The Expressive Power of Complex Values in Object-Based Data Models

In object based data models complex values such as tuples or sets have no special status and must therefore be represented by objects As a consequence di erent objects may represent the same value i e duplicates may occur This paper contains a study of the precise expressive power required for the representation of complex values in typical object based data models supporting rst order queries object creation and while loops Such models are su ciently powerful to ex press any reasonable collection of complex values provided duplicates are allowed It is shown that in general the presence of such dupli cates is unavoidable in the case of set values In contrast duplicates of tuple values can easily be eliminated A fundamental operation for duplicate elimination of set values called abstraction is considered and shown to be a tractable alternative to explicit powerset construc tion Other means of avoiding duplicates such as total order equality axioms or copy elimination are also discussed Extended and revised version of a paper presented at the Tenth ACM Symposium on Principles of Database Systems VP Research Assistant of the Belgian National Fund for Scienti c Research