Schema design for XML repositories: complexity and tractability

Abiteboul et al. initiated the systematic study of distributed XML documents consisting of several logical parts, possibly located on different machines. The physical distribution of such documents immediately raises the following question: how can a global schema for the distributed document be broken up into local schemas for the different logical parts? The desired set of local schemas should guarantee that, if each logical part satisfies its local schema, then the distributed document satisfies the global schema. Abiteboul et al. proposed three levels of desirability for local schemas: local typing, maximal local typing, and perfect local typing. Immediate algorithmic questions are: (i) given a typing, determine whether it is local, maximal local, or perfect, and (ii) given a document and a schema, establish whether a (maximal) local or perfect typing exists. This paper improves the open complexity results in their work and initiates the study of (i) and (ii) for schema restrictions arising from the current standards: DTDs and XML Schemas with deterministic content models. The most striking result is that these restrictions yield tractable complexities for the perfect typing problem. Furthermore, an open problem in Formal Language Theory is settled: deciding language primality for deterministic finite automata is pspace-complete.