Query containment under constraints is the problem of checking whether for every database satisfying a given set of constraints, the result of one query is a subset of the result of another query, Recent research points out that this is a central problem in severa database applications, and we address it within A setting where constraints are specified in the form of special inclusion dependencies over complex expressions, built by using intersection and difference of relations, special forms of quantification, regular expressions over binary relations, and cardinality constraints. These types of constraints capture a great variety of data models, including the relational, the entity-relational, and the object-oriented model, We study the problem of checking whether q is contained in q’ with respect to the constraints specified in a schema S, where q and q’ are nonrecursive Datalog programs whose atoms are complex expressions. We present the following results on query containment. For the case where q does not contain regular expressions, we provide a method for deciding query containment, and analyze its computational complexity. We do the same for the case where neither S nor q, q’ contain number restrictions. To the best of our knowledge, this yields the first decidability result on containment of conjunctive queries with regular expressions. Finally, we Provo that the problem is undecidable for the case where we admit inequalities in q’,
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