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When delegating computation to a service provider, as in the cloud computing paradigm, we seek some reassurance that the output is correct and complete. Yet recomputing the output as a check is inefficient and expensive, and it may not even be feasible to store all the data locally. We are therefore interested in what can be validated by a streaming(More)
The central goal of data stream algorithms is to process massive streams of data using <i>sublinear</i> storage space. Motivated by work in the database community on outsourcing database and data stream processing, we ask whether the space usage of such algorithms can be further reduced by enlisting a more powerful &#8220;helper&#8221; that can(More)
When computation is outsourced, the data owner would like to be assured that the desired computation has been performed correctly by the service provider. In theory, proof systems can give the necessary assurance, but prior work is not sufficiently scalable or practical. In this paper, we develop new proof protocols for verifying computations which are(More)
Motivated by the trend to outsource work to commercial cloud computing services, we consider a variation of the streaming paradigm where a streaming algorithm can be assisted by a powerful helper that can provide annotations to the data stream. We extend previous work on such annotation models by considering a number of graph streaming problems. Without(More)
The ε-approximate degree of a Boolean function f : {−1, 1} n → {−1, 1} is the minimum degree of a real polynomial that approximates f to within error ε in the ℓ ∞ norm. We prove several lower bounds on this important complexity measure by explicitly constructing solutions to the dual of an appropriate linear program. Our first result resolves the(More)
We study the problem of releasing k-way marginals of a database D ∈ ({0, 1} d) n , while preserving differential privacy. The answer to a k-way marginal query is the fraction of D's records x ∈ {0, 1} d with a given value in each of a given set of up to k columns. Marginal queries enable a rich class of statistical analyses of a dataset, and designing(More)
We establish a generic form of hardness amplification for the approximability of constant-depth Boolean circuits by polynomials. Specifically, we show that if a Boolean circuit cannot be pointwise approximated by low-degree polynomials to within constant error in a certain one-sided sense, then an OR of disjoint copies of that circuit cannot be pointwise(More)
We introduce online interactive proofs (OIP), which are a hierarchy of communication complexity models that involve both randomness and nondeterminism (thus, they belong to the Arthur–Merlin family), but are online in the sense that the basic communication flows from Alice to Bob alone. The complexity classes defined by these OIP models form a natural(More)
The approximate degree of a Boolean function f : {−1, 1} n → {−1, 1} is the minimum degree of a real polynomial that approximates f to within error 1/3 in the ∞ norm. In an influential result, Aaronson and Shi (J. ACM 2004) proved tight˜Ω(n 1/3) and˜Ω(n 2/3) lower bounds on the approximate degree of the Collision and Element Distinctness functions,(More)