White-Box Testing Techniques II

1
White-Box Testing Techniques II
Dataflow Testing

• Originals prepared by
• Stephen M. Thebaut, Ph.D.
• University of Florida

2
White-Box Testing Topics

• Logic coverage
• Dataflow coverage
• Path conditions and symbolic execution (lecture
  III)
• Other white-box testing strategies
• e.g. fault-based testing

3
Dataflow Coverage

• Basic idea
• Program paths along which variables are defined
  and then used should be covered
• A family of path selection criteria has been
  defined, each providing a different degree of
  coverage
• CASE tool support is very desirable

4
Variable Definition

• A program variable is DEFINED when it appears
• on the left hand side of an assignment statement
  eg y 17
• in an input statement eg read(y)
• as an call-by-reference parameter in a subroutine
  call eg update(x, y)

5
Variable Use

• A program variable is USED when it appears
• on the right hand side of an assignment statement
  eg y x17
• as an call-by-value parameter in a subroutine or
  function call eg y sqrt(x)
• in the predicate of a branch statement eg if ( x
  gt 0 )

6
Variable Use p-use and c-use

• Use in the predicate of a branch statement is a
  predicate-use or p-use
• Any other use is a computation-use or c-use
• For example, in the program fragment
• if ( x gt 0 )
• print(y)
• there is a p-use of x and a c-use of y

7
Variable Use

• A variable can also be used and then re-defined
  in a single statement when it appears
• on both sides of an assignment statement eg y
  y x
• as an call-by-reference parameter in a subroutine
  call eg increment( y )

8
More Dataflow Terms and Definitions

• A path is definition clear (def-clear) with
  respect to a variable v if it has no variable
  re-definition of v on the path
• A complete path is a path whose initial node is a
  start node and whose final node is an exit node

9
Dataflow Terms and Definitions

• A definition-use pair (du-pair) with respect to
  a variable v is a double (d,u) such that
• d is a node in the programs flow graph at which
  v is defined,
• u is a node or edge at which v is used and
• there is a def-clear path with respect to v from
  d to u
• Note that the definition of a du-pair does not
  require the existence of a feasible def-clear
  path from d to u

10
Example 1

• 1. input(A,B)
• if (Bgt1)
• 2. A A7
• 3. if (Agt10)
• 4. B AB
• 5. output(A,B)

input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
11
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
12
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
13
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
14
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
15
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
16
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
17
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
18
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
19
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
20
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
21
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
22
Identifying DU-Pairs Variable A
du-pair path(s)
(1,2) lt1,2gt
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt
(2,5) lt2,3,4,5gt
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
23
Identifying DU-Pairs Variable B
input(A,B)
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,3,4gt
(1,5) lt1,2,3,5gt
lt1,3,5gt
(1,lt1,2gt) lt1,2gt
(1,lt1,3gt) lt1,3gt
(4,5) lt4,5gt
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
24
Dataflow Test Coverage Criteria

• All-Defs for every program variable v, at
  least one def-clear path from every definition of
  v to at least one c-use or one p-use of v must
  be covered

25
Dataflow Test Coverage Criteria

• Consider a test case executing path
• 1. lt1,2,3,4,5gt
• Identify all def-clear paths covered (ie
  subsumed) by this path for each variable
• Are all definitions for each variable associated
  with at least one of the subsumed def-clear
  paths?

