Chasing One's Tail: XPath Containment Under Cyclic DTDs

The problem of finding subclasses of XPath queries and document type definitions (DTDs) for which containment can be tested efficiently has been much studied. Along the way, a number of constraints inferred from DTDs have been used to characterise containment in terms of the chase procedure. However, previous attempts have resulted in procedures that are non-terminating for cyclic DTDs, even when the queries include only the child and descendant operators (i.e., no predicates or wildcards). In this paper, we introduce a rewriting of such XPath queries in the presence of cyclic (but simplified) DTDs, using an operator that generalises the child and descendant operators, and show that doing so allows us to produce a complete procedure for containment using the chase and previous classes of constraints. We also characterise a set of constraints that allows for a complete chase procedure for this fragment of XPath in the case of general, non-cyclic DTDs.