Recent work has introduced Boolean kernels with which one can learn over a feature space containing all conjunctions of length up to k (for any 1 k n) over the original n Boolean features in the input space. This motivates the question of whether maximum margin algorithms such as support vector machines can learn Disjunctive Normal Form expressions in the PAC learning model using this kernel. We study this question, as well as a variant in which structural risk minimization (SRM) is performed where the class hierarchy is taken over the length of conjunctions.