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# Path selection criteria

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1. Path selection criteria Tor Stålhane & ‘Wande Daramola

2. Why path selection criteria Doing white box testing (Control flow testing, data flow testing, coverage testing)using the test-all-paths strategy can be a tedious and expensive affair. The strategies discussed here are alternative ways to reduce the number of paths to be tested. As with all white box tests, it should only be used for small chunks of code – less than say 200 lines.

3. Data flow testing -1 • Data flow testing is a powerful tool to detect improper use of data values due to coding errors. main() { int x; if (x==42){ ...} }

4. Data flow testing -2 • Variables that contain data values have a defined life cycle. They are created, they are used, and they are killed (destroyed) - Scope { // begin outer block int x; // x is defined as an integer within this outer block …; // x can be accessed here { // begin inner block int y; // y is defined within this inner block ...; // both x and y can be accessed here } // y is automatically destroyed at the end of this block ...; …; // x can still be accessed, but y is gone } // x is automatically destroyed

5. Static data flow testing • Variables can be used • in computation • in conditionals • Possibilities for the first occurrence of a variable through a program path • ~d the variable does not exist, then it is defined (d) • ~u the variable does not exist, then it is used (u) • ~k the variable does not exist, then it is killed or destroyed (k)

6. define, use, kill (duk) – 1 We define three usages of a variable: • d – define the variable • u – use the variable • k – kill the variable. A large part of those who use this approach will only use define and use – du. Based on the usages we can define a set of patterns potential problems.

7. duk – 2 We have the following nine patterns: • dd: define and then define again – error • dk: define and then kill – error • ku: kill and then used – error • kk: kill and then kill again – error • du: define and then use – OK • kd: kill and then redefine – OK • ud: use and then redefine – OK • uk: use and then kill – OK • uu: use and then use – OK

8. Example: Static data flow testing For each variable within the module we will examine define-use-kill patterns along the control flow paths

9. Example cont’d: Consider variable x as we traverse the left and then the right path ~define correct, the normal case define-define suspicious, perhaps a programming error define-use correct, the normal case ddu du

10. duk examples (x) – 1 Define x Define x Define x Use x Use x Use x Define x Use x du ddu

11. Example Cont’d: Consider variable y ~use major blunder use-define acceptable define-use correct, the normal case use-kill acceptable udk uduk

12. duk examples (y)- 2 Use y Use y Define y Define y Use y Use y Kill y Kill y udk uduk

13. Example Cont’d: Consider variable z ~kill programming error kill-use major blunder use-use correct, the normal case use-define acceptable kill-kill probably a programming error kill-define acceptable define-use correct, the normal case kkduud kuuud

14. duk examples (z) - 3 Kill z Kill z Use z Kill z Define z Kill z Define z Use z Use z Use z Use z Use z Define z Define z kuuud kkduud

15. Dynamic data flow testingTest strategy – 1 Based on the three usages we can define a total of seven testing strategies. We will have a quick look at each • All definitions (AD): test cases cover each definition of each variable for at least one use of the variable. • All predicate-uses (APU): there is at least one path of each definition to p-use of the variable

16. Test strategy – 2 • All computational uses (ACU): there is at least one path of each variable to each c-use of the variable • All p-use/some c-use (APU+C): there is at least one path of each variable to each c-use of the variable. If there are any variable definitions that are not covered then cover a c-use

17. Test strategy – 3 • All c-uses/some p-uses (ACU+P): there is at least one path of each variable to each c-use of the variable. If there are any variable definitions that are not covered then cover a p-use. • All uses (AU): there is at least one path of each variable to each c-use and each p-use of the variable.

18. Test strategy – 4 • All du paths (ADUP): test cases cover every simple sub-path from each variable definition to every p-use and c-use of that variable. Note that the “kill” usage is not included in any of the test strategies.

