Reducing testing affine spaces to testing linearity
نویسنده
چکیده
We consider the task of testing whether a Boolean function f : {0, 1} → {0, 1} is the indicator function of an (l − k)-dimensional affine space. 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 reduced to testing the linearity of a related function g : {0, 1} → {0, 1}, yielding an almost optimal tester.
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عنوان ژورنال:
- Electronic Colloquium on Computational Complexity (ECCC)
دوره 23 شماره
صفحات -
تاریخ انتشار 2016