Software Testing

Activity: Graph: Data flow coverage criteria

(no submission)

Purpose: Understand Defs, Uses, DU-pairs, DU-paths; apply data flow coverage to design tests

You may make a copy of a worksheet and complete this activity, or simply type your answers in any text editor.

You may work alone or with another student in this course (max team size = 2).

Consider the following graph and test paths (Ref: AO exercise 7.2.3, Q1, Graph II)

   N  = { 1, 2, 3, 4, 5, 6 }
   N0 = { 1 }
   Nf = { 6 }
   E  = { (1, 2), (2, 3), (2, 6), (3, 4), (3, 5), (4, 5), (5, 2) }
   def(1) = def(3) = use(3) = use(6) = { x }   
   // Assume the use of x in node 3 precedes the def
   
   Test paths
   t1 = [1, 2, 6]
   t2 = [1, 2, 3, 4, 5, 2, 3, 5, 2, 6]
   t3 = [1, 2, 3, 5, 2, 3, 4, 5, 2, 6]
   t4 = [1, 2, 3, 5, 2, 6]

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Draw the graph. Annotate all defs and uses.

List all of the du-paths with respect to x. (Note: include all du-paths, even those that are subpaths of some other du-paths)

x has 6 du-paths          

          DU-pair
              DU-path(s)
          
          (1,3) [1,2,3]
          (1,6) [1,2,6]
          (3,3) [3,5,2,3], [3,4,5,2,3]
          (3,6) [3,5,2,6], [3,4,5,2,6]
                      
du-paths = { [1,2,3], [1,2,6], [3,5,2,3], [3,4,5,2,3], [3,5,2,6], [3,4,5,2,6] }

Determine which du-paths each test path tours.


          Test path
              DU-path(s) the test tours (direct)
              DU-pair(s) the test covers
          
          t1 [1,2,6] (1,6)
          t2 [1,2,3], [3,4,5,2,3], [3,5,2,6] (1,3), (3,3), (3,6)
          t3 [1,2,3], [3,4,5,2,6], [3,5,2,3] (1,3), (3,3), (3,6)
          t4 [1,2,3], [3,5,2,6] (1,3), (3,6)
          
Note: t2 tours [3,5,2,3] with a detour.

List a minimal test set that satisfies all defs coverage with respect to x (direct tours only). If possible, use the given test paths. If not, provide additional test path(s) to satisfy the criterion.
```
This question has multiple possible answers. 
All test paths use the def in 1, and test paths t2, t3, t4 each use the def in 3. 
Possible answers: {t2} or {t3} or {t4}
```
List a minimal test set that satisfies all uses coverage with respect to x (direct tours only). If possible, use the given test paths. If not, provide additional test path(s) to satisfy the criterion.
```
This question only has two possible answers. 
t1 is required for the def in 1 to reach the use in 6. 
Either t2 or t3 is required for the def in 3 to reach the use in 3. 
Possible answers: {t1, t2} or {t1, t3}.
```

List a minimal test set that satisfies all du-paths coverage with respect to x (direct tours only). If possible, use the given test paths. If not, provide additional test path(s) to satisfy the criterion.

This question has one possible answer: {t1, t2, t3}. 
t1 is required for path [1,2,6]. 
t2 is required for path [3,4,5,2,3]. 
t3 is required for path [3,4,5,2,6] and [3,5,2,3]. 
Since t1, t2, and t3 together tour all six du-paths, t4 is not needed.

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CC-BY-NC-SA 4.0 license.
Last updated 2026-10-08 7:42

DU-pair	DU-path(s)
(1,3)	[1,2,3]
(1,6)	[1,2,6]
(3,3)	[3,5,2,3], [3,4,5,2,3]
(3,6)	[3,5,2,6], [3,4,5,2,6]

Test path	DU-path(s) the test tours (direct)	DU-pair(s) the test covers
t1	[1,2,6]	(1,6)
t2	[1,2,3], [3,4,5,2,3], [3,5,2,6]	(1,3), (3,3), (3,6)
t3	[1,2,3], [3,4,5,2,6], [3,5,2,3]	(1,3), (3,3), (3,6)
t4	[1,2,3], [3,5,2,6]	(1,3), (3,6)