A Normal Form for Relational Databases That Is Based on Domains and Keys
A Normal Form for Relational Databases That Is Based on Domains and Keys RONALD FAGIN IBM Research Laboratory A new normal form for relational databases, called domain-key normal form (DK/NF), is defined. Also, formal definitions of insertion anomaly and deletion anomaly are presented. It is shown that a schema is in DK/NF if and only if it has no insertion or deletion anomalies. Unlike previously defined normal forms, DK/NF is not defined in terms of traditional dependencies (functional, multivalued, or join). Instead, it is defined in terms of the more primitive concepts of domain and key, along with the general concept of a “constraint.” We also consider how the definitions of traditional normal forms might be modified by taking into consideration, for the first time, the combinatorial consequences of bounded domain sizes. It is shown that after this modification, these traditional normal forms are all implied by DK/NF. In particular, if all domains are infinite, then these traditional normal forms are all implied by DK/NF. Key Words and Phrases: normalization, database design, functional dependency, multivalued de- pendency, join dependency, domain-key normal form, DK/NF, relational database, anomaly, com- plexity CR Categories: 3.73, 4.33, 4.34, 5.21 1. INTRODUCTION Historically, the study of normal forms in a relational database has dealt with two separate issues. The first issue concerns the definition of the normal form in question, call it Q normal form (where Q can be “third” [lo], “Boyce-Codd” [ 111, “fourth” [16], “projection-join” [17], etc.). A relation schema (which, as we shall see, can be thought of as a set of constraints that the instances must obey) is considered to be “good” in some sense if it is in Q normal form.
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