1. SIM5102 SOFTWARE EVALUATION
Measuring Internal Product Attributes :Flowgraph measurement(structure) 1

2. Objectives
Be able to measure internal product attributes based on flowgraph 2

3. Overview from last lecture
McCabe's metric based on flowgraph
Draw flowgraphs 3

4. Flowgraph : Basic Control Structure
Sequence : eg a list of instructions with no other control structure involved
Selection : eg if ...then... else
Iteration : eg do...while, repeat...until 4

5. Flowgraph : terminologies
In-degree : number of arcs arrive at the node
Out-degree : number of arcs leaves the node
Procedure nodes : nodes with out-degree 1
Predicate nodes : nodes with out-degree other than 1 (except stop node)
Stop node : node with out-degree 0
Path : sequence of consecutive edges, may be traversed more than once
Simple path : traversing without repeating the edges 5

6. Basic flowgraph structures
Sequence : Pn or Pn(X1,X2,...,Xn) or X1;X2;...Xn
Selection x1 x2 x3 x4 A A t f t f X Y x
D0 or D0(A,X)
if A then X
D1 or D1(A,X,Y)
if A then X else Y 6

7. Basic flowgraph structure (cont..)an a2 X1 Xn
Cn or Cn(A, X1,X2,...,Xn)
Case A of
a1 : X1
a2 : X2 .
an : Xn 7

8. Basic flowgraph structure
Iteration A X f t f X t A
D2 or D2(A,X)
while A do X
D3 or D3(A,X)
repeat X until A 8

9. Sequencing operation Let F1 and F2 be two flowgraphs.
The sequence of F1 and F2 is the flowgraph formed by merging the stop node of F1 with the start node of F2
The resulting flowgraph can be written as
F1;F2
Seq(F1,F2)
P2(F1,F2) 9

10. Sequencing (cont...)
Merging two flowgraphs
sequence D1 D3
D1;D3 10

11. Nesting operation
Let F1 and F2 be two flowgraphs. Suppose F1 has a procedure node X
The nesting of F2 on to F1 at X is the flowgraph formed from F1 by replacing the arc from X with the whole of F2
The resulting flowgraph can be written as
F1(F2 on X)
F1(F2) 11

12. Nesting (cont...) X
with
Nested
on X D1 D3
D1(D3) 12

13. Prime flowgraph
Flowgraphs that cannot be decomposed non- trivially by sequencing or nesting
Examples Pn
D0, D1, D2 and D3 Cn 13

14. S-structured Graph
A family (S) of prime flowgraph is called S- structured Graph (or S-graphs) if it satisfies the following recursive rules:
1. Each member of S is S-structure
2. if F and G are S-structured flowgraphs, so is the sequences F;G and nesting of F(G)
3. No flowgraph is S-structured unless it can be generated by finite number of application of the above (step 2) rules 14

15. Prime decomposition
Any flowgraph can be uniquely decomposed into a hierarchy of sequencing and nesting primes
Decomposition tree – can be determined from a given graph
It describes how the flowgraph is built by sequencing and nesting 15

16. Hierarchical Measures
Assume that S in an arbitrary set of primes. We say a measure m is a
hierarchical measure if it can be defined on the set of S-graphs by specifying
- m(F) for each F is a member of S (we call this as M1)
- the sequencing function(s) (e call this as M2)
- the nesting functions hF for each F is a member of S (we call this as M3) 16

17. Depth of Nesting
Depth of nesting, a, for a flowgraph F can be expressed in terms of:
- primes: a(P1) = 0, and if F is a prime is not equal to P1, then a(F) = 1
- sequence : a(F1;...;Fn) = max(a(F1),..,a(Fn))
- nesting : a(F(F1,...,Fn))
= 1 + max(a(F1),..,a(Fn)) 17

18. Example F = D1((D0;P1;D2),D0(D3))
a(F) = 1 + max(a(D0;P1;D3),a(D0(D3)))
= 1 + max(max(a(D0),a(P1),a(D3)), 1 + a(D3))
= 1 + max(max(1,0,1), 1 + 1)
= 1 + max(1,2)
= 3 18

19. Test Coverage Measures
Statement coverage
- a set of paths that every node lies on at least one path
Branch coverage
- a set of paths such that every edge lies on at least one path
All Path coverage
- exercising every single path
- infinite number if there any loop 19

20. Test Coverage Measures
Simple path coverage
- every path which does not contain the same edge more than once
Visit-each-loop
- branch coverage is satisfied
- for every loop, there are paths for each control flows both straight pass the loop and around the loop at least once
Linearly independent paths
- the execution of set of linearly independent paths
- an independent path must move along at least one edge that has not been traversed before the path is defined 20

21. Minimum Number of test cases
Have to know the minimum number of test cases in order to
- plan the testing
- generating data
- how long testing will take
Minimum number of path m(F) can be computed from the decomposition tree
- strategy of testing
- value for the primes, sequencing, and nesting
- appendix 21

22. Example : statement coverage
F = D1((D0;P1;D2),D0(D3)) please refer to app
m(F) = m(D1(D0;P1;D2),D0(D3))
= m(D0;P1;D2) + m(D0(D3))
= max(m(D0),m(P1),m(D2)) + m(D3)
= max(1,1,1) + 1
= 2
required paths : < > < > 22

23. Class exercise 1. draw the flowgraph 2. draw the decomposition tree
begin
Read input list
if the list is empty then
output “list empty
else
sum := 0;
repeat
read next list entry A;
sum := sum + A;
until end of list
output sum;
end;
end.
1. draw the flowgraph
2. draw the decomposition tree
3. write the expression for the decomposition tree
4. calculate the depth of nesting using hierarchical
measure
5. compute the minimum number of test cases
for statement coverage.

24. Software Architecture

25. Morphology

26. Morphology - example

27. Tree Impurity

28. Tree Impurity

29. Internal Reuse

30. Modules and Components

31. Software Architecture

32. Cohesion

33. Cohesion

34. Coupling

35. Coupling

36. Coupling : Representation

37. Information Flow Measures

38. Information Flow Measures

39. Information Flow Measures

40. Information Flow Measures