On the menbership problem for functional and multivalued dependencies in relational databases

The problem of whether a given dependency in a database relation can be derived from a given set of dependencies is investigated. We show that the problem can be decided in polynomial time when the given set consists of either multivalued dependencies only or of both functional and multivalued dependencies and the given dependency is also either a functional or a multivalued dependency. These results hold when the derivations are restricted not to use the complementation rule.