On accessing object-oriented databases: expressive power, complexity, and restrictions

A formal framework for studying the expressive power and complexity of OODB queries is developed. Three approaches to modeling sets are articulated and compared. The class of regular OODB schemas supports the explicit representation of set-valued types. Using an object-based semantics for sets, the regular schemas correspond to most implemented OODB systems in the literature; a value-based semantics for sets is also introduced. Without restrictions, both of these approaches support the specification of all computable queries. Assuming that the new operator is prohibited, the query language of the regular OODB schemas under the object-based semantics is complete in PSPACE; and under the value-based semantics it has hyper-exponential complexity. The third approach to modeling sets is given by the algebraic OODB model, in which multi-valued attributes rather than set-valued types are supported. method implementations can use operators stemming from the relational algebra, and do not have side-effects. The query language of algebraic OODBs is more powerful than the relational algebra but has complexity bounded by PTIME. The expressive power and complexity of data access for other variations of OODBs are also considered. Finally, a new relational query language, called algebra + pointwise recursion, is introduced. This is equivalent to the algebraic OODB language, and can compute generalized transitive closure.