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Definition
Let R(A 1,..., A n ) be a relation schema and Σ a set of functional dependencies over R(A 1,..., A n ). An attribute A i (i ∈{1,...,n}) is a prime attribute if A i is an element of some key of R(A 1,..., A n ). Then specification (R, Σ) is said to be in third normal form (3NF) if for every nontrivial functional dependency X → A implied by Σ, it holds that X is a superkey for R or A is a prime attribute [1].
Key Points
In order to avoid update anomalies in database schemas containing functional dependencies, 3NF was introduced by Codd in [1]. This normal form is defined in terms of the notions of prime attribute and key as shown above. For example, given a relation schema R(A, B, C) and a set of functional dependencies Σ = {AB → C, C → B}, it holds that (R(A, B, C), Σ) is in 3NF since AB is a superkey and C is a prime attribute (given that AC is a key for R). On the other hand, (S(A, B, C), Γ) is not in 3NF if Γ = {A → B}, since A is not a superkey for S and B...
Recommended Reading
Codd EF. Further normalization of the data base relational model. In: Proceedings of data base systems. Englewood Cliffs: Prentice-Hall; 1972. p. 33–64.
Biskup J, Dayal U, Bernstein P. Synthesizing independent database schemas. In: Proceedings of ACM SIGMOD international conference on management of data; 1979, p. 143–51.
Jou J, Fischer P. The complexity of recognizing 3NF relation schemes. Inf Process Lett. 1982;14(4):187–90.
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Arenas, M. (2017). Third Normal Form. In: Liu, L., Özsu, M. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-7993-3_1264-2
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DOI: https://doi.org/10.1007/978-1-4899-7993-3_1264-2
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