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The Implication Problem for Functional and Multivalued Dependencies

Lakshmanan, VS and Madhavan, CEV (1985) The Implication Problem for Functional and Multivalued Dependencies. In: Lecture Notes in Computer Science, 206 . pp. 303-328.

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Computation of the dependency basis is the fundamental step in solving the implication problem for MVDs in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of an MVD-lattice and develop an algebraic characterization of the inference basis using simple notions from lattice theory. We also establish several properties of MVD-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a) computing the inference basis of a given set M of MVDs; (b) computing the dependency basis of a given attribute set w.r.t. M; and (c) solving the implication problem for MVDs. Finally, we show that our results naturally extend to incorporate FDs also in a way that enables the solution of the implication problem for both FDs and MVDs put together.

Item Type: Journal Article
Publication: Lecture Notes in Computer Science
Publisher: Springer
Additional Information: Copyright of this article Springer.
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 17 Aug 2009 11:00
Last Modified: 17 Aug 2009 11:00
URI: http://eprints.iisc.ac.in/id/eprint/20058

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