Black-Box Testing Techniques II
Prepared by
Stephen M. Thebaut, Ph.D.
University of Florida
Software Testing and Verification
Lecture 5
Black-Box Test Case Design Techniques
Considered
• Partition testing
• Combinatorial Approaches
• Boundary Value Analysis
• Intuition & Experience
Cause-Effect Analysis
• Cause-Effect Analysis is a combinatorial approach that can be viewed as a logical extension of partition testing.
• It extends the idea of partitioning a multi-dimensional input space by providing a systematic means for generating test case templates to cover different combinationsof input “Causes” resulting in output “Effects.”
Causes and Effects
• A CAUSE may be thought of as a distinct input condition, or an “equivalence class” of input conditions.
• An EFFECT may be thought of as a distinct output condition or change in program state.
Causes and Effects
• Causes and Effects are represented as Boolean variables.
• The logical relationships among them CAN (but need not) be represented as one or more Boolean graphs.
Л
V
Causes Effects
C-E Analysis Process Steps
1. Identify Causes and Effects
– The most critical and usually the most difficult step
– Choose an appropriate level of abstraction.
– Divide and conquer as necessary.
– Effects may or may not be mutually exclusive.
C-E Analysis Process Steps (cont’d)
2. Deduce Logical Relationships and Constraints
– Relationships take the form of conditionals and utilize the logical operators AND, OR, and NOT.
– Constraints describe relationships among Causes that allow for the identification of infeasible (i.e., impracticable) combinations.
(cont’d)
C-E Analysis Process Steps (cont’d)
2. Deduce Logical Relationships and Constraints (cont’d)
– Boolean graphs provide a convenient and economical way to visualize relationships and constraints.
C-E Analysis Process Steps (cont’d)
3. Identify an appropriate Test Case Coverage/ Selection Strategy
– Determines the number and nature of Cause-combinations to be considered.
– Strategies can be designed to meet a variety of coverage requirements/cost constraints.
C-E Analysis Process Steps (cont’d)
4. Construct a Test Case Coverage Matrix
– Typically involves tracing through the Cause-Effect relationships to identify one or more combinations of Causes resulting in each Effect according to the coverage strategy chosen.
– This can be extremely tedious if done manually...
Question…
To what extent do you think CASE support might be applicable to each step in the process? For which steps do you think it might be most important?
Question…
To what extent do you think CASE support might be applicable to each step in the process? For which steps do you think it might be most important?
(We’ll come back to this after illustrating the process steps with some examples.)
Illustration of Step 1 (Identify Causes
and Effects)
The first input is a yes/no response to the question
“Do you reside within the city?” The second input is gross pay for the year in question.
A non-resident will pay 1% of the gross pay in city tax.
Residents pay on the following scale:
- If gross pay is no more than $30,000, the tax is 1%.
- If gross pay is more than $30,000, but no more than
$50,000, the tax is 5%.
- If gross pay is more than $50,000, the tax is 15%.
Guidelines for identifying Causes
and Effects
• Underline words or phrases in the specification that correspond to input/output conditions or changes in state.
Guidelines for identifying Causes
and Effects (cont’d)
The first input is a yes/no response to the question “Do
you reside within the city?” The second input is gross pay for the year in question.
A non-resident will pay 1% of the gross pay in city tax.
Residents pay on the following scale:
- If gross pay is no more than $30,000, the tax is 1%.
- If gross pay is more than $30,000, but no more than
$50,000, the tax is 5%.
- If gross pay is more than $50,000, the tax is 15%.
Guidelines for identifying Causes
and Effects (cont’d)
• List each Cause and Effect.
• Assign a unique number to each (use different number ranges to differentiate Causes from Effects).
Illustration of Step 1 (cont’d)
Ignoring, again, the unspecified responses to “invalid” inputs, we have:
Causes: Effects:
(1) Non-Resident (11) 1% tax
(2) Resident (12) 5% tax
(3) $0 Gross Pay $30K (13) 15% tax
(4) $30K Gross Pay $50K
(5) Gross Pay $50K
Illustration of Step 2 (Deduce Logical
Relationships and Constraints)
The first input is a yes/no response to the question “Do
you reside within the city?” The second input is gross pay for the year in question.
A non-resident will pay 1% of the gross pay in city tax.
Residents pay on the following scale:
- If gross pay is no more than $30,000, the tax is 1%.
- If gross pay is more than $30,000, but no more than
$50,000, the tax is 5%.
- If gross pay is more than $50,000, the tax is 15%.
What are the constraints?
Causes: Effects:
(1) Non-Resident (11) 1% tax
(2) Resident (12) 5% tax
(3) $0 Gross Pay $30K (13) 15% tax
(4) $30K Gross Pay $50K
(5) Gross Pay $50K
Constraints deducible from spec,
problem domain knowledge, etc.
