1. Effectiveness of Pair-wise Testing on Logical Expressions Presented by William Ballance

2. Overview Introduction Fault Types Fault Evaluator Experiment Results

3. Introduction Effectiveness of pair-wise testing to reveal fault in logical expressions Only one previous paper that investigate this Non-specification-based approaches to logic testing for software Non-specification-based approaches to logic testing for software

4. Fault Types VNF (Variable Negation Fault) ORF (Operator Reference Fault) VRF (Variable Reference Fault) ENF (Expression Negation Fault) ASF (Associative Shift Fault)

5. VNF Fault type where Boolean variable x is replaced by !x. Original expression: a ∧ (!b ∨ !c) ∧ d ∨ e Expression with VNF: !a ∧ (!b ∨ !c) ∧ d ∨ e

6. ORF Fault type where Boolean AND operator is incorrectly used instead of Boolean OR operator or vice versa. Original expression: a ∧ (!b ∨ !c) ∧ d ∨ e Expression with ORF: a ∨ (!b ∨ !c) ∧ d ∨ e

7. VRF Fault type where Boolean variable x is replaced by another variable y. Original expression: a ∧ (!b ∨ !c) ∧ d ∨ e Expression with VRF: b ∧ (!b ∨ !c) ∧ d ∨ e

8. ENF Fault type where Boolean expression p is replaced by !p. Original expression: a ∧ (!b ∨ !c) ∧ d ∨ e Expression with ENF: a ∧ !(!b ∨ !c) ∧ d ∨ e

9. ASF Fault type where parentheses in Boolean expression is misused. Original expression: a ∧ (!b ∨ !c) ∧ d ∨ e Expression with ENF: a ∧ !(b ∨ !c) ∧ d ∨ e

10. Fault Evaluator A software tool that can generate faulty Boolean expressions and evaluate those faulty expressions with test sets that are loaded in the software.

11. Fault Evaluator Steps 1.Load in the correct Boolean expressions 2.Load in the test cases 3.Generate faults (specify which faults or all faults) 4.Evaluate – Fault Evaluator applies the test sets to the original expressions and the faulty expressions. – If the result from applying the test case to the faulty expression was different from the result obtained from the original expression, then the fault was revealed.

12. Comparison of Our Results and Kobayashi’s Results

13. Number of Faults for each Expression Set

14. Effectiveness of Pair-wise testing on 5 different sets of expressions Percentages of pair-wise testing to reveal faults for each expression set.

15. Comparison of Pair-wise testing and random testing Percentages of Pair-wise and random testing

16. Pair-wise testing depending on size of expression Effectiveness of Pair-wise testing for each expression set

17. Pair-wise testing depending on size of expression Effectiveness of Pair-wise testing for each fault type