Distribution-Free Testing Lower Bounds for Basic Boolean Functions

  • Dana Glasner
  • Rocco A. Servedio
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4627)

Abstract

In the distribution-free property testing model, the distance between functions is measured with respect to an arbitrary and unknown probability distribution \(\mathcal{D}\) over the input domain. We consider distribution-free testing of several basic Boolean function classes over {0,1}n, namely monotone conjunctions, general conjunctions, decision lists, and linear threshold functions. We prove that for each of these function classes, Ω((n/logn)1/5) oracle calls are required for any distribution-free testing algorithm. Since each of these function classes is known to be distribution-free properly learnable (and hence testable) using Θ(n) oracle calls, our lower bounds are within a polynomial factor of the best possible.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Dana Glasner
    • 1
  • Rocco A. Servedio
    • 1
  1. 1.Department of Computer Science, Columbia University, New York, NY 10027USA

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