A Theory of Regular Queries

Abstract

A major theme in relational database theory is navigating the tradeoff between expressiveness and tractability for query languages, where the query-containment problem is considered a benchmark of tractability. The query class UCQ, consisting off unions of conjunctive queries, is a fragment of first-order logic that has a decidable query containment problem, but its expressiveness is limited. Extending UCQ with recursion yields Datalog, an expressive query language that has been studied extensively and has recently become popular in application areas such as declarative networking. Unfortunately, Datalog has an undecidable query containment problem. Identifying a fragment of Datalog that is expressive enough for applications but has a decidable query-containment problem has been an open problem for several years. In the area of graph databases, there has been a similar search for a query language that combines expressiveness and tractability. Because of the need to navigate along graph paths of unspecified length, transitive closure has been considered a fundamental operation. Query classes of increasing complexity -- using the operations of disjunction, conjunction, projection, and transitive closure -- have been studied, but the classes lacked natural closure properties. The class RQ of regular queries has emerged only recently as a natural query class that is closed under all of its operations and has a decidable query-containment problem. RQ turned out to be a fragment of Datalog where recursion can be used only to express transitive closure. Furthermore, it turns out that applying this idea to Datalog, that is, restricting recursion to the expression of transitive closure, does yield the long-sought goal -- an expressive fragment of Datalog with a decidable query-optimization problem.