Property testing is concerned with the design of super-fast algorithms for the structural
analysis of large quantities of data. The aim is to unveil global features of the data, such as …

We show a directed and robust analogue of a boolean isoperimetric-type theorem of
Talagrand Geom. Funct. Anal., 3 (1993), pp. 295--314. As an application, we give a …

Given oracle access to a Boolean function f:{0, 1} n->{0, 1}, we design a randomized tester
that takes as input a parameter ε> 0, and outputs Yes if the function is monotonically non …

We consider the problem of testing whether an unknown Boolean function f:{-1, 1} n→{-1, 1}
is monotone versus ε-far from every monotone function. The two main results of this paper …

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 give a 2^̃O(n/ε)-time algorithm for properly learning monotone Boolean functions under
the uniform distribution over {0,1\}^n. Our algorithm is robust to adversarial label noise and …

We initiate a systematic study of sublinear algorithms for approximately testing properties of
real-valued data with respect to L p distances for p= 1, 2. Such algorithms distinguish …

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 …

For positive integers n, d, consider the hypergrid [n] d with the coordinate-wise product
partial ordering denoted by≺. A function f:[n] d→ ℕ is monotone if∀ x≺ y, f (x)≤ f (y). A …