The Relative Complexity of Updates for a Class of Database Views

Abstract

Abstract. It is well known that the complexity of testing the correctness of an arbitrary update to a database view can be far greater than the complexity of testing a corresponding update to the main schema. However, views are generally managed according to some protocol which limits the admissible updates to a subset of all possible changes. The question thus arises as to whether there is a more tractable relationship between these two complexities in the presence of such a protocol. In this paper, this question is answered in the affirmative for closed update strategies, which are based upon the constant-complement approach of Bancilhon and Spyratos. Working within a very general framework which is independent of any particular data model, but which recaptures relational schemata constrained by so-called equality-generating dependencies (EGDs), (which include functional dependencies (FDs)), it is shown that the complexity of testing the correctness of a view update which follows a closed update strategy is no greater than that of testing a corresponding update to the main schema. In particular, if the main schema is relational and constrained by FDs, then there exists a set of FDs on the view, against which any candidate update may be tested for correctness. This holds even though the entire view may not be finitely axiomatizable, much less constrained by FDs alone.

The complexity of embedded axiomatization for a class of closed database views

“…A fundamental condition in the study of view updates,as reported in [Heg02], [Heg04a], and [Heg04b], is that the update strategies should be closed. The formal definition of an update strategy, and the list of conditions which render it closed, are quite technical and are not needed to understand the work reported here.…”

“…Although it has much in common with the earlier work [Heg04b], it differs in a very fundamental way. Specifically, in [Heg04b], the starting point was the so-called semantic schemata -those which include only the databases which satisfy the constraints of the schema.…”

“…Although it has much in common with the earlier work [Heg04b], it differs in a very fundamental way. Specifically, in [Heg04b], the starting point was the so-called semantic schemata -those which include only the databases which satisfy the constraints of the schema. From the semantic schemata the more general syntactic schemata -those which embody all databases, regardless of whether or not they satisfy the constraints -were constructed, using a sort of "completion" operation.…”

“…Second, there is no measure of database size, without which there is no possibility of measuring complexity. To address these issues, in [Heg04b] the notions of CFAschema and CFA-morphism were introduced. In the current paper, these notions have been replaced by the more flexible PF-schema and PF-morphism, respectively.…”

“…In all cases, the question of view update complexity is then answered via a corollary to this main result. † Parts of this paper are based upon work reported in [Heg04b] 1 …”