First-Order Types and Redundant Relations in Relational Databases

Roughly, we define a redundant relation in a database instance (dbi) as a k-ary relation R such that there is a first-order query which evaluated in the reduced dbi, gives us R. So, we can eliminate that relation R as long as the equivalence classes of the relation of equality of the first-order types for all k-tuples in the dbi are not altered. It turns out that in a fixed dbi, the problem of deciding whether a given relation in the dbi is redundant is decidable, though intractable. We then study redundant relations with a restricted notion of equivalence so that the problem becomes tractable.