Finite Satis ability of Keys and Foreign Keys for XML

Key and foreign key constraints are useful for XML 5] data in semantic speciication, query optimization and more importantly, for information preservation in data exchange. Several XML proposals, e.g., XML Schema 28] and XML Data 21], support key and foreign key speciications. These constraints, however, may not be nitely satissable in the XML context. More specifically , given a DTD D and a nite set of key and foreign key constraints, there may not exist any nite XML documents that both conform to D and satisfy. This paper investigates nite satissability problems associated with key and foreign key constraints for XML. We show that DTDs impose a class of cardinality constraints on XML documents, and these cardinality constraints interact with keys and foreign keys. We investigate the interaction and in particular, establish complexity results for the analysis of nite satissability of keys and foreign keys deened in two constraint languages. One language, L u , deenes unary keys and foreign keys in terms of XML attributes, and the other, L, deenes multi-attribute keys and foreign keys. We show that the nite satissability problem for L u constraints is NP-complete, and the nite satissability problem for L constraints is undecidable. We also establish PTIME decidability for several special cases of the nite satis-ability problems.