Investigations on Armstrong Relations , Dependency Inference , andExcluded Functional

This paper rst presents some new results on excluded functional dependencies, i.e., FDs which do not hold on a given relation schema. In particular, we show how excluded dependencies relate to Armstrong relations, and we state criteria for deciding whether a set of excluded dependencies characterizes a set of FDs. In the rest of the paper, complexity issues related to the following three problems are studied : to construct an Armstrong relation for a cover F of functional dependencies (FDs), to construct a cover of FDs that hold in a relation R (dependency inference), and, given a cover F and a relation R, to decide if all the FDs that hold in R can be derived from F. The rst two problems are known to have exponential complexity. We give a new proof for the second problem by showing that dependency inference can be used to compute all keys of a relation instance. We prove that the third problem is co-NP-complete. Further, it is shown that the problems can be solved in polynomial time if it is known that a relation scheme satisses some additional properties, which are polynomially recognizable themselves.