Boyce-Codd normal form

Boyce–Codd normal form (or BCNF or 3.5NF) is a normal form used in database normalization. It is a slightly stronger version of the third normal form (3NF). BCNF was developed in 1974 by Raymond F. Boyce and Edgar F. Codd to address certain types of anomalies not dealt with by 3NF as originally defined.

If a relational schema is in BCNF then all redundancy based on functional dependency has been removed, 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 dependencies X → Y, at least one of the following conditions hold:

Chris Date has pointed out that a definition of what we now know as BCNF appeared in a paper by Ian Heath in 1971. Date writes:

"Since that definition predated Boyce and Codd's own definition by some three years, it seems to me that BCNF ought by rights to be called Heath normal form. But it isn't."

Edgar F. Codd released his original paper "A Relational Model of Data for Large Shared Databanks" in June 1970. This was the first time the notion of a relational database was published. All work after this, including the Boyce-Codd normal form method was based on this relational model.

Only in rare cases does a 3NF table not meet the requirements of BCNF. A 3NF table that does not have multiple overlapping candidate keys is guaranteed to be in BCNF. Depending on what its functional dependencies are, a 3NF table with two or more overlapping candidate keys may or may not be in BCNF.

An example of a 3NF table that does not meet BCNF is:

The table's superkeys are:

Note that even though in the above table Start Time and End Time attributes have no duplicate values for each of them, we still have to admit that in some other days two different bookings on court 1 and court 2 could start at the same time or end at the same time. This is the reason why {Start Time} and {End Time} cannot be considered as the table's superkeys.

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