# Functional Dependency

In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database.

Given a relation R, a set of attributes X in R is said to functionally determine another set of attributes Y, also in R, (written XY) if, and only if, each X value is associated with precisely one Y value; R is then said to satisfy the functional dependency XY. Equivalently, the projection is a function, i.e. Y is a function of X. In simple words, if the values for the X attributes are known (say they are x), then the values for the Y attributes corresponding to x can be determined by looking them up in any tuple of R containing x. Customarily X is called the determinant set and Y the dependent set. A functional dependency FD: XY is called trivial if Y is a subset of X.

The determination of functional dependencies is an important part of designing databases in the relational model, and in database normalization and denormalization. A simple application of functional dependencies is Heath’s theorem; it says that a relation R over an attribute set U and satisfying a functional dependency XY can be safely split in two relations having the lossless-join decomposition property, namely into where Z = UXY are the rest of the attributes. (Unions of attribute sets are customarily denoted by mere juxtapositions in database theory.) An important notion in this context is a candidate key, defined as a minimal set of attributes that functionally determine all of the attributes in a relation. The functional dependencies, along with the attribute domains, are selected so as to generate constraints that would exclude as much data inappropriate to the user domain from the system as possible.

A notion of logical implication is defined for functional dependencies in the following way: a set of functional dependencies logically implies another set of dependencies, if any relation R satisfying all dependencies from also satisfies all dependencies from ; this is usually written . The notion of logical implication for functional dependencies admits a sound and complete finite axiomatization, known as Armstrong's axioms.

Read more about Functional Dependency:  Properties and Axiomatization of Functional Dependencies, Irreducible Function Depending Set

### Famous quotes containing the words functional and/or dependency:

In short, the building becomes a theatrical demonstration of its functional ideal. In this romanticism, High-Tech architecture is, of course, no different in spirit—if totally different in form—from all the romantic architecture of the past.
Dan Cruickshank (b. 1949)

Fate forces its way to the powerful and violent. With subservient obedience it will assume for years dependency on one individual: Caesar, Alexander, Napoleon, because it loves the elemental human being who grows to resemble it, the intangible element. Sometimes, and these are the most astonishing moments in world history, the thread of fate falls into the hands of a complete nobody but only for a twitching minute.
Stefan Zweig (18811942)