Equivalences Among Relational Expressions with the Union and Difference Operators
Journal of the ACM (JACM)
On the Complexity of Testing Implications of Functional and Join Dependencies
Journal of the ACM (JACM)
A relational model of data for large shared data banks
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of facets (and some facets of complexity)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
The consistency of "P = NP" and related problems with fragments of number theory
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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We prove a sequence of results which characterize exactly the complexity of problems related to the evaluation of relational queries consisting of projections and natural joins. We show that testing whether the result of a given query on a given relation equals some other given relation is Dp complete (Dp is a class which includes both NP and co-NP, and was recently introduced in a totally different context [13]). We show that testing inclusion or equivalence of queries with respect to a fixed relation (or of relations with respect to a fixed query) is Π2p-complete. We also examine the complexity of estimating the number of tuples of the answer.