THE BOUNDED INJURY PRIORITY METHOD AND THE LEARNABILITY OF UNIONS OF RECTANGLES

We develop a bounded version of the finite injury priority method in r ecursion theory. We use this to study the learnability of unions of re ctangles over the domain {O,..., n - 1}(d) with only equivalence queri es. Applying this method, we show three main results: (1) The class of unions of rectangles is polynomial time learnable for constant dimens ion 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.