On Monotonicity Testing and Boolean Isoperimetric Type Theorems - Khot, Subhash; Minzer, Dor; Safra, Muli (2015 IEEE 56th Annual Symposium on Foundations of Computer Science, 2015)
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.