On the complexity of verifying consistency of XML specifications. http://dx.doi.org/10.1137/050646895

Abstract

XML specifications often consist of a type definition (typically, a document type definition (DTD)) and a set of integrity constraints. It has been shown previously that such specifications can be inconsistent, and thus it is often desirable to check consistency at
compile time. It is known [W. Fan and L. Libkin, J. ACM, 49 (2002), pp. 368-406] that for general keys, foreign keys, and DTDs the consistency problem is undecidable; however, it becomes NP-complete when all keys are one-attribute (unary) and tractable, if no foreign
keys are used. In this paper, we consider a variety of previously studied constraints for XML data and investigate the complexity of the consistency problem. Our main conclusion is that, in the presence of foreign key constraints, compile-time verification of consistency is
infeasible. We look at absolute constraints that hold in the entire document and relative constraints that hold only in a part of the document. For absolute constraints, we prove decidability and establish complexity bounds for primary multiattribute keys and unary
foreign keys and study unary constraints that involve regular expressions. For relative constraints, we prove that even for unary constraints the consistency problem is undecidable. We also show that results continue to hold for extended DTDs, a more expressive typing
mechanism for XML.