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A set S of functional dependencies is irreducible if the set has the following three properties: Each right set of a functional dependency of S contains only one attribute. Each left set of a functional dependency of S is irreducible. It means that reducing any one attribute from left set will change the content of S (S will lose some information).
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 .
Embedded dependencies can express functional dependencies, join dependencies, multivalued dependencies, inclusion dependencies, foreign key dependencies, and many more besides. An algorithm known as the chase takes as input an instance that may or may not satisfy a set of EDs, and, if it terminates (which is a priori undecidable), output an ...
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 data dependency in computer science is a situation in which a program statement (instruction) refers to the data of a preceding statement. In compiler theory , the technique used to discover data dependencies among statements (or instructions) is called dependence analysis .
There is a functional dependency from the candidate key to all the attributes in the relation. The superkeys of a relation are all the possible ways we can identify a row. The candidate keys are the minimal subsets of each superkey and as such, they are an important concept for the design of database schema.
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.
The chase is a simple fixed-point algorithm testing and enforcing implication of data dependencies in database systems. It plays important roles in database theory as well as in practice. It is used, directly or indirectly, on an everyday basis by people who design databases, and it is used in commercial systems to reason about the consistency ...