Generic Computation and its complexity
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
About primitive recursive algorithms
Selected papers of the 16th international colloquium on Automata, languages, and programming
Conservativity of nested relational calculi with internal generic functions
Information Processing Letters
ACM SIGMOD Record
Principles of programming with complex objects and collection types
ICDT '92 Selected papers of the fourth international conference on Database theory
Normal forms and conservative extension properties for query languages over collection types
Journal of Computer and System Sciences
Query languages for bags and aggregate functions
Journal of Computer and System Sciences - Special issue on principles of database systems
The complexity of the evaluation of complex algebra expressions
Journal of Computer and System Sciences - Special issue on principles of database systems
Local properties of query languages
Theoretical Computer Science - Special issue on the 6th International Conference on Database Theory—ICDT '97
Logics with aggregate operators
Journal of the ACM (JACM)
The power of languages for the manipulation of complex values
The VLDB Journal — The International Journal on Very Large Data Bases
On Two Forms of Structural Recursion
ICDT '95 Proceedings of the 5th International Conference on Database Theory
On the Forms of Locality over Finite Models
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Solving Equations in the Relational Algebra
SIAM Journal on Computing
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The extensional aspect of expressive power---i.e., what queries can or cannot be expressed---has been the subject of many studies of query languages. Paradoxically, although efficiency is of primary concern in computer science, the intensional aspect of expressive power---i.e., what queries can or cannot be implemented efficiently---has been much neglected. Here, we discuss the intensional expressive power of NRC(Q, +, ·, , ÷, Σ, powerset), a nested relational calculus augmented with aggregate functions and a powerset operation. We show that queries on structures such as long chains, deep trees, etc. have a dichotomous behaviour: Either they are already expressible in the calculus without using the powerset operation or they require at least exponential space. This result generalizes in three significant ways several old dichotomy-like results, such as that of Suciu and Paredaens that the complex object algebra of Abiteboul and Beeri needs exponential space to implement the transitive closure of a long chain. Firstly, a more expressive query language---in particular, one that captures SQL---is considered here. Secondly, queries on a more general class of structures than a long chain are considered here. Lastly, our proof is more general and holds for all query languages exhibiting a certain normal form and possessing a locality property.