Database System Concepts, 7th Ed.
©Silberschatz, Korth and Sudarshan
See www.db-book.com for conditions on re-use
Chapter 7: Normalization
©Silberschatz, Korth and Sudarshan7.2Database System Concepts - 7th Edition
Outline
▪ Features of Good Relational Design
▪ Functional Dependencies
▪ Decomposition Using Functional Dependencies
▪ Normal Forms
▪ Functional Dependency Theory
▪ Algorithms for Decomposition using Functional Dependencies
©Silberschatz, Korth and Sudarshan7.4Database System Concepts - 7th Edition
Features of Good Relational Designs
▪ Suppose we combine instructor and department into in_dep, which
represents the natural join of the relations instructor and department
▪ There is a repetition of information
▪ Need to use null values (if we add a new department with no instructors)
©Silberschatz, Korth and Sudarshan7.6Database System Concepts - 7th Edition
Decomposition
▪ The only way to avoid the repetition-of-information problem in the in_dep
schema is to decompose it into two schemas – instructor and department
schemas.
▪ Not all decompositions are good. Suppose we decompose
employee(ID, name, street, city, salary)
into
employee1 (ID, name)
employee2 (name, street, city, salary)
The problem arises when we have two employees with the same name
▪ The next slide shows how we lose information -- we cannot reconstruct
the original employee relation -- and so, this is a lossy decomposition.
©Silberschatz, Korth and Sudarshan7.7Database System Concepts - 7th Edition
A Lossy Decomposition
©Silberschatz, Korth and Sudarshan7.8Database System Concepts - 7th Edition
Lossless Decomposition
▪ Let R be a relation schema and let R1 and R2 form a decomposition of R.
That is R = R1 U R2
▪ We say that the decomposition is a lossless decomposition if there is
no loss of information by replacing R with the two relation schemas R1
U R2
▪ Formally:
 R1
(r)  R2
(r) = r
▪ Conversely, a decomposition is lossy if:
r   R1
(r)  R2
(r)
©Silberschatz, Korth and Sudarshan7.9Database System Concepts - 7th Edition
Example of Lossless Decomposition
▪ Decomposition of R = (A, B, C)
R1 = (A, B) R2 = (B, C)
©Silberschatz, Korth and Sudarshan7.10Database System Concepts - 7th Edition
Normalization Theory
▪ Decide whether a particular relation R is in “good” form.
▪ In the case that a relation R is not in “good” form, decompose it into set
of relations {R1, R2, ..., Rn} such that
• Each relation is in good form
• The decomposition is the lossless decomposition
▪ Our theory is based on:
• Functional dependencies
©Silberschatz, Korth and Sudarshan7.11Database System Concepts - 7th Edition
Functional Dependencies
▪ There are usually a variety of constraints (rules) valid on the data in the
real world.
▪ For example, some of the constraints that are expected to hold in a
university database are:
• Students and instructors are uniquely identified by their ID.
• Each student and instructor has only one name.
• Each instructor and student is (primarily) associated with only one
department.
• Each department has only one value for its budget, and only one
associated building.
©Silberschatz, Korth and Sudarshan7.12Database System Concepts - 7th Edition
Functional Dependencies (Cont.)
▪ An instance of a relation that satisfies all such real-world constraints is a
legal instance of the relation;
▪ A legal instance of a database requires all the relation instances to be
legal instances
▪ Constraints on the set of legal relations require that the value for a certain
set of attributes determines uniquely the value for another set of
attributes.
▪ A functional dependency is a generalization of the notion of a key.
©Silberschatz, Korth and Sudarshan7.13Database System Concepts - 7th Edition
Functional Dependencies Definition
▪ Let R be a relation schema
  R and   R
▪ The functional dependency
 → 
holds on R if and only if for any legal relations r(R), whenever any two
tuples t1 and t2 of r agree on the attributes , they also agree on the
attributes . That is,
t1[] = t2 []  t1[ ] = t2 [ ]
▪ Example: Consider r(A,B ) with the following instance of r.
▪ On this instance, B → A hold; A → B does NOT hold,
1 4
1 5
3 7
©Silberschatz, Korth and Sudarshan7.14Database System Concepts - 7th Edition
Closure of a Set of Functional Dependencies
▪ Given a set F of functional dependencies, there are certain other
functional dependencies that are logically implied by F.
• If A → B and B → C, then we can infer that A → C
• etc.
