Adaptivity Is Exponentially Powerful for Testing Monotonicity of Halfspaces

We give a poly(logn, 1/ε)-query adaptive algorithm for testing whether an unknown Boolean function f : {−1, 1}n → {−1, 1}, which is promised to be a halfspace, is monotone versus ε-far from monotone. Since non-adaptive algorithms are known to require almost Ω(n) queries to test whether an unknown halfspace is monotone versus far from monotone, this shows that adaptivity enables an exponential improvement in the query complexity of monotonicity testing for halfspaces. Columbia University, email: [email protected]. Columbia University, email: [email protected]. Toyota Technological Institute, email: [email protected]. Columbia University, email: [email protected].