Low-Sensitivity Functions from Unambiguous Certificates

We provide new query complexity separations against sensitivity for total Boolean functions: a power 3 separation between deterministic (and even randomized or quantum) query complexity and sensitivity, and a power 2.1 separation between certificate complexity and sensitivity. We get these separations by using a new connection between sensitivity and a seemingly unrelated measure called one-sided unambiguous certificate complexity (UCmin). Finally, we show that UCmin is lower-bounded by fractional block sensitivity, which means we cannot use these techniques to get a super-quadratic separation between bs(f) and s(f).