▪ The set of all functional dependencies logically implied by F is the
closure of F.
▪ We denote the closure of F by F+
.
©Silberschatz, Korth and Sudarshan7.15Database System Concepts - 7th Edition
Keys and Functional Dependencies
▪ K is a superkey for relation schema R if and only if K → R
▪ K is a candidate key for R if and only if
• K → R, and
• for no   K,  → R
▪ Functional dependencies allow us to express constraints that cannot be
expressed using superkeys. Consider the schema:
in_dep (ID, name, salary, dept_name, building, budget ).
We expect the following functional dependencies to hold:
dept_name→ building
ID → building
but would not expect the following to hold:
dept_name → salary
©Silberschatz, Korth and Sudarshan7.16Database System Concepts - 7th Edition
Use of Functional Dependencies
▪ We use functional dependencies to:
• To test relations to see if they are legal under a given set of
functional dependencies.
▪ If a relation r is legal under a set F of functional dependencies,
we say that r satisfies F.
• To specify constraints on the set of legal relations
▪ We say that F holds on R if all legal relations on R satisfy the set
of functional dependencies F.
▪ Note: A specific instance of a relation may satisfy a functional
dependency even if the functional dependency does not hold on all legal
instances.
• For example, a specific instance of instructor may, by chance, satisfy
name → ID.
©Silberschatz, Korth and Sudarshan7.17Database System Concepts - 7th Edition
Trivial Functional Dependencies
▪ A functional dependency is trivial if it is satisfied by all instances of a
relation
▪ Example:
• ID, name → ID
• name → name
▪ In general,  →  is trivial if   
©Silberschatz, Korth and Sudarshan7.18Database System Concepts - 7th Edition
Lossless Decomposition
▪ We can use functional dependencies to show when certain
decompositions are lossless.
▪ For the case of R = (R1, R2), we require that for all possible relations r on
schema R
r = R1 (r ) R2 (r )
▪ A decomposition of R into R1 and R2 is lossless decomposition if at least
one of the following dependencies is in F+:
• R1  R2 → R1
• R1  R2 → R2
▪ The above functional dependencies are a sufficient condition for lossless
join decomposition; the dependencies are a necessary condition only if all
constraints are functional dependencies
©Silberschatz, Korth and Sudarshan7.19Database System Concepts - 7th Edition
Example
▪ R = (A, B, C)
F = {A → B, B → C)
▪ R1 = (A, B), R2 = (B, C)
• Lossless decomposition:
R1  R2 = {B} and B → BC
▪ R1 = (A, B), R2 = (A, C)
• Lossless decomposition:
R1  R2 = {A} and A → AB
▪ Note:
• B → BC
is a shorthand notation for
• B → {B, C}
©Silberschatz, Korth and Sudarshan7.20Database System Concepts - 7th Edition
Dependency Preservation
▪ Testing functional dependency constraints each time the database is
updated can be costly
▪ It is useful to design the database in a way that constraints can be
tested efficiently.
▪ If testing a functional dependency can be done by considering just one
relation, then the cost of testing this constraint is low
▪ When decomposing a relation, it may no longer be possible testing the
dependence without performing a Cartesian Product (Join)
▪ A decomposition that makes it computationally hard to enforce
functional dependency is said to be NOT dependency preserving.
©Silberschatz, Korth and Sudarshan7.21Database System Concepts - 7th Edition
Dependency Preservation Example
▪ Consider a schema:
dept_advisor(s_ID, i_ID, dept_name)
▪ With function dependencies:
i_ID → dept_name
s_ID, dept_name → i_ID
▪ In the above design we are forced to repeat the department name once
for each time an instructor participates in a dept_advisor relationship.
▪ To fix this, we need to decompose dept_advisor
▪ Any decomposition will not include all the attributes in
s_ID, dept_name → i_ID
▪ Thus, any decomposition is NOT dependency preserving
©Silberschatz, Korth and Sudarshan7.23Database System Concepts - 7th Edition
Boyce-Codd Normal Form
▪ A relation schema R is in BCNF with respect to a set F of functional
dependencies if for all functional dependencies in F+ of the form
 → 
where   R and   R, at least one of the following holds:
•  →  is trivial (i.e.,   )
•  is a superkey for R
©Silberschatz, Korth and Sudarshan7.24Database System Concepts - 7th Edition
Boyce-Codd Normal Form (Cont.)
