The Bounded Injury Priority Method and the Learnability of Unions of Rectangles

We develop a bounded version of the nite injury priority method in recursion theory. We use this to study the learnability of unions of rectangles over the domain f0; : : :; n? 1g d with only equivalence queries. Applying this method, we show three main results: (1) The class of unions of rectangles is polynomial time learnable for constant dimension d. (2) The class of unions of rectangles whose projections at some unknown dimension are pairwise-disjoint is polynomial time learnable. (3) The class of unions of two disjoint rectangles is polynomial time learnable with unions of two rectangles as hypotheses.