Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure
Dan Mircea Suciu, Jan Paredaens · 1994
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. 1 Introduction Abiteboul and Beeri in [AB88] have shown that powerset can express transitive closure (tc), in a language for complex objects without fixpoints or any other form of iterations. But the obvious way of doing that is by a query whose naturally associated algorithm requires exponential space (and time). We prove here that in order to express tc with powerset, exponential space (and time) is indeed needed. This result is of a different nature than classical inexpressibility results (like transitive closure is not expressible in FO [AU79] or even is not expressible in FO+LFP), because it...