26
Def-Clear Paths subsumed by lt1,2,3,4,5gt for
Variable A
du-pair path(s)
(1,2) lt1,2gt ?
(1,4) lt1,3,4gt
(1,5) lt1,3,4,5gt
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt ?
(2,5) lt2,3,4,5gt ?
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt ?
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
27
Def-Clear Paths Subsumed by lt1,2,3,4,5gt for
Variable B
input(A,B)
du-pair path(s)
(1,4) lt1,2,3,4gt ?
lt1,3,4gt
(1,5) lt1,2,3,5gt
lt1,3,5gt
(4,5) lt4,5gt ?
(1,lt1,2gt) lt1,2gt ?
(1,lt1,3gt) lt1,3gt
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
28
Dataflow Test Coverage Criteria

• Since lt1,2,3,4,5gt covers at least one def-clear
  path from every definition of A or B to at least
  one c-use or p-use of A or B, All-Defs coverage
  is achieved

29
Dataflow Test Coverage Criteria

• All-Uses for every program variable v, at
  least one def-clear path from every definition
  of v to every c-use and every p-use of v must be
  covered
• Consider additional test cases executing paths
• 2. lt1,3,4,5gt
• 3. lt1,2,3,5gt
• Do all three test cases provide All-Uses coverage?

30
Def-Clear Paths Subsumed by lt1,3,4,5gt for
Variable A
du-pair path(s)
(1,2) lt1,2gt ?
(1,4) lt1,3,4gt ?
(1,5) lt1,3,4,5gt ?
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt ?
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt ?
(2,5) lt2,3,4,5gt ?
lt2,3,5gt
(2,lt3,4gt) lt2,3,4gt ?
(2,lt3,5gt) lt2,3,5gt
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
31
Def-Clear Paths Subsumed by lt1,3,4,5gt for
Variable B
input(A,B)
du-pair path(s)
(1,4) lt1,2,3,4gt ?
lt1,3,4gt ?
(1,5) lt1,2,3,5gt
lt1,3,5gt
(4,5) lt4,5gt ??
(1,lt1,2gt) lt1,2gt ?
(1,lt1,3gt) lt1,3gt ?
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
32
Def-Clear Paths Subsumed by lt1,2,3,5gt for
Variable A
du-pair path(s)
(1,2) lt1,2gt ? ?
(1,4) lt1,3,4gt ?
(1,5) lt1,3,4,5gt ?
lt1,3,5gt
(1,lt3,4gt) lt1,3,4gt ?
(1,lt3,5gt) lt1,3,5gt
(2,4) lt2,3,4gt ?
(2,5) lt2,3,4,5gt ?
lt2,3,5gt ?
(2,lt3,4gt) lt2,3,4gt ?
(2,lt3,5gt) lt2,3,5gt ?
input(A,B)
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
33
Def-Clear Paths Subsumed by lt1,2,3,5gt for
Variable B
input(A,B)
du-pair path(s)
(1,4) lt1,2,3,4gt ?
lt1,3,4gt ?
(1,5) lt1,2,3,5gt ?
lt1,3,5gt
(4,5) lt4,5gt ??
(1,lt1,2gt) lt1,2gt ? ?
(1,lt1,3gt) lt1,3gt ?
1
Bgt1
2
A A7
B?1
3
Agt10
4
B AB
A?10
5
output(A,B)
34
Dataflow Test Coverage Criteria

• None of the three test cases covers the du-pair
  (1,lt3,5gt) for variable A,
• All-Uses Coverage is not achieved

35
Example 2

• 1. input(X,Y)
• 2. while (Ygt0)
• 3. if (Xgt0)
• 4. Y Y-X
• else
• 5. input(X)
• 6.
• 7. output(X,Y)

1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
36
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
37
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
38
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
39
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
40
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
41
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
42
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
43
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
44
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
45
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
46
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
47
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
48
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
49
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
50
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
51
Identifying DU-Pairs Variable X
du-pair path(s)
(1,4) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,7) lt1,2,7gt
lt1,2,3,4,6,7gt
lt1,2,3,4,6,(3,4,6),7gt
(1,lt3,4gt) lt1,2,3,4gt
lt1,2,3,4,(6,3,4)gt
(1,lt3,5gt) lt1,2,3,5gt
(5,4) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
52
Identifying DU-Pairs Variable X
du-pair path(s)
(5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6),7gt
(5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
(5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt

