Dynamic functional dependencies and database aging

Reviewer: Catriel Beeri

The study of constraints in database systems has traditionally focused on static constraints, especially data dependencies. In contrast, this paper deals with both static and dynamic constraints; dynamic constraints specify relationships between the database states before and after an update. The emphasis is on the evolution of the database state, as updates that satisfy the dynamic constraints are applied to an initial state that satisfies the static constraints. Questions of potential interest in this framework include: what are the static constraints that must hold after one or some number of updates; can these constraints be (efficiently) computed; and what are the effects of dynamic constraints on the process of database design. The paper deals with the first two questions, with a few hints on the third, for the case where the static constraints are the well-known functional dependencies, and the dynamic constraints are dynamic versions of the functional dependencies. The choice of these classes of dependencies is well motivated: functional dependencies have well-behaved algorithmic properties, and these carry over to the new framework. The basic idea is that a dynamic dependency can be converted to a static dependency by considering two copies of the scheme's attributes, for the old and the new databases. Using this simple idea, the paper presents algorithms for computing the mappings between the (static) constraints sets of the old and new databases. The results are extended to arbitrary sequences of databases obtained by successive updates. The major result here is that the sets of static constraints on the elements of the sequence are monotone increasing, hence a limit exists. Several algorithms for computing this limit are presented. Regarding the third question above, it is shown that given sets of static and dynamic constraints may imply an exponentially larger set of static constraints for the new database. This is a hint that, in some cases, a specification using both types of constraints may be much easier to check than one using static constraints only. The basic techniques of the paper are those of functional dependency theory, but the author develops a set of concepts and tools specific to the case at hand. While some of the proofs are quite complicated, one should not have a problem understanding the main results and their significance. A problem not considered in the paper, which I certainly would like to see addressed in future research, is the following: Given static and possibly also dynamic constraints, is there a set of dynamic constraints such that it suffices to check only those during updates. The results of the paper may serve as a basis for addressing this issue for the type of constraints defined here.