19. Define x All definitions All c-use Define x All p-use p-use y Kill z p-use y Kill z Define x c-use x c-use z Kill z c-use x Define z Define x c-use x c-use z Kill z c-use x Define z Define y p-use z Define y p-use z c-use c-use z c-use c-use z Kill y Define z Kill y Define z Application of test strategies – 1

20. Application of test strategies – 2 ACU APU+C Define x p-use y Kill z Define x c-use x c-use z Kill z c-use x Define z Define y p-use z c-use c-use z Kill y Define z

21. Relationship between strategies - 1 All paths All du-paths All uses All p/some c All c/some p All p-uses All c-uses All defs Branch The higher up in the hierarchy, the better is thetest strategy Statement

22. Relationship between strategies - 2 To make the relationships clear: The main testing method here is path-testing. However, since full path testing often will require us to execute a large number of paths, the duk-strategy helps us to reduce the number of paths necessary. The diagram on the preceding slide helps us to make the necessary decisions.

23. Acknowledgement The material on the duk patterns and testing strategies are taken from a presentation made by L. Williams at the North Carolina State University. Available at: http://agile.csc.ncsu.edu/testing/DataFlowTesting.pdf Further Reading: An Introduction to data flow testing – Janvi Badlaney et al., 2006 Available at: ftp://ftp.ncsu.edu/pub/tech/2006/TR-2006-22.pdf

24. Use of coverage measures Tor Stålhane

25. Model – 1 We will use the following notation: • c: a coverage measure • r(c): reliability • 1 – r(c): failure rate • r(c) = 1 – k*exp(-b*c) Thus, we also have that ln[1 – r(c)] = ln(k) – b*c

26. Model – 2 The equation ln[1 – r(c)] = ln(k) – b*c is of the same type as Y = α*X + β. We can thus use linear regression to estimate the parameters k and b by doing as follows: • Use linear regression to estimate α and β • We then have • k = exp(α) • b = - β

27. Coverage measures considered We have studied the following coverage measures: • Statement coverage: percentage of statements executed. • Branch coverage:percentage of branches executed • LCSAJLinear Code Sequence And Jump

28. Statement coverage

29. Graph summary

30. Equation summary Statements: -ln(F) = 6.5 + 6.4 Cstatement, R2(adj) = 85.3 Branches: -ln(F) = 7.5 + 6.2 Cbranches, R2(adj) = 82.6 LCSAJ -ln(F) = 6.5 + 6.4 CLCSAJ, R2(adj) = 77.8

31. Usage patterns – 1 Not all parts of the code are used equally often. When it comes to reliability, we will get the greatest effect if we have a high coverage for the code that is used most often. This also explains why companies or user groups disagrees so much when discussing the reliability of a software product.

32. input domain X X X X X X X X Input space A X X Corrected Usage patterns – 2

33. Usage patterns – 3 As long as we do not change our input space – usage pattern – we will experience no further errors. New user groups with new ways to use the system will experience new errors.

34. Usage patterns – 4 input domain Input space B X X X X X X Input space A

35. Extended model – 1 We will use the following notation: • c: coverage measure • r(c): reliability • 1 – r(c): failure rate • r(c) = 1 – k*exp(-a*p*c) • p: the strength of the relationship between c and r. p will depend the coupling between coverage and faults. • a: scaling constant

36. Extended model – 2 Residual unreliability R(C) 1 Large p Small p 1 - k C 1.0 0.0

37. Extended model - comments The following relation holds: ln[1 – r(c)] = ln(k) – a*p*c • Strong coupling between coverage and faults will increase the effect of test coverage on the reliability. • Weak coupling will create a residual gap for reliability that cannot be fixed by more testing, only by increasing the coupling factor p – thus changing the usage pattern.

38. Bishop’s coverage model – 1 Bishop’s model for predicting remaining errors is different from the models we have looked at earlier. It has a • Simpler relationship between number of remaining errors and coverage • More complex relationship between number of tests and achieved coverage

39. Bishop’s coverage model – 2 We will use f = P(executed code fails). Thus, the number of observed errors will depend on three factors • Whether the code • Is executed – C • Fails during execution – f • Coupling between coverage and faults - p N0 – N(n) = F(f, C(n, p)) C(n) = 1 – 1/(1 + knp)

40. Bishop’s coverage model – 3 Based on the assumptions and expression previously presented , we find that If we use the expression on the previous slide to eliminate C(n) we get

41. A limit result It is possible to show that the following relation holds under a rather wide set of conditions: The initial number of defects – N0 – must be estimated e.g. based on experience from earlier projects as number of defects per KLOC.

42. An example from telecom