USA

    Chee K. Yap

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Férée, H., Ziegler, M. (2016). On the Computational Complexity of Positive Linear Functionals on \(\mathcal{C}[0;1]\) . In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_42

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  • DOI: https://doi.org/10.1007/978-3-319-32859-1_42

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32858-4

  • Online ISBN: 978-3-319-32859-1

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