We consider the problem of privately releasing a low dimensional approximation to a set of data records, represented as a matrix A in which each row corresponds to an individual and each column to an attribute. Our goal is to compute a subspace that ...

We consider the task of interactive communication in the presence of adversarial errors and present tight bounds on the tolerable error-rates in a number of different settings.

Most significantly, we explore adaptive interactive communication where the ...

The threshold degree of a Boolean function f is the minimum degree of a real polynomial p that represents f in sign: f(x) ≡ sgn p(x). In a seminal 1969 monograph, Minsky and Papert constructed a polynomial-size constant-depth {∧, ∨)-circuit in n ...

Let ACC o THR be the class of constant-depth circuits comprised of AND, OR, and MODm gates (for some constant m > 1), with a bottom layer of gates computing arbitrary linear threshold functions. This class of circuits can be seen as a "midpoint" between ...

We use critical block sensitivity, a new complexity measure introduced by Huynh and Nordström (STOC 2012), to study the communication complexity of search problems. To begin, we give a simple new proof of the following central result of Huynh and ...

We describe Zig-zag Sort---a deterministic data-oblivious sorting algorithm running in O(n log n) time that is arguably simpler than previously known algorithms with similar properties, which are based on the AKS sorting network. Because it is data-...

We give the first super-polynomial separation in the power of bounded-depth boolean formulas vs. circuits. Specifically, we consider the problem Distance k(n) Connectivity, which asks whether two specified nodes in a graph of size n are connected by a ...

We introduce a new technique, that we call punctured programs, to apply indistinguishability obfuscation towards cryptographic problems. We use this technique to carry out a systematic study of the applicability of indistinguishability obfuscation to a ...

Does derandomization of probabilistic algorithms become easier when the number of "bad" random inputs is extremely small?

In relation to the above question, we put forward the following quantified derandomization challenge: For a class of circuits C (...