Editing Functional dependency (section)

== Irreducible function depending set ==
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).
# 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 time.<ref>{{Cite journal|last1=Meier|first1=Daniel|title=Minimum covers in the relational database model|year=1980|journal=[[Journal of the ACM]]|volume=27 |issue=4 |pages=664–674 |doi=10.1145/322217.322223|s2cid=15789293 |doi-access=free}}{{Closed access}}</ref>