Average-Case Bit-Complexity Theory of Real Functions

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


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.


Represented Spaces Average Polynomial Explicit Continuous Function Average-case Complexity Theory Exponential Tower 
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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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