Fixpoints and 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 flat relations as first order logic with fixpoints. The language is obtained by extending the nested relational algebra NRA with a "bounded fixpoint" operator. As in the flat case, 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 first order logic with fixpoints, or of the whilequeries (depending on the interpretation of the bounded fixpoint: inflationary or partial). The proof technique uses indexes, to encode complex objects into flat relations, and is strong enough to allow for the encoding of NRA with unbounded fixpoints into flat relations. We also define a logic based language with fixpoints, the "nested relational calculus", and prove that its range restricted version is equivalent to NRA with bounded fixpoints. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-93-32. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/283 Fixpoints and Bounded Fixpoints for Complex Objects Dan Suciu * Department of Computer and Information Science University of Pennsylvania Philadelphia, PA 19104-6389 Email: [email protected]