On Monotonicity Testing and Boolean Isoperimetric Type Theorems

We show a directed and robust analogue of a boolean isoperimetric type theorem of Talagrand [13]. As an application, we give a monotonicity testing algorithm that makes O̅(√n/ε
²
) non-adaptive queries to a function f : {0, 1}
ⁿ
→ {0, 1}, always accepts a monotone function and rejects a function that is ε-far from being monotone with constant probability.