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. 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. (shrink)

Reviewed Works:Andrea Sorbi, Complexity, Logic, and Recursion Theory.Klaus Ambos-Spies, Elvira Mayordomo, Resource-Bounded Measure and Randomness.Marat Arslanov, Degree Structures in Local Degree Theory.Jose L. Balcazar, Ricard Gavalda, Montserrat Hermo, Compressibility of Infinite Binary Sequences.S. Barry Cooper, Beyond Godel's Theorem: The Failure to Capture Information Content.Robert A. Di Paola, Franco Montagna, Progressions of Theories of Bounded Arithmetic.Rodney G. Downey, On Presentations of Algebraic Structures.Sophie Fischer, Lane Hemaspaandra, Leen Torenvliet, Witness-Isomorphic Reductions and Local Search.William Gasarch, Carl H. Smith, A Survey of Inductive Inference (...) with an Emphasis on Queries.Andre Nies, A Uniformity of Degree Structures.Piergiorgio Odifreddi, Short Course on Logic, Algebra, and Topology.Andrea Sorbi, The Enumeration Degrees of the $\sigma^0_2$ Sets.Peter van Emde Boas, The Convenience of Tilings. (shrink)