Given two testable properties $\mathcal{P}_{1}$ and $\mathcal{P}_{2}$, under what conditions are the union, intersection or set-difference
of these two properties also testable?
We initiate a systematic study of these basic set-theoretic operations in the context of property
testing. As an application, we give a conceptually different proof that linearity is ... more >>>

The rich collection of successes in property testing raises a natural question: Why are so many different properties turning out to be locally testable? Are there some broad "features" of properties that make them testable? Kaufman and Sudan (STOC 2008) proposed the study of the relationship between the invariances satisfied ... more >>>

We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the
decoder with high probability either answers correctly or declares ``don't know.'' Furthermore, if there is no ... more >>>

A hypergraph dictatorship test is first introduced by Samorodnitsky
and Trevisan and serves as a key component in
their unique games based $\PCP$ construction. Such a test has oracle
access to a collection of functions and determines whether all the
functions are the same dictatorship, or all their low degree ... more >>>

We consider the task of testing properties of Boolean functions that
are invariant under linear transformations of the Boolean cube. Previous
work in property testing, including the linearity test and the test
for Reed-Muller codes, has mostly focused on such tasks for linear
properties. The one exception is a test ... more >>>