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E.g. a call to a log() function may induce a transitive dependency to a library that manages the I/O of writing a message to a log file. Dependencies and transitive dependencies can be resolved at different times, depending on how the computer program is assembled and/or executed: e.g. a compiler can have a link phase where the dependencies are ...
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).
To make a 1NF relation a 2NF relation, remove the functionally dependent attributes in the partial dependencies of the first normal form relation, and place those partial dependency dependent attributes in a relation where their corresponding determinant attributes are an entire candidate key.
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
If a relational schema is in BCNF, then all redundancy based on functional dependency has been removed, [4] although other types of redundancy may still exist. 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]
A depends on B and C; B depends on D. Given a set of objects and a transitive relation with (,) modeling a dependency "a depends on b" ("a needs b evaluated first"), the dependency graph is a graph = (,) with the transitive reduction of R.
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 X → Y can be safely split in two relations having the lossless-join decomposition property, namely into () = where Z = U − XY are the rest of the attributes.
A multivalued dependency is a special case of a join dependency, with only two sets of values involved, i.e. it is a binary join dependency. A multivalued dependency exists when there are at least three attributes (like X,Y and Z) in a relation and for a value of X there is a well defined set of values of Y and a well defined set of values of Z.