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Average-Case Bit-Complexity Theory of Real Functions

  • Matthias Schröder
  • Florian Steinberg
  • Martin ZieglerEmail author
Conference paper
  • 547 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)

Abstract

We introduce, and initiate the study of, average-case bit-complexity theory over the reals: Like in the discrete case a first, naïve notion of polynomial average runtime turns out to lack robustness and is thus refined. Standard examples of explicit continuous functions with increasingly high worst-case complexity are shown to be in fact easy in the mean; while a further example is constructed with both worst and average complexity exponential: for topological/metric reasons, i.e., oracles do not help. The notions are then generalized from the reals to represented spaces; and, in the real case, related to randomized computation.

Keywords

Represented Spaces Average Polynomial Explicit Continuous Function Average-case Complexity Theory Exponential Tower 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Matthias Schröder
    • 1
  • Florian Steinberg
    • 1
  • Martin Ziegler
    • 1
    • 2
    Email author
  1. 1.TU DarmstadtDarmstadtGermany
  2. 2.KAISTDaejeonSouth Korea

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