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A few years ago, Blais, Brody, and Matulef (2012) presented a methodology for proving lower bounds for property testing problems by reducing them from problems in communication complexity. Recently, Bhrushundi, Chakraborty, and Kulkarni (2014) showed that some reductions of this type can be deconstructed to two separate reductions, from communication… (More)

We consider the following problem. A deterministic algorithm tries to find a string in an unknown set S ⊆ {0, 1} n that is guaranteed to have large density (e.g., |S| ≥ 2 n−1). However, the only information that the algorithm can obtain about S is estimates of the density of S in adaptively chosen subsets of {0, 1} n , where the estimates are up to a… (More)

This work studies a new type of problems in property testing, called <i>dual problems</i>. For a set Ϊ in a metric space and δ > 0, denote by <b>F</b><sub>δ</sub>(Ϊ) the set of elements that are δ-far from Ϊ. Then, in property testing, a δtester for π is required to accept inputs from Ϊ and reject inputs from… (More)

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