Abstract We consider the problem of learning monotone Boolean functions over under the uniform distribution. Specifically, given a polynomial number of uniform random samples for an unknown monotone Boolean function , and given polynomial computing time, we would like to approximate as well as possible. We describe a simple algorithm that we prove achieves error at most , improving on the previ...

The rst main result of this paper is a novel non-uniform approximation method for the kinody-namic motion-planning problem. The kinodynamic motion-planning problem is to compute a collision-free, minimum-time trajectory for a robot whose accelerations and velocities are constrained. Previous approximation methods are all based on a uniform dis-cretization in time space. On the contrary, our met...