We consider the feature-generation task wherein we are given a database with entities A1:K111 as positive and negative examples, and we want to find feature queries that linearly separate the two sets of examples. We focus on conjunctive feature queries, and explore two problems: (a) deciding if separating feature queries exist (separability), and (b) generating such queries when they exist. To restrict the complexity of the generated classifiers, we explore various ways of regularizing them by limiting their dimension, the number of joins in feature queries, and their generalized hypertreewidth (ghw). We show that the separability problem is tractable for bounded ghw; yet, the generation problem is not because feature queries might be too large. So, we explore a third problem: classifying new entities without necessarily generating the feature queries. Interestingly, in the case of bounded ghw we can efficiently classify without explicitly generating such queries.