Functional dependencies among Boolean dependencies

J. Demetrovics, L. Rónyai, Hua Nam Son

Research output: Contribution to journalArticle

Abstract

In this paper, we consider functional dependencies among Boolean dependencies (BDs, for short). Armstrong relations are defined for BDs (called BD-Armstrong relations). For BDs, two necessary and sufficient conditions for the existence of BD-Armstrong relations are given. A necessary and sufficient condition for the existence of Armstrong relations for functional dependencies (FDs, for short) is given, which in some sense is more convenient than the condition given in [3]. We give an algorithm that solves the problem of deciding if two BDs imply the same set of functional dependencies. If the BDs are given in perfect disjunctive normal form, then the algorithm requires only polynomial time. Although Mannila and Räihä have shown that for some relations exponential time is needed for computing any cover of the set of FDs defined in this relation, as a consequence, we show that the problem of deciding if two relations satisfy the same set of FDs can be solved in polynomial time. Another consequence is a new correspondence of the families of functional dependencies to the families of Sperner systems. By this correspondence, the estimate of the number of databases given previously in [6] is improved. It is shown that there is a one-to-one correspondence between the closure of the FDs that hold in a BD and its so-called basic cover. As applications of basic covers, we obtain a representation of a key, the family of minimal keys and a representation of canonical covers.

Original languageEnglish
Pages (from-to)83-106
Number of pages24
JournalAnnals of Mathematics and Artificial Intelligence
Volume7
Issue number1-4
DOIs
Publication statusPublished - Mar 1993

Fingerprint

Functional Dependency
Polynomials
Cover
Polynomial time
Correspondence
Necessary Conditions
Sufficient Conditions
Exponential time
One to one correspondence
Normal Form
Closure
Imply
Computing
Estimate
Family

Keywords

  • Armstrong relations
  • Boolean dependencies
  • cover
  • functional dependencies
  • key
  • Relational database
  • Sperner system

ASJC Scopus subject areas

  • Applied Mathematics
  • Artificial Intelligence

Cite this

Functional dependencies among Boolean dependencies. / Demetrovics, J.; Rónyai, L.; Son, Hua Nam.

In: Annals of Mathematics and Artificial Intelligence, Vol. 7, No. 1-4, 03.1993, p. 83-106.

Research output: Contribution to journalArticle

Demetrovics, J. ; Rónyai, L. ; Son, Hua Nam. / Functional dependencies among Boolean dependencies. In: Annals of Mathematics and Artificial Intelligence. 1993 ; Vol. 7, No. 1-4. pp. 83-106.
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