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Fourth Normal Form and its Associated Decomposition Algorithm

IP.com Disclosure Number: IPCOM000079414D
Original Publication Date: 1973-Jun-01
Included in the Prior Art Database: 2005-Feb-26
Document File: 2 page(s) / 13K

IBM

Related People

Boyce, RF: AUTHOR

Abstract

One of the key data-base problems is redundancy and its associated update difficulties. For a relational system, in which the data base is viewed as a collection of time-varying relations, E. F. Codd [] has proposed storing relations in a standard form, third normal form (sNF), which has the property that certain functional associations of the data are stored nonredundantly. Fourth normal form (4NF) is an extension of this work, in which each relation has the property that all functional associations are stored nonredundantly.

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Fourth Normal Form and its Associated Decomposition Algorithm

One of the key data-base problems is redundancy and its associated update difficulties. For a relational system, in which the data base is viewed as a collection of time-varying relations, E. F. Codd [] has proposed storing relations in a standard form, third normal form (sNF), which has the property that certain functional associations of the data are stored nonredundantly. Fourth normal form (4NF) is an extension of this work, in which each relation has the property that all functional associations are stored nonredundantly.

In order to point out the differences between 3NF and 4NF, the following definitions are introduced. A relation is normalized if it contains no repeating groups. A field or group of fields that uniquely identify the remaining fields of a relation, such that no subset of this group still retains this property, is known as a key. A field that is contained in some key is a prime field, while those that are not in any key are nonprime.

Let R(A,C) be a normalized relation over the set of fields A = AuC, where A is the set of prime fields and C is the set of nonprime fields. R is in 3NF whenever vC(j)epsilon C, v alpha A such that C(j) epsilon alpha, alpha identifies A. In other words, for a relation in 3NF the only minimal identifiers of nonprime fields are entire keys. Thus, 3NF has the effect of removing the redundancy in functional associations between prime and nonprime fields, but functional associations between prime fields may still be redundant.

Frequently, in a data base a particular key is distinguished as the primary key. Let...