Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Boyce-Codd Normal Form

  • Marcelo Arenas
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1245

Synonyms

BCNF

Definition

Let R(A1, …,An) be a relation schema and Σ a set of functional dependencies over R(A1,…,An). Then (R, Σ) is said to be in Boyce-Codd normal form (BCNF) if for every nontrivial functional dependency X → A implied by Σ, it holds that X is a superkey for R.

Key Points

In order to avoid update anomalies in database schemas containing functional dependencies, BCNF was introduced by Codd in [1] (Codd pointed out in [1] that this normal form was developed by Raymond F. Boyce and himself.). This normal form is defined in terms of the notion of superkey as shown above. For example, given a relation schema R(A, B, C) and a set of functional dependencies Σ = {ABC, C → B}, it does not hold that (R(A, B, C), Σ) is in BCNF since C is not a superkey for R. On the other hand, (S (A, B, C), Γ) is in BCNF if Γ = {A → BC}, since A is a superkey for S in this case.

It should be noticed that relation schema R(A, B, C) above is in 3NF if Σ = {ABC, C → B}, although this schema...

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Recommended Reading

  1. 1.
    Codd EF. Recent investigations in relational data base systems. In: Proceedings of the IFIP Congress, Information Processing 74; 1974, p. 1017–21.Google Scholar
  2. 2.
    Beeri C, Bernstein P. Computational problems related to the design of normal form relational schemas. ACM Trans Database Sys. 1979;4(1):30–59.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Pontifical Catholic University of ChileSantiagoChile

Section editors and affiliations

  • Leonid Libkin
    • 1
  1. 1.School of InformaticsUniversity of EdinburghEdinburghUK