Functional dependency implications, inducing horizontal decompositions

  • P. De Bra
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 305)


A new decomposition theory for the Relational Database Model is given. It uses a horizontal decomposition of a relation into two disjoint subrelations, of which the union is the given relation. This horizontal decomposition is based on a new constraint, the functional dependency implication (fdi), which is a partial implication between functional dependencies (fd's). This horizontal decomposition is especially useful for databases which cannot be decomposed vertically (in the classical way) because no (or too few) fd's hold.

The “goals”, conditional-functional dependencies (cfd's) and imposed-functional dependencies (ifd's), introduced in previous work, all are special kinds of fdi's, and so are functional dependencies.

The horizontal decomposition induces another new constraint: the anti-functional dependency (afd), of which the afunctional dependency (ad), introduced in previous work, is a special case. The membership problem is solved for mixed fdi's and afd's, and a complete set of inference rules is given. The inheritance problem, i.e. which dependencies hold in the subrelations (generated by the horizontal decomposition), is shown to be solvable in polynomial time.


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  1. [Ar]
    Armstrong W., Dependency structures of database relationships, Proc. IFIP 74, North Holland, pp. 580–583, 1974.Google Scholar
  2. [Be]
    Beeri C., Bernstein P.A., Computational Problems related to the Design of Normal Form Relation Schemes, ACM TODS, vol. 4.1, pp. 30–59, 1979.Google Scholar
  3. [BV]
    Beeri C., Vardi M. Y., Formal Systems for Tuple and Equality Generating Dependencies. SIAM Journal on Computing, 13.1, pp. 76–98, 1984.Google Scholar
  4. [Ber]
    Bernstein P.A., Normalization and Functional Dependencies in the Relational Database Model, CSRG-60, 1975.Google Scholar
  5. [Co]
    Codd E., Further normalizations of the database relational model, In Data Base Systems (R. Rustin, ed.) Prentice Hall, N.J., pp. 33–64, 1972.Google Scholar
  6. [De1]
    De Bra P., Paredaens J., The membership and the inheritance of functional and afunctional dependencies, Proc. of the Colloquium on Algebra, Combinatorics and Logic in Computer Science, Gyor, Hungary.Google Scholar
  7. [De2]
    De Bra P., Paredaens J., Horizontal Decompositions for Handling Exceptions to Functional Dependencies, in “Advances in Database Theory”, Vol. II, pp. 123–144, 1983.Google Scholar
  8. [De3]
    De Bra P., Paredaens J., Conditional Dependencies for Horizontal Decompositions, in “Lecture Notes in Computer Science”, Vol. 154, pp. 67–82, (10-th ICALP), Springer-Verlag, 1983.Google Scholar
  9. [De4]
    De Bra P., Imposed-Functional Dependencies Inducing Horizontal Decompositions, in “Lecture Notes in Computer Science”, Vol. 194, pp. 158–170, (12-th ICALP), Springer-Verlag, 1985.Google Scholar
  10. [Fa]
    Fagin R., Armstrong Databases, IBM RJ 3440, 1982.Google Scholar
  11. [Pa]
    Paredaens J., De Bra P., On Horizontal Decompositions, XP2-Congress, State Univ. of Pennsylvania, 1981.Google Scholar
  12. [Ul]
    Ullman J., Principles of Database Systems, Pitman, 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • P. De Bra
    • 1
  1. 1.Department of MathematicsUniversity of Antwerp, U.I.A.AntwerpBelgium

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