A. [(1) Л ¬(2)] V [¬(1) Л (2)] (i.e., one, and only one of (1) and (2) must be true.)
B. [(3) Л ¬(4) Л ¬(5)] V [¬(3) Л (4) Л ¬(5)] V
[¬(3) Л ¬(4) Л (5)]
C. [(11) Л ¬(12) Л ¬(13)] V [¬(11) Л (12) Л
¬(13)] V [¬(11) Л ¬(12) Л (13)]
What are the logical relationships?
The first input is a yes/no response to the question “Do
you reside within the city?” The second input is gross pay for the year in question.
A non-resident will pay 1% of the gross pay in city tax.
Residents pay on the following scale:
- If gross pay is no more than $30,000, the tax is 1%.
- If gross pay is more than $30,000, but no more than
$50,000, the tax is 5%.
- If gross pay is more than $50,000, the tax is 15%.
Conditionals deducible from
specification and constraints
• From the specification we have:
(1) => (11)
[(2) Л (3)] => (11)
[(2) Л (4)] => (12)
[(2) Л (5)] => (13)
Conditionals deducible from
specification and constraints (cont’d)
• Which, in light of the identified constraints, simplify to:
[(1) V (3) => (11)
[(2) Л (4)] => (12)
[(2) Л (5)] => (13)
Boolean Graph Representation
(1)
(11)
(3)
(4)
(12)
(2)
(13)
(5)
Л
Л
V
Boolean Graph Representation
Non-Res (1)
(11) 1% tax
[0,30K] (3)
(30K,50K] (4)
(12) 5% tax
Res (2)
(13) 15% tax
>50K (5)
Л
Л
V
Boolean Graph Representation
Non-Res (1)
(11) 1% tax
[0,30K] (3)
(30K,50K] (4)
(12) 5% tax
Res (2)
(13) 15% tax
>50K (5)
Л
Л
V
O
O
O
Cause/Effect Constraints
E
O
I
Exclusive Inclusive
One & Only One Requires
A
B
“at most one” “at least one”
A => B“one and only one”
Illustration of Step 3 (Identify Test
Case Coverage/Selection Strategy)
• Simple (but extreme) strategies:
– “All Feasible Combinations of Cause Values” (AFCCV)
– “All Effects” (AE)
• For the relationships depicted in our graph, how many test cases would be required to achieve AFCCV coverage? AE coverage?
AFCCV and AE Coverage
Non-Res (1)
(11) 1% tax
[0,30K] (3)
(30K,50K] (4)
(12) 5% tax
Res (2)
(13) 15% tax
>50K (5)
Л
Л
V
O
O
O
AFCCV and AE Coverage (cont’d)
• AFCCV:
– There are 25 = 32 possible value combinations for all 5 Causes.
– For Causes (1) and (2), there are 2 feasible value combination pairs (due to the “one and only one” constraint): TF and FT.
(cont’d)
AFCCV and AE Coverage (cont’d)
• AFCCV: (cont’d)
– Similarly, for Causes (3), (4), and (5), there are 3 feasible value combination triples: TFF, FTF, and FFT.
– Thus, there are 2 X 3 = 6 feasiblecombinations of values for all 5 Causes, requiring a total of 6 test cases.
How about AE Coverage?
Non-Res (1)
(11) 1% tax
[0,30K] (3)
(30K,50K] (4)
(12) 5% tax
Res (2)
(13) 15% tax
>50K (5)
Л
Л
V
O
O
O
AFCCV and AE Coverage (cont’d)
• AE:
– There are 3 mutually exclusive Effects.
– Thus, a different combination of Cause values is required for each Effect to evaluate to True.
– Therefore, 3 test cases are required.
(cont’d)
AFCCV and AE Coverage (cont’d)
• AE: (cont’d)
– In general, when there are N Effects, N or fewer test cases are required for AE Coverage.
– When the N Effects are mutually exclusive, all N test cases are required.
(Question: If the N Effects are NOT mutually exclusive, how could you identify combinations of Cause values that result in more than 1 Effect evaluating to True?)
AFCCV and AE Coverage (cont’d)
• Note that AE is analogous to partitioning an input space based solely on the specified outputs...
• AFCCV is analogous to associating a separate equivalence class with every (feasible) combination of the individual input classes (i.e., the “brute-force” approach)...
• Question: do these strategies depend on the Cause-Effect relationships?
Partitioning Based on Specified Output
Would you be comfortable with the degree of coverage afforded by choosing ONE test case from each of these 3 partitions? Why or why not?
5% 15%Res?
yes
no
Gross_Pay
30K (30K, 50K] > 50K
1%
AFCCV and AE Coverage (cont’d)
• Note that AE is analogous to partitioning an input space based solely on the specified outputs...
