Implication Problems for Functional Constraints on Databases Supporting Complex Objects

Virtually all semantic or object-oriented data models assume that objects have an identity separate from any of their parts and allow uses to define complex object types in which part values may be any other objects. In G. E. Weddell (ACM Trans. Database Systems17, No. 1 (1992), 32-64), a more general form of functional dependency is proposed for such models in which component attributes may correspond to descriptions of property paths, called path functional dependencies (PFDs). The main contribution of the reference is a sound and complete axiomatization for PFDs when databases may be infinite. However, a number of issues were left open which are resolved in this paper. We first prove that the same axiomatization remains complete if PFDs are permitted empty left-hand sides, but that this is not true if logical consequence is defined with respect to finite databases. We then prove that the implication problem for arbitrary PFDs is decidable. The proof suggests a means of characterizing an important function closure which is then used to derive an effective procedure for constructing a deterministic finite state automaton representing the closure. The procedure is further refined to efficient polynomial time algorithms for the implication problem for cases in which antecedent PFDs are a form of complex key constraint.