▪ Example schema that is not in BCNF:
in_dep (ID, name, salary, dept_name, building, budget )
because :
• dept_name→ building, budget
▪ holds on in_dep
▪ but
• dept_name is not a superkey
▪ When decompose in_dept into instructor and department
• instructor is in BCNF
• department is in BCNF
©Silberschatz, Korth and Sudarshan7.25Database System Concepts - 7th Edition
Decomposing a Schema into BCNF
▪ Let R be a schema that is not in BCNF. Let  → be the FD that
causes a violation of BCNF.
▪ We decompose R into:
• ( U  )
• ( R - (  -  ) )
▪ In our example of in_dep,
•  = dept_name
•  = building, budget
and in_dep is replaced by
• ( U  ) = ( dept_name, building, budget )
• ( R - (  -  ) ) = ( ID, name, dept_name, salary )
©Silberschatz, Korth and Sudarshan7.26Database System Concepts - 7th Edition
Example
▪ R = (A, B, C)
F = {A → B, B → C)
▪ R1 = (A, B), R2 = (B, C)
• Lossless-join decomposition:
R1  R2 = {B} and B → BC
• Dependency preserving
▪ R1 = (A, B), R2 = (A, C)
• Lossless-join decomposition:
R1  R2 = {A} and A → AB
• Not dependency preserving
(cannot check B → C without computing R1 R2)
©Silberschatz, Korth and Sudarshan7.27Database System Concepts - 7th Edition
BCNF and Dependency Preservation
▪ It is not always possible to achieve both BCNF and dependency
preservation
▪ Consider a schema:
dept_advisor(s_ID, i_ID, department_name)
▪ With function dependencies:
i_ID → dept_name
s_ID, dept_name → i_ID
▪ dept_advisor is not in BCNF
• i_ID is not a superkey.
▪ Any decomposition of dept_advisor will not include all the attributes in
s_ID, dept_name → i_ID
▪ Thus, the composition is NOT dependency preserving
©Silberschatz, Korth and Sudarshan7.28Database System Concepts - 7th Edition
Third Normal Form
▪ A relation schema R is in the third normal form (3NF) if for all:
 →  in F+
at least one of the following holds:
•  →  is trivial (i.e.,   )
•  is a superkey for R
• Each attribute A in  –  is contained in a candidate key for R.
(NOTE: each attribute may be in a different candidate key)
▪ If a relation is in BCNF it is in 3NF (since in BCNF one of the first two
conditions above must hold).
▪ Third condition is the minimal relaxation of BCNF to ensure dependency
preservation.
©Silberschatz, Korth and Sudarshan7.29Database System Concepts - 7th Edition
3NF Example
▪ Consider a schema:
dept_advisor(s_ID, i_ID, dept_name)
▪ With function dependencies:
i_ID → dept_name
s_ID, dept_name → i_ID
▪ Two candidate keys = {s_ID, dept_name}, {s_ID, i_ID }
▪ We have seen before that dept_advisor is not in BCNF
▪ R, however, is in 3NF
• s_ID, dept_name is a superkey
• i_ID → dept_name and i_ID is NOT a superkey, but:
▪ { dept_name} – {i_ID } = {dept_name } and
▪ dept_name is contained in a candidate key
©Silberschatz, Korth and Sudarshan7.30Database System Concepts - 7th Edition
Redundancy in 3NF
▪ Consider the schema R below, which is in 3NF
▪ What is wrong with the table?
• R = (J, K, L )
• F = {JK → L, L → K }
• And an instance table:
• Repetition of information
• Need to use null values (e.g., to represent the relationship l2, k2
where there is no corresponding value for J)
©Silberschatz, Korth and Sudarshan7.31Database System Concepts - 7th Edition
Comparison of BCNF and 3NF
▪ Advantages of 3NF over BCNF. It is always possible to obtain a 3NF
design without sacrificing losslessness or dependency preservation.
▪ Disadvantages to 3NF.
• We may have to use null values to represent some of the possible
meaningful relationships among data items.
• There is the problem of repetition of information.
©Silberschatz, Korth and Sudarshan7.32Database System Concepts - 7th Edition
Goals of Normalization
▪ Let R be a relation scheme with a set F of functional dependencies.
▪ Decide whether a relation scheme R is in “good” form.
▪ In the case that a relation scheme R is not in “good” form, decompose
R into a set of relation schemes {R1, R2, ..., Rn} such that:
• Each relation scheme is in good form
• The decomposition is a lossless decomposition
• Preferably, the decomposition should be dependency preserving.
