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In relational database theory, a functional dependency is the following constraint between two attribute sets in a relation: Given a relation R and attribute sets X,Y R, X is said to functionally determine Y (written X → Y) if each X value is associated with precisely one Y value.
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 .
In database theory, a join dependency is a constraint on the set of legal relations over a database scheme. A table T {\displaystyle T} is subject to a join dependency if T {\displaystyle T} can always be recreated by joining multiple tables each having a subset of the attributes of T {\displaystyle T} .
A relational schema R is in Boyce–Codd normal form if and only if for every one of its functional dependencies X → Y, at least one of the following conditions hold: [5] X → Y is a trivial functional dependency (Y ⊆ X), X is a superkey for schema R. [5]
In graph theory, the trivial graph is a graph which has only 1 vertex and no edge. Database theory has a concept called functional dependency, written . The dependence is true if Y is a subset of X, so this type of dependence is called "trivial". All other dependences, which are less obvious, are called "nontrivial".
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).
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 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.