Learning unions of boxes with membership and equivalence queries
Paul W. Goldberg, Sally A. Goldman, H. David Mathias · 1994
We present two algorithms that use membership and equivalence queries to exactly identify the concepts given by the union of s discretized axis-parallel boxes in d-dimensional discretized Euclidean space where there are n discrete values that each coordinate can have. The first algorithm receives at most sd counterexamples and uses time and membership queries polynomial in s and logn for any d constant. Further, all equivalence queries made can be formulated as the union of O(sdlogs) axis parallel boxes.