Boyce-Codd Normal Form (BCNF)
The relation NEWSTUDENT (Enrolmentno, Sno, Sname, Cname, Cno,) has every attributes participating in candidate keys as all the attributes are assumed to be unique. We thus had the following candidate keys.
(Enrolmentno, Cno)
(Enrolmentno, Cname)
(Sname, Cno)
(Sname, Cname)
As the relation has no non-key attributes, the relation is in 2NF and as well in 3NF. Though, the relation suffers from the anomalies (please check it yourself by making the relational instance of the NEWSTUDENT relation).
The complexity in this relation is being caused by dependence within the candidate keys.
Definition: A relation is in BCNF, if it is in 3NF and if each determinant is a candidate key.
- A determinant is the left side of an FD
- Most relations that are in 3NF are also in BCNF. A 3NF relation is not in
BCNF if all the following conditions apply.
(a) The candidate keys in the relation are composite keys.
(b) There is more than one overlapping candidate keys in the relation and a number of attributes in the keys are overlapping and some are not overlapping.
(c) There is a FD from the non-overlapping attribute(s) of single candidate key to non-overlapping attribute(s) of other candidate key.
Let us recall the NEWSTUDENT relation:
NEWSTUDENT (Enrolmentno, Sname, Sno, Cno, Cname) Set of FDs:
Enrolmentno → Sname (1)
Sname → Enrolmentno (2)
Cno → Cname (3)
Cname → Cno (4)
The relation even though in 3NF, but is not in BCNF and can be decomposed on any one of the FDs in (1) & (2); and any one of the FDs in (3) & (4) as:
STUD1 (Enrolmentno, Sname) COUR1 (Cno, Cname)
The third relation that will join the two relation will be:
ST_CO(Enrolmentno, Cno)
Since this is a slightly complex form, let us give one more example, for BCNF. Consider for example, the relation:
ENROL(Enrolmentno, Sname, Cno, Cname, Dateenrolled)
Let us suppose that the relation has the following candidate keys:
(Enrolmentno, Cno)
(Enrolmentno, Cname)
(Sname, Cno)
(Sname, Cname)
(We have supposed Cname and Sname are unique identifiers).
The relation has the following set of dependencies:
Enrolmentno → Sname
Sname → Enrolmentno
Cno → Cname
Cname → Cno
Enrolmentno, Cno → Dateenrolled
The relation is in 3NF but not in BCNF as there are dependencies. The relation suffers from all anomalies. Please draw the relational instance and checks these troubles. The BCNF decomposition of the relation would be:
STUD1 (Enrolment no, Sname)
COU1 (Cno, Cname)
ENROL1 (Enrolmentno, Cno, Dateenrolled)
We now have a relation that only has information about students, another only about subjects and the third only about relationship enrolls.