There has been a surge of progress in recent years in developing algorithms for testing and
learning quantum states that achieve optimal copy complexity 1–6. Unfortunately, they …

We prove a lower bound of Ω (n 1/3) for the query complexity of any two-sided and adaptive
algorithm that tests whether an unknown Boolean function f:{0, 1} n→{0, 1} is monotone …

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 design a nonadaptive algorithm that, given oracle access to a function which is‐far from
monotone, makes poly queries and returns an estimate that, with high probability, is an …

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 prove that any non-adaptive algorithm that tests whether an unknown Boolean function
f:{0, 1} n→{0, 1} is ak-junta or ε-far from every k-junta must make Ω̃ (k 3/2)/ε) many queries for …

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 …

We study the problem of testing whether an unknown n-variable Boolean function is ak-junta
in the distribution-free property testing model, where the distance between functions is …

We give an adaptive algorithm that tests whether an unknown Boolean function f:{0, 1}
n→{0, 1} is unate (ie every variable of f is either non-decreasing or non-increasing) or ε-far …

We study the problem of testing unateness of functions $ f:\{0, 1\}^ d\to\mathbb {R}. $ We
give a $ O (\frac {d}{\epsilon}\cdot\log\frac {d}{\epsilon}) $-query nonadaptive tester and a …