Functional and inclusion dependencies a graph theoretic approach

We present a new graph theoretic approach to the implication problem for functional (FD) and inclusion (IND) dependencies. Using this methodology we prove decidability for the case of typed IND's and acyclic FD's. We provide new lower bounds for the implication of typed, acyclic IND's and FD's --- NP-hardness and PSPACE-hardness for bounded domains. Finally, we show that there is no k-ary complete axiomatization for implication of FD's, even when we have pairwise consistency, i.e., all possible typed IND's hold.

[1]  John C. Mitchell.  The Implication Problem for Functional and Inclusion Dependencies , 1984, Inf. Control..

[2]  Paris C. Kanellakis.  On the Computational Complexity of Cardinality Constraints in Relational Databases , 1980, Inf. Process. Lett..

[3]  Ronald Fagin,et al.  Inclusion dependencies and their interaction with functional dependencies , 1982, PODS.

[4]  Marco A. Casanova,et al.  Towards a sound view integration methodology , 1983, PODS.

[5]  Diane C. P. Smith,et al.  Database abstractions: aggregation and generalization , 1977, TODS.

[6]  Diane C. P. Smith,et al.  Database abstractions: aggregation , 1977, CACM.

[7]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[8]  Ronald Fagin,et al.  A normal form for relational databases that is based on domains and keys , 1981, TODS.

[9]  E. F. Codd,et al.  Extending the database relational model to capture more meaning , 1979, ACM Trans. Database Syst..

[10]  David S. Johnson,et al.  Testing containment of conjunctive queries under functional and inclusion dependencies , 1982, J. Comput. Syst. Sci..

[11]  C. J. Date.  Referential Integrity , 1981, VLDB.

[12]  Alberto O. Mendelzon,et al.  Functional dependencies on cyclic database schemes , 1983, SIGMOD '83.

[13]  John C. Mitchell.  Inference rules for functional and inclusion dependencies , 1983, PODS '83.

[14]  Edward Sciore.  Inclusion dependencies and the universal instance , 1983, PODS '83.

[15]  Moshe Y. Vardi,et al.  Unary inclusion dependencies have polynomial time inference problems , 1983, STOC '83.

[16]  Moshe Y. Vardi,et al.  The Implication Problem for Functional and Inclusion Dependencies is Undecidable , 1985, SIAM J. Comput..