Date of this Version
The Abiteboul and Beeri algebra for complex objects can express a query whose meaning is transitive closure, but the algorithm naturally associated to this query needs exponential space. We show that any other query in the algebra which expresses transitive closure needs exponential space. This proves that in general the powerset is an intractable operator for implementing fixpoint queries.
Dan Suciu and Jan Paredaens, "Any Algorithm in the Complex Object Algebra With Powerset Needs Exponential Space to Compute Transitive Closure", . February 1994.
Date Posted: 25 July 2007