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Improved Testing Algorithms for Monotonicity

  • Yevgeniy Dodis
  • Oded Goldreich
  • Eric Lehman
  • Sofya Raskhodnikova
  • Dana Ron
  • Alex Samorodnitsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1671)

Abstract

We present improved algorithms for testing monotonicity of functions. Namely, given the ability to query an unknown function f: Σ n ↦ Ξ, where Σ and Ξ are finite ordered sets, the test always accepts a monotone f, and rejects f with high probability if it is ε-far from being monotone (i.e., every monotone function differs from f on more than an ε fraction of the domain). For any ε > 0, the query complexity of the test is O((n/ε) · log ∣Σ ∣ · log ∣Ξ∣). The previous best known bound was \(\tilde{O}((n^2/\epsilon) \cdot \vert\Sigma\vert^2 \cdot \vert\Xi\vert)\).

We also present an alternative test for the boolean range Ξ = {0,1} whose query complexity O(n 2/ε 2 ) is independent of alphabet size ∣Σ∣.

Keywords

Boolean Function Monotone Function Query Complexity Algorithmic Schema Proof Sketch 
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-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Yevgeniy Dodis
    • 1
  • Oded Goldreich
    • 2
  • Eric Lehman
    • 1
  • Sofya Raskhodnikova
    • 1
  • Dana Ron
    • 3
  • Alex Samorodnitsky
    • 4
  1. 1.Lab for Computer Science, MITCambridgeUSA
  2. 2.Dept. of Computer Science and Applied MathematicsWeizmann Institute of ScienceRehovotIsrael
  3. 3.Dept. of EE-SystemsTel Aviv UniversityRamat AvivIsrael
  4. 4.DIMACS CenterRutgers UniversityPiscatawayUSA

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