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One of the classic results in analysis of Boolean functions is a result of Friedgut [Fri98] that states that Boolean functions over the hypercube of low influence are essentially determined by few coordinates, called juntas. While this result has also been extended to product distributions, not much is known in the case of nonproduct distributions. We(More)
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 give the first efficient algorithms for testing whether a Boolean function has a sparse(More)
In recent work, Kalai, Klivans, Mansour, and Serve-dio [KKMS05] studied a variant of the " Low-Degree (Fourier) Algorithm " for learning under the uniform probability distribution on {0, 1} n. They showed that the L 1 polynomial regression algorithm yields agnostic (tolerant to arbitrary noise) learning algorithms with respect to the class of threshold(More)
A function f is d-resilient if all its Fourier coefficients of degree at most d are zero, i.e. f is uncorre-lated with all low-degree parities. We study the notion of approximate resilience of Boolean functions, where we say that f is α-approximately d-resilient if f is α-close to a [−1, 1]-valued d-resilient function in 1 distance. We show that approximate(More)
We study lower bounds for testing membership in families of linear/affine-invariant Boolean functions over the hypercube. A family of functions P ⊆ {{0, 1} n → {0, 1}} is linear/affine invariant if for any f ∈ P, it is the case that f • L ∈ P for any linear/affine transformation L of the domain. Motivated by the recent resurgence of attention to the(More)