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ICALP
2009
Springer

Testing Fourier Dimensionality and Sparsity

12 years 1 months ago
Testing Fourier Dimensionality and Sparsity
We present a range of new results for testing properties of Boolean functions that are defined in terms of the Fourier spectrum. Broadly speaking, our results show that the property of a Boolean function having a concise Fourier representation is locally testable. We first give an efficient algorithm for testing whether the Fourier spectrum of a Boolean function is supported in a low-dimensional subspace of Fn 2 (equivalently, for testing whether f is a junta over a small number of parities). We next give an efficient algorithm for testing whether a Boolean function has a sparse Fourier spectrum (small number of nonzero coefficients). In both cases we also prove lower bounds showing that any testing algorithm -- even an adaptive one -must have query complexity within a polynomial factor of our algorithms, which are nonadaptive. Finally, we give an "implicit learning" algorithm that lets us test any sub-property of Fourier concision. Our technical contributions include new str...
Parikshit Gopalan, Ryan O'Donnell, Rocco A. Served
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2009
Where ICALP
Authors Parikshit Gopalan, Ryan O'Donnell, Rocco A. Servedio, Amir Shpilka, Karl Wimmer
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