On a hierarchy of classes for nested databases

The nested relational model is nowadays generally accepted as a valid alternative to the flat relational model of Codd, because of its greater ability to model the structure of the real world. Not all nested relations however correspond to representations of the real world. Therefore, a hierarchy of more restricted classes of nested relations was defined. For one such class, called hierarchical nested relations (HNR), we give a characterization in terms of closure properties with respect to algebraic operations. For the largest subclass, the normalization-lossless relations (NL), consisting of all relations obtainable from flat relations using restructing operators only, we show membership to be decidable. At the same time, we provide arguments indicating that an efficient algorithm to decide this membership probably does not exist.