This book introduces important results and techniques in property testing, where the goal is
to design algorithms that decide whether their input satisfies a predetermined property in …

We study the problems of learning and testing junta distributions on $\{-1, 1\}^ n $ with
respect to the uniform distribution, where a distribution $ p $ is a $ k $-junta if its probability …

We prove a strong composition theorem for junta complexity and show how such theorems
can be used to generically boost the performance of property testers. The ε-approximate …

We give the first super-polynomial (in fact, mildly exponential) lower bounds for tolerant
testing (equivalently, distance estimation) of monotonicity, unateness, and juntas with a …

We consider the problem of testing whether an unknown $ n $-variable Boolean function is a
$ k $-junta in the distribution-free property testing model, where the distance between …

Leveraging tools of De, Mossel, and Neeman [FOCS, 2019], we show two different results
pertaining to the\emph {tolerant testing} of juntas. Given black-box access to a Boolean …

We consider the problems of testing and learning quantum k-junta channels, which are n-
qubit to n-qubit quantum channels acting non-trivially on at most k out of n qubits and …

We establish new hardness results for decision tree optimization problems, adding to a line
of work that dates back to Hyafil and Rivest in 1976. We prove, under the randomized …

We give improved and almost optimal testers for several classes of Boolean functions on $ n
$ inputs that have concise representation in the uniform and distribution-free model …

Motivated by the fact that input distributions are often unknown in advance, distribution-free
property testing considers a setting in which the algorithmic task is to accept functions …