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Spectral properties of threshold functions

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Abstract

We examine the spectra of boolean functions obtained as the sign of a real polynomial of degreed. A tight lower bound on various norms of the lowerd levels of the function's Fourier transform is established. The result is applied to derive best possible lower bounds on the influences of variables on linear threshold functions. Some conjectures are posed concerning upper and lower bounds on influences of variables in higher order threshold functions.

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Authors and Affiliations

  1. Department of Computer Science, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Craig Gotsman

  2. Department of Computer Science, The Hebrew University, 91904, Jerusalem, Israel

    Nathan Linial

Authors
  1. Craig Gotsman
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  2. Nathan Linial
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Additional information

Supported by an Eshkol fellowship, administered by the National Council for Research and Development—Israel Ministry of Science and Development.

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Gotsman, C., Linial, N. Spectral properties of threshold functions. Combinatorica 14, 35–50 (1994). https://doi.org/10.1007/BF01305949

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  • DOI: https://doi.org/10.1007/BF01305949

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