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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 ...
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.
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
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).
In this example, {Manufacturer country} is the functionally dependent attribute which will be removed. Place those partial dependency-dependent attributes (i.e. {Manufacturer country}) in a relation where their corresponding determinant attributes are a candidate key (i.e. {Manufacturer}).
For example, if we can do a lossless join on a pair of schemas , to form a new schema ,, we use this new schema (rather than or ) to form a lossless join with another schema (which may already be joined (e.g., ,)).
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 .