©Silberschatz, Korth and Sudarshan7.33Database System Concepts - 7th Edition
How good is BCNF?
▪ There are database schemas in BCNF that do not seem to be
sufficiently normalized
▪ Consider a relation
inst_info (ID, child_name, phone)
• where an instructor may have more than one phone and can have
multiple children
• Instance of inst_info
©Silberschatz, Korth and Sudarshan7.34Database System Concepts - 7th Edition
▪ There are no non-trivial functional dependencies and therefore the
relation is in BCNF
▪ Insertion anomalies – i.e., if we add a phone 981-992-3443 to 99999, we
need to add two tuples
(99999, David, 981-992-3443)
(99999, William, 981-992-3443)
How good is BCNF? (Cont.)
©Silberschatz, Korth and Sudarshan7.35Database System Concepts - 7th Edition
▪ It is better to decompose inst_info into:
• inst_child:
• inst_phone:
▪ This suggests the need for higher normal forms, such as Fourth
Normal Form (4NF).
Higher Normal Forms
©Silberschatz, Korth and Sudarshan7.37Database System Concepts - 7th Edition
Functional-Dependency Theory Roadmap
▪ We now consider a formal theory that tells us which functional
dependencies are implied logically by a given set of functional
dependencies.
▪ We then develop algorithms to generate lossless decompositions into
BCNF and 3NF
▪ We then develop algorithms to test if a decomposition is dependency-
preserving
©Silberschatz, Korth and Sudarshan7.38Database System Concepts - 7th Edition
Closure of a Set of Functional Dependencies
▪ Given a set F set of functional dependencies, there are certain other
functional dependencies that are logically implied by F.
• If A → B and B → C, then we can infer that A → C
• etc.
▪ The set of all functional dependencies logically implied by F is the closure
of F.
▪ We denote the closure of F by F+
.
©Silberschatz, Korth and Sudarshan7.39Database System Concepts - 7th Edition
Closure of a Set of Functional Dependencies
▪ We can compute F+, the closure of F, by repeatedly applying Armstrong’s
Axioms:
• Reflexive rule: if   , then  → 
• Augmentation rule: if  → , then   →  
• Transitivity rule: if  → , and  → , then  → 
▪ These rules are
• Sound -- generate only functional dependencies that actually hold,
and
• Complete -- generate all functional dependencies that hold.
©Silberschatz, Korth and Sudarshan7.40Database System Concepts - 7th Edition
Example of F+
▪ R = (A, B, C, G, H, I)
F = { A → B
A → C
CG → H
CG → I
B → H}
▪ Some members of F+
• A → H
▪ by transitivity from A → B and B → H
• AG → I
▪ by augmenting A → C with G, to get AG → CG
and then transitivity with CG → I
• CG → HI
▪ by augmenting CG → I to infer CG → CGI,
and augmenting CG → H to infer CGI → HI,
and then transitivity
©Silberschatz, Korth and Sudarshan7.41Database System Concepts - 7th Edition
Closure of Functional Dependencies (Cont.)
▪ Additional rules:
• Union rule: If  →  holds and  →  holds, then  →   holds.
• Decomposition rule: If  →   holds, then  →  holds and  →
 holds.
• Pseudotransitivity rule:If  →  holds and   →  holds, then 
 →  holds.
▪ The above rules can be inferred from Armstrong’s axioms.
©Silberschatz, Korth and Sudarshan7.42Database System Concepts - 7th Edition
Procedure for Computing F+
▪ To compute the closure of a set of functional dependencies F:
F + = F
repeat
for each functional dependency f in F+
apply reflexivity and augmentation rules on f
add the resulting functional dependencies to F +
for each pair of functional dependencies f1 and f2 in F +
if f1 and f2 can be combined using transitivity
then add the resulting functional dependency to F +
until F + does not change any further
▪ NOTE: We shall see an alternative procedure for this task later
©Silberschatz, Korth and Sudarshan7.43Database System Concepts - 7th Edition
Closure of Attribute Sets
▪ Given a set of attributes , define the closure of  under F (denoted by
+) as the set of attributes that are functionally determined by  under F
▪ Algorithm to compute +, the closure of  under F
result := ;
while (changes to result) do
for each  →  in F do
begin
if   result then result := result  
end
©Silberschatz, Korth and Sudarshan7.44Database System Concepts - 7th Edition
Example of Attribute Set Closure
▪ R = (A, B, C, G, H, I)
▪ F = {A → B
A → C
CG → H
CG → I
B → H}
▪ (AG)+
1. result = AG
2. result = ABCG (A → C and A → B)
3. result = ABCGH (CG → H and CG  AGBC)
4. result = ABCGHI (CG → I and CG  AGBCH)
▪ Is AG a candidate key?
