Functional Dependency (FD)

1
Functional Dependency (FD)

• FD imposes restrictions within a single schema.
• It restricts the data in the database follows
  certain kind of rules.
• Armstrongs Relations generalize six important
  rules in describing the FD in schema

2
Functional Dependency (FD)

• Consider the student relation

sid sname sfullname sprogram sdept
1001 stud_A stud_A Au BEng(COMP) 1
1002 stud_B stud_B Lo BEng(COMP) 1
1003 stud_C stud_C Ko BEng(ELEC) 2
1004 stud_D stud_D Ng BEng(ELEC) 2
3
Functional Dependency (FD)

• Reflexivity
• If Y ? X ? schema(R) then we have FX?Y.
• Example
• sname ? sfullname gt F sfullname ? sname
• each students name (sname) is a subset of
  his/her full name (sfullname). Hence we can
  determine the students name from his/her full
  name.

4
Functional Dependency (FD)

• Augmentation
• If FX?Y and W is a (set of) attribute(s) in the
  schema, then FXW?YW
• Example
• F sid ? sprogram gt F sid, sdept ?
  sprogram, sdept
• A students student ID (sid) can determine
  his/her program of study (sprogram).
• Then the students ID together with his/her
  belonging department can determine the program
  he/she is studying together with the department
  he/she belongs to.

5
Functional Dependency (FD)

• Transitivity
• If FX?Y and FY?Z, then FX?Z.
• Example
• F sid ? sprogram and F sprogram ? sdeptthen
  F sid ? sdept
• Student identity number (sid) determines the
  program (sprogram) he/she has registered, and
  each program must refer to a department (sdept).
  We can find the department that the student
  belongs to by the student identity number.

6
Functional Dependency (FD)

• Union
• If FX?Y and FX?Z, then FX?YZ.
• Example
• F sid ? sname and F sid ? sprogramthen F
  sid ? sname, sprogram
• Student ID (sid) determines the name of the
  student (sname), it also determines the program
  the student has registered (sprogram).
• Thus if we know the student ID, we can altogether
  know the student name and the program of that
  student.

7
Functional Dependency (FD)

• Decomposition
• If FX?YZ, then FX?Y and FX?Z.
• Example
• F sid ? sprogram, sdeptthen F sid ? sprogram
  and F sid ? sdept.
• Student ID (sid) determines the program
  registered (sprogram) and the department he/she
  belongs to (sdept).
• With this student ID, we can find the program
  he/she has registered and the department he/she
  belongs to separately.

8
Functional Dependency (FD)

• Pseudo-transitivity
• If FX?Y and FYW?Z, then FXW?Z.
• Example
• If F sid ? sname and F sname, sprogram ?
  sdept , then F sid, sprogram ? sdept
• Student ID (sid) determines the student name
  (sname). Knowing the student name and the program
  that he/she has registered (sprogram), we can
  know the department he/she belongs to (sdept).
• Then, if we know the student ID of the student
  and the the registered program, we can know the
  department this student belongs to.