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Given a set of functional dependencies , an Armstrong relation is a relation which satisfies all the functional dependencies in the closure + and only those dependencies. . Unfortunately, the minimum-size Armstrong relation for a given set of dependencies can have a size which is an exponential function of the number of attributes in the dependencies conside
Reducing any functional dependency will change the content of S. Sets of functional dependencies with these properties are also called canonical or minimal. Finding such a set S of functional dependencies which is equivalent to some input set S' provided as input is called finding a minimal cover of S': this problem can be solved in polynomial ...
Every non-trivial functional dependency begins with a superkey (a stricter form of 3NF) — Every non-trivial multivalued dependency begins with a superkey — Every join dependency has a superkey component [8] — Every join dependency has only superkey components — Every constraint is a consequence of domain constraints and key constraints
A table is in EKNF if and only if all its elementary functional dependencies begin at whole keys or end at elementary key attributes. For every full non-trivial functional dependency of the form X→Y, either X is a key or Y is (a part of) an elementary key.
A canonical cover for F (a set of functional dependencies on a relation scheme) is a set of dependencies such that F logically implies all dependencies in , and logically implies all dependencies in F. The set has two important properties:
A database relation (e.g. a database table) is said to meet third normal form standards if all the attributes (e.g. database columns) are functionally dependent on solely a key, except the case of functional dependency whose right hand side is a prime attribute (an attribute which is strictly included into some key).
Dependency theory is a subfield of database theory which studies implication and optimization problems related to logical constraints, commonly called dependencies, on databases. The best known class of such dependencies are functional dependencies , which form the foundation of keys on database relations .
A trivial multivalued dependency X Y is one where either Y is a subset of X, or X and Y together form the whole set of attributes of the relation. A functional dependency is a special case of multivalued dependency. In a functional dependency X → Y, every x determines exactly one y, never more than one.