1. Is AG a super key?
1. Does AG → R? == Is R  (AG)+
2. Is any subset of AG a superkey?
1. Does A → R? == Is R  (A)+
2. Does G → R? == Is R  (G)+
3. In general: check for each subset of size n-1
©Silberschatz, Korth and Sudarshan7.45Database System Concepts - 7th Edition
Uses of Attribute Closure
There are several uses of the attribute closure algorithm:
▪ Testing for superkey:
• To test if  is a superkey, we compute +, and check if + contains all
attributes of R.
▪ Testing functional dependencies
• To check if a functional dependency  →  holds (or, in other words,
is in F+), just check if   +.
• That is, we compute + by using attribute closure, and then check if it
contains .
• Is a simple and cheap test, and very useful
▪ Computing closure of F
• For each   R, we find the closure +, and for each S  +, we output
a functional dependency  → S.
©Silberschatz, Korth and Sudarshan7.46Database System Concepts - 7th Edition
Canonical Cover
▪ Suppose that we have a set of functional dependencies F on a relation
schema. Whenever a user performs an update on the relation, the
database system must ensure that the update does not violate any
functional dependencies; that is, all the functional dependencies in F are
satisfied in the new database state.
▪ If an update violates any functional dependencies in set F, the system
must roll back the update.
▪ We can reduce the effort spent in checking for violations by testing a
simplified set of functional dependencies that has the same closure as the
given set.
▪ This simplified set is termed the canonical cover
▪ To define canonical cover we must first define extraneous attributes.
• An attribute of a functional dependency in F is extraneous if we can
remove it without changing F +
©Silberschatz, Korth and Sudarshan7.47Database System Concepts - 7th Edition
Extraneous Attributes
▪ Removing an attribute from the left side of a functional dependency could
make it a stronger constraint.
• For example, if we have AB → C and remove B, we get the possibly
stronger result A → C. It may be stronger because A → C logically
implies AB → C, but AB → C does not, on its own, logically imply
A → C
▪ But, depending on what our set F of functional dependencies happens to
be, we may be able to remove B from AB → C safely.
• For example, suppose that
• F = {AB → C, A → D, D → C}
• Then we can show that F logically implies A → C, making B
extraneous in AB → C.
©Silberschatz, Korth and Sudarshan7.48Database System Concepts - 7th Edition
Extraneous Attributes
▪ An attribute of a functional dependency in F is extraneous if we can
remove it without changing F +
▪ Consider a set F of functional dependencies and the functional
dependency  →  in F.
• Remove from the left side: Attribute A is extraneous in  if
▪ A   and
▪ F logically implies (F – { → })  {( – A) → }.
• Remove from the right side: Attribute A is extraneous in  if
▪ A   and
▪ The set of functional dependencies
(F – { → })  { →( – A)} logically implies F.
▪ Note: implication in the opposite direction is trivial in each of the cases
above since a “stronger” functional dependency always implies a weaker
one
©Silberschatz, Korth and Sudarshan7.49Database System Concepts - 7th Edition
Testing if an Attribute is Extraneous
▪ Let R be a relation schema and let F be a set of functional
dependencies that hold on R . Consider an attribute in the functional
dependency  → .
▪ To test if attribute A   is extraneous in 
• Consider the set:
F' = (F – { → })  { →( – A)},
• check that + contains A; if it does, A is extraneous in 
▪ To test if attribute A   is extraneous in 
• Let  =  – {A}. Check if  →  can be inferred from F.
