@inbook{b10a0c2c526a4179949e2926f9484c3c,
title = "Reducing testing affine spaces to testing linearity of functions",
abstract = "For any finite field F and k<ℓ, we consider the task of testing whether a function f:Fℓ→\{0,1\} is the indicator function of an (ℓ-k)-dimensional affine space. For the case of F=GF(2), an optimal tester for this property was presented by Parnas, Ron, and Samorodnitsky (SIDMA 2002), by mimicking the celebrated linearity tester of Blum, Luby and Rubinfeld (JCSS 1993) and its analysis. We show that the former task (i.e., testing (ℓ-k)-dimensional affine spaces) can be efficiently reduced to testing the linearity of a related function g:Fℓ→Fk. This reduction yields an almost optimal tester for affine spaces (represented by their indicator function). Recalling that Parnas, Ron, and Samorodnitsky used testing (ℓ-k)-dimensional affine spaces as the first step in a two-step procedure for testing k-monomials, we also show that the second step in their procedure can be reduced to testing whether the foregoing function g depends on k of its variables.",
author = "Oded Goldreich",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.",
year = "2020",
month = apr,
day = "4",
doi = "10.1007/978-3-030-43662-9\_13",
language = "الإنجليزيّة",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "199--219",
editor = "Oded Goldreich",
booktitle = "Computational Complexity and Property Testing",
address = "ألمانيا",
}