Almost optimal testers for concise representations

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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. [24], Bshouty [13], Goldreich et al. [32], 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.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2020
EditorsJaroslaw Byrka, Raghu Meka
ISBN (Electronic)9783959771641
DOIs
StatePublished - 1 Aug 2020
Event23rd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 24th International Conference on Randomization and Computation, APPROX/RANDOM 2020 - Virtual, Online, United States
Duration: 17 Aug 202019 Aug 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume176

Conference

Conference23rd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 24th International Conference on Randomization and Computation, APPROX/RANDOM 2020
Country/TerritoryUnited States
CityVirtual, Online
Period17/08/2019/08/20

Keywords

  • Boolean function
  • Junta
  • Property Testing

All Science Journal Classification (ASJC) codes

  • Software

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