Given query access to a monotone function f\colon\{0,1\}^n\to\{0,1\} with certificate complexity C(f) and an input x^{\star}, we design an algorithm that outputs a size-C(f) subset of x^{\star} certifying the value of f(x^{\star}). Our algorithm makes O(C(f) \cdot \log n) queries to f, which matches the information-theoretic lower bound for this ... more >>>