License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.5
URN: urn:nbn:de:0030-drops-126087
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12608/
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Bshouty, Nader H.

Almost Optimal Testers for Concise Representations

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LIPIcs-APPROX5.pdf (0.6 MB)

Abstract

We give improved and almost optimal testers for several classes of Boolean functions on n variables that have concise representation in the uniform and distribution-free model. Classes, such as k-Junta, k-Linear, s-Term DNF, s-Term Monotone DNF, r-DNF, Decision List, r-Decision List, size-s Decision Tree, size-s Boolean Formula, size-s Branching Program, s-Sparse Polynomial over the binary field and functions with Fourier Degree at most d.
The approach is new and combines ideas from Diakonikolas et al. [Ilias Diakonikolas et al., 2007], Bshouty [Nader H. Bshouty, 2018], Goldreich et al. [Oded Goldreich et al., 1998], and learning theory. The method can be extended to several other classes of functions over any domain that can be approximated by functions with a small number of relevant variables.

BibTeX - Entry

@InProceedings{bshouty:LIPIcs:2020:12608,
  author =	{Nader H. Bshouty},
  title =	{{Almost Optimal Testers for Concise Representations}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Jaros{\l}aw Byrka and Raghu Meka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12608},
  URN =		{urn:nbn:de:0030-drops-126087},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.5},
  annote =	{Keywords: Property Testing, Boolean function, Junta}
}

Keywords: Property Testing, Boolean function, Junta
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Issue Date: 2020
Date of publication: 11.08.2020

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