The bounded injury priority method and the learnability of unions of rectangles Original Research Article

We develop a bounded version of the finite injury priority method in recursion theory. We use this to study the learnability of unions of rectangles over the domain {0, …, n − 1}d with only equivalence queries. Applying this method, we show three main results: 1. (1)The class of unions of rectangles is polynomial time learnable for constant dimension d. 2. (2)The class of unions of rectangles whose projections at some unknown dimension are pairwise-disjoint is polynomial time learnable. 3. (3)The class of unions of two disjoint rectangles is polynomial time learnable with unions of two rectangles as hypotheses.