1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
53
Identifying DU-Pairs Variable X
du-pair path(s)
(5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6),7gt
(5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
(5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt
infeasible infeasible
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
54
Identifying DU-Pairs Variable X
du-pair path(s)
(5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6),7gt
(5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
(5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt
infeasible infeasible
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
55
Identifying DU-Pairs Variable X
du-pair path(s)
(5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6),7gt
(5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
(5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt
infeasible infeasible
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
56
Identifying DU-Pairs Variable X
du-pair path(s)
(5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6),7gt
(5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
(5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt
infeasible infeasible
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
57
Identifying DU-Pairs Variable X
du-pair path(s)
(5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6),7gt
(5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
(5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt
infeasible infeasible
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
58
Identifying DU-Pairs Variable X
du-pair path(s)
(5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6),7gt
(5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
(5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt
infeasible infeasible
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
59
Identifying DU-Pairs Variable X
du-pair path(s)
(5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6)7gt
(5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
(5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt
infeasible infeasible
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
60
Identifying DU-Pairs Variable X
du-pair path(s)
(5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6)7gt
(5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
(5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt
infeasible infeasible
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
61
Identifying DU-Pairs Variable X
du-pair path(s)
(5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6)7gt
(5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
(5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt
infeasible infeasible
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
62
Identifying DU-Pairs Variable X
du-pair path(s)
(5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6)7gt
(5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
(5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt
infeasible infeasible
1
input(X,Y))
2
Ygt0
Y?0
3
Xgt0
X?0
Y Y-X
input(X)
4
5
6
Y?0
Ygt0
7
output(X,Y)
63
More Dataflow Terms and Definitions

• A path (either partial or complete) is simple if
  all edges within the path are distinct ie
  different
• A path is loop-free if all nodes within the path
  are distinct ie different

64
Simple and Loop-Free Paths
path Simple? Loop-free?
lt1,3,4,2gt
lt1,2,3,2gt
lt1,2,3,1,2gt
lt1,2,3,2,4gt
65
More Dataflow Terms and Definitions

• A path ltn1,n2,...,nj,nkgt is a du-path with
  respect to a variable v if v is defined at node
  n1 and either
• there is a c-use of v at node nk and
  ltn1,n2,...,nj,nkgt is a def-clear simple path, or
• there is a p-use of v at edge ltnj,nkgt and
  ltn1,n2,...njgt is a def-clear loop-free path.

66
More Dataflow Terms and Definitions

• A path ltn1,n2,...,nj,nkgt is a du-path with
  respect to a variable v if v is defined at node
  n1 and either
• there is a c-use of v at node nk and
  ltn1,n2,...,nj,nkgt is a def-clear simple path, or
• there is a p-use of v at edge ltnj,nkgt and
  ltn1,n2,...njgt is a def-clear loop-free path.

NOTE!
67
Identifying du-paths
du-pair path(s) du-path?
X (5,7) lt5,6,7gt
lt5,6,3,4,6,7gt
lt5,6,3,4,6,(3,4,6),7gt
X (5,lt3,4gt) lt5,6,3,4gt
lt5,6,3,4,(6,3,4)gt
X (5,lt3,5gt) lt5,6,3,5gt
lt5,6,3,4,6,3,5gt
lt5,6,3,4,6,(3,4,6),3,5gt
infeasible infeasible
68
Another Dataflow Test Coverage Criterion

• All-DU-Paths for every program variable v,
  every du-path from every definition of v to
  every c-use and every p-use of v must be covered

69
Exercise

• Identify all c-uses and p-uses for variable Y in
  Example 2
• For each c-use or p-use, identify (using the
  notation) all def-clear paths
• Identify whether or not each def-clear path is
  feasible, and whether or not it is a du-path

70
White-Box Coverage Subsumption Relationships
Path
Compound Condition
All du-paths
Branch / Condition
All-Uses
Basis Paths
Loop
Condition
Branch
All-Defs
Statement