Equivalence of relational database schemes

We investigate the question of when two database schemes embody the same information. We argue that this question reduces to the equivalence of the sets of fixed points of the project-join mappings associated with the two database schemes in question. When data dependencies are given, we need only consider those fixed points that satisfy the dependencies. A polynomial algorithm to test the equivalence of database schemes, when there are no dependencies, is given. We also provide an exponential algorithm to handle the case where there are functional and/or multivalued dependencies. Furthermore, we give a polynomial time test to determine whether a project-join mapping preserves a set of functional dependencies, and a polynomial time algorithm for equivalence of database schemes whose project-join mappings do preserve the given set of functional dependencies. Lastly, we introduce the "update sets" approach to database design as an application of these results.