Dependency Preserving Refinements and the Fundamental Problem of Database Design

40 { How the folklore heuristics of splitting attributes can be made into a precise design tool for obtaining dependency preserving BCNF. { Why the Embedded Implicational Dependencies are all needed, when we deal with stepwise reenements of database schemes speciied by Functional and Inclusion Dependencies. As the material presented grew slowly while teaching database theory, its foundational and didactic merits should not be underestimated. Over the years our students of the advanced database theory course connrmed our view that traditional database design lacks coherence and that this approach makes many issues accessible to deeper understanding. Our approach via dependency preserving translation{reenements can be extended to a full edged design theory for Entity{Relationship design or, equivalently , for database schemes in ER-normal form, cf. MR92]. It is also the appropriate framework to compare transformations of ER-schemes and to address the Fundamental Problem of ER{Database Design. Translation schemes can also be used to deal with views and view updates, as views are special cases of translation schemes. The theory of complementary views from BS81] can be rephrased elegantly in this framework. It is connected with the notion of translation schemes invariant under a relation and implicit de-nability, Kol90]. Order invariant translation schemes play an important role in descriptive complexity theory, Daw93] and Mak94]. The theory of independent complementary views of KU84] exhibits some severe limitations on the applicability of BS81]. In spite of these limitations it seems worthwhile to explore the connection between independent views and transformation invariant for certain relations further. The latter two applications are currently being developed by the authors and their students. A uniform method for proving lower bounds on the computational complexity of logical theories.