Bounded Fixpoints for Complex Objects

We investigate a query language for complex-object databases, which is designed to (1) express only tractable queries, and (2) be as expressive over at relations as rst order logic with xpoints. The language is obtained by extending the nested relational algebra NRA, of 9], with a \bounded xpoint" operator. Extending the at case 15, 21] , all PTime computable queries over ordered databases are expressible in this language. The main result consists in proving that this language is a conservative extension of the rst order logic with xpoints, or of the while-queries (depending on the interpretation of the bounded xpoint: innationary or partial). The proof technique uses indexes, to encode complex objects into at relations, and is strong enough to allow for the encoding of NRA with unbounded xpoints into at relations. We also deene a complex object logic based language with xpoints and prove that its range restricted fragment is equivalent to NRA with bounded xpoints.