@inproceedings{0d0b3afa9f51462198eef348d105bb23,

title = "Testing fourier dimensionality and sparsity",

abstract = "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 (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 structural results about sparse Boolean functions and new analysis of the pairwise independent hashing of Fourier coefficients from [12].",

author = "Parikshit Gopalan and Ryan O'Donnell and Servedio, {Rocco A.} and Amir Shpilka and Karl Wimmer",

year = "2009",

doi = "10.1007/978-3-642-02927-1_42",

language = "אנגלית",

isbn = "3642029264",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

number = "PART 1",

pages = "500--512",

booktitle = "Automata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings",

edition = "PART 1",

note = "null ; Conference date: 05-07-2009 Through 12-07-2009",

}