On the dependency on the size of the data when chasing under conceptual dependencies

Conceptual dependencies (CDs) are particular kinds of key dependencies (KDs) and inclusion dependencies (IDs) that precisely characterize relational schemata modeled according to the main features of the Entity-Relationship (ER) model. An instance for such a schema may be inconsistent (data violate the dependencies) and incomplete (data constitute a piece of correct information, but not necessarily all the relevant information). While undecidable under general KDs and IDs, query answering under incomplete data is known to be decidable for CDs. The known techniques are based on the chase -- a special instance, organized in levels of depth, that is a representative of all the instances that satisfy the dependencies and that include the initial instance. Although the chase generally has infinite size, query answering can be addressed by posing the query (or a rewriting thereof) on a finite, initial part of the chase. Contrary to previous claims, we show that the maximum level of such an initial part cannot be bounded by a constant that does not depend on the size of the initial instance.Comment: 22 pages, 2 figures (one of which with 5 subfigures). arXiv admin note: substantial text overlap with arXiv:1003.313

On the difference between checking integrity constraints before or after updates

Integrity checking is a crucial issue, as databases change their instance all the time and therefore need to be checked continuously and rapidly. Decades of research have produced a plethora of methods for checking integrity constraints of a database in an incremental manner. However, not much has been said about when to check integrity. In this paper, we study the differences and similarities between checking integrity before an update (a.k.a. pre-test) or after (a.k.a. post-test) in order to assess the respective convenience and properties.Comment: 16 page