Computational learning algorithms for geometric and algebraic objects

he goal of this thesis is to study the efficient learnability of basic geometric and algebraic objects in on-line learning models. Computational learning algorithms for rectangles and unions of rectangles over the domain ;Next we study the problem of learning DNF formulas with equivalence queries and incomplete membership queries. We show that there is a subclass of k-term DNF formulas for nonconstant k such that one can learn any formula in this class with high probability.;Finally we study the problem of learning disjunctions of counting functions with modulus q over the domain...