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In this paper we define and examine the power of the <i>conditional sampling</i> oracle in the context of distribution-property testing. The conditional sampling oracle for a discrete distribution μ takes as input a subset S ⊂ [n] of the domain, and outputs a random sample i ∈ S drawn according to μ, conditioned on S (and independently… (More)

For a property <i>P</i> and a sub-property <i>P'</i>, we say that <i>P</i> is <i>P'</i>-partially testable with <i>q</i> queries} if there exists an algorithm that distinguishes, with high probability, inputs in <i>P'</i> from inputs ε-far from <i>P</i>, using <i>q</i> queries. Some natural properties require many queries to test, but can be… (More)

For a property P and a sub-property P ′ , we say that P is P ′-partially testable with q queries if there exists an algorithm that distinguishes, with high probability, inputs in P ′ from inputs ǫ-far from P by using q queries. There are natural properties that require many queries to test, but can be partitioned into a small number of subsets for which… (More)

We study the query complexity of testing for properties defined by read once formulas, as instances of massively parametrized properties, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in… (More)

We study the query complexity of testing for properties defined by read-once formulas, as instances of <i>massively parametrized properties</i>, and prove several testability and nontestability results. First, we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries… (More)

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