On Monotonicity Testing and Boolean Isoperimetric type Theorems.

We show a directed and robust analogue of a boolean isoperimetric type theorem of Talagrand. As an application, we give a monotonicity testing algorithm that makes, up to polylog factors, (square root of n)/ε2 non-adaptive queries to a function f:0, 1n -> 0, 1, always accepts a monotone function and rejects a function that is ε-far from being monotone with constant probability.