Some properties of relational expressions

Abstract

We obtain certain results concerning the power of expressions in relational (calculus and algebra) database sublanguages. Our main results state the undecidability of the equivalence and finite equivalence problems for relational expressions. We also observe that the type of join used in a relational algebra affects the complexity of problems for that algebra. For example, using equi-joins instead of natural joins leads to unnecessarily complex expressions. We relate these results to the problems of query optimization and concurrency control.