▪ Compute + using the dependencies in F
▪ If + includes all attributes in  then, A is extraneous in 
©Silberschatz, Korth and Sudarshan7.50Database System Concepts - 7th Edition
Examples of Extraneous Attributes
▪ Let F = {AB → CD, A → E, E → C }
▪ To check if C is extraneous in AB → CD, we:
• Compute the attribute closure of AB under F' = {AB → D, A → E, E →
C}
• The closure is ABCDE, which includes CD
• This implies that C is extraneous
©Silberschatz, Korth and Sudarshan7.51Database System Concepts - 7th Edition
Canonical Cover
▪ F logically implies all dependencies in Fc, and
▪ Fc logically implies all dependencies in F, and
▪ No functional dependency in Fc contains an extraneous attribute, and
▪ Each left side of functional dependency in Fc is unique. That is, there
are no two dependencies in Fc
• 1 → 1 and 2 → 2 such that
• 1 = 2
A canonical cover for F is a set of dependencies Fc such that
©Silberschatz, Korth and Sudarshan7.52Database System Concepts - 7th Edition
Canonical Cover
▪ To compute a canonical cover for F:
repeat
Use the union rule to replace any dependencies in F of the form
1 → 1 and 1 → 2 with 1 → 1 2
Find a functional dependency  →  in Fc with an extraneous
attribute either in  or in 
/* Note: test for extraneous attributes done using Fc, not F+
If an extraneous attribute is found, delete it from  → 
until Fc not change
▪ Note: Union rule may become applicable after some extraneous attributes
have been deleted, so it must be re-applied
©Silberschatz, Korth and Sudarshan7.53Database System Concepts - 7th Edition
Example: Computing a Canonical Cover
▪ R = (A, B, C)
F = {A → BC
B → C
A → B
AB → C}
▪ Combine A → BC and A → B into A → BC
• Set is now {A → BC, B → C, AB → C}
▪ A is extraneous in AB → C
• Check if the result of deleting A from AB → C is implied by the other
dependencies
▪ Yes: in fact, B → C is already present!
• Set is now {A → BC, B → C}
▪ C is extraneous in A → BC
• Check if A → C is logically implied by A → B and the other dependencies
▪ Yes: using transitivity on A → B and B → C.
• Can use attribute closure of A in more complex cases
▪ The canonical cover is: A → B
B → C
©Silberschatz, Korth and Sudarshan7.54Database System Concepts - 7th Edition
Dependency Preservation
▪ Let Fi be a subset of dependencies F + that include only attributes in Ri.
• A decomposition is dependency preserving, if
(F1  F2  …  Fn )+ = F +
▪ Using the above definition, testing for dependency preservation takes
exponential time.
▪ Note that if decomposition is NOT dependency preserving then checking
updates for violation of functional dependencies may require computing
joins, which is expensive.
©Silberschatz, Korth and Sudarshan7.55Database System Concepts - 7th Edition
Dependency Preservation (Cont.)
▪ Let F be the set of dependencies on schema R and let R1, R2, .., Rn be a
decomposition of R.
▪ The restriction of F to Ri is the set Fi of all functional dependencies in F +
that include only attributes of Ri .
▪ Since all functional dependencies in a restriction involve attributes of only
one relation schema, it is possible to test such a dependency for
satisfaction by checking only one relation.
▪ Note that the definition of restriction uses all dependencies in F +, not just
those in F.
▪ The set of restrictions F1, F2, .. , Fn is the set of functional dependencies
that can be checked efficiently.
©Silberschatz, Korth and Sudarshan7.56Database System Concepts - 7th Edition
Testing for Dependency Preservation
▪ To check if a dependency  →  is preserved in a decomposition of R into
R1, R2, …, Rn , we apply the following test (with attribute closure done with
respect to F)
• result = 
repeat
for each Ri in the decomposition
t = (result  Ri)+  Ri
result = result  t
until (result does not change)
• If the result contains all attributes in , then the functional dependency
 →  is preserved.
▪ We apply the test on all dependencies in F to check if a decomposition is a
dependency preserving
▪ This procedure takes polynomial time, instead of the exponential time
required to compute F+ and (F1  F2  …  Fn)+
©Silberschatz, Korth and Sudarshan7.57Database System Concepts - 7th Edition
Design Goals - Summary
▪ Goal for a relational database design is:
• BCNF.
• Lossless join.
• Dependency preservation.
▪ If we cannot achieve this, we accept one of
• Lack of dependency preservation
• Redundancy due to the use of 3NF
▪ Interestingly, SQL does not provide a direct way of specifying functional
dependencies other than superkeys.
Can specify FDs using assertions, but they are expensive to test, (and
currently not supported by any of the widely used databases!)
▪ Even if we had a dependency preserving decomposition, using SQL we
would not be able to efficiently test a functional dependency whose lefthand
side is not a key.
©Silberschatz, Korth and Sudarshan7.58Database System Concepts - 7th Edition
End of Chapter 7