• AFCCV is analogous to associating a separate equivalence class with every (feasible) combination of the individual input classes (i.e., the “brute-force” approach)...
• Question: do these strategies depend on the Cause-Effect relationships?
The “Brute-Force” Approach
We could “hedge our bet” by associating a separate partition with every (feasible) combination of classes from the sets:
1% 5% 15%
1% 1% 1%Res?
yes
no
Gross_Pay
30K (30K, 50K] > 50K
What are the pros and cons of this approach?
AFCCV and AE Coverage (cont’d)
• Note that AE is analogous to partitioning an input space based solely on the specified outputs...
• AFCCV is analogous to associating a separate equivalence class with every (feasible) combination of the individual input classes (i.e., the “brute-force” approach)...
• Question: do these strategies depend on the Cause-Effect relationships?
AFCCV and AE Coverage (cont’d)
• Note that AE is analogous to partitioning an input space based solely on the specified outputs...
• AFCCV is analogous to associating a separate equivalence class with every (feasible) combination of the individual input classes (i.e., the “brute-force” approach)...
• Question: do these strategies depend on the Cause-Effect relationships?
AFCCV: no AE: yes
Another Test Case Coverage/
Selection Strategy…
Non-Res (1)
(11) 1% tax
[0,30K] (3)
(30K,50K] (4)
(12) 5% tax
Res (2)
(13) 15% tax
>50K (5)
Л
Л
V
O
O
O
Another Test Case Coverage/
Selection Strategy…
REPEAT
Select the next (initially, the first) Effect.
Tracing back through the graph (right to left), find all feasible combinations of connectedCause values that result in the Effect being True.
For each new such combination found:
Determine values of all other Effects, andEnter values for each Cause and Effect in anew column of the test case coverage matrix.
UNTIL each Effect has been selected.
What Should We Call this Strategy?
How about: All Feasible Combinations of Connected Cause Values that Result in Each Effect being True (AFCCCVREET)?
What Should We Call this Strategy?
How about: All Feasible Combinations of Connected Cause Values that Result in Each Effect being True (AFCCCVREET)?
Nah…let’s just call it “Strategy #3”.
Illustration of Step 4 (Construct a
Test Case Coverage Matrix)
For “Strategy #3”, this involves tracing through the Cause-Effect relationships to identify all feasible combinations of connected Causes resulting in each Effect being true…
Applying Strategy #3
Non-Res (1)
(11) 1% tax
[0,30K] (3)
(30K,50K] (4)
(12) 5% tax
Res (2)
(13) 15% tax
>50K (5)
Л
Л
V
O
O
O
Applying Strategy #3
Non-Res (1)
(11) 1% tax
[0,30K] (3)
(30K,50K] (4)
(12) 5% tax
Res (2)
(13) 15% tax
>50K (5)
Л
Л
V
O
O
O
Applying Strategy #3
• Cause Value Combinations for Effect 11:
(1) V (3) 1, 3 or
1, 3 or
1, 3
• Cause Value Combinations for Effect 12:
• Cause Value Combinations for Effect 13:
Coverage Matrix
TEST CASES
CAUSES 1 2 3 4 5
Non-Resident (1) T T F
Resident (2) F F T
$0 Gross Pay $30K (3) T F T
$30K Gross Pay $50 (4) F F
Gross Pay $50K (5) F F
EFFECTS
1% tax (11) T T T
5% tax (12) F F F
15% tax (13) F F F
don’t care, subject to Cause constraint B
Applying Strategy #3
Non-Res (1)
(11) 1% tax
[0,30K] (3)
(30K,50K] (4)
(12) 5% tax
Res (2)
(13) 15% tax
>50K (5)
Л
Л
V
O
O
O
Applying Strategy #3
• Cause Value Combinations for Effect 11:
(1) V (3) 1, 3 or
1, 3 or
1, 3
• Cause Value Combinations for Effect 12:
(4) Л (2) 2, 4
• Cause Value Combinations for Effect 13:
Coverage Matrix (cont’d)
TEST CASES
CAUSES 1 2 3 4 5
Non-Resident (1) T T F F
Resident (2) F F T T
$0 Gross Pay $30K (3) T F T F
$30K Gross Pay $50K (4) F F T
Gross Pay $50K (5) F F F
EFFECTS
1% tax (11) T T T F
5% tax (12) F F F T
15% tax (13) F F F F
don’t care, subject to Cause constraint B
Applying Strategy #3
Non-Res (1)
(11) 1% tax
[0,30K] (3)
(30K,50K] (4)
(12) 5% tax
Res (2)
(13) 15% tax
>50K (5)
Л
Л
V
O
O
O
Applying Strategy #3
• Cause Value Combinations for Effect 11:
(1) V (3) 1, 3 or
1, 3 or
1, 3
• Cause Value Combinations for Effect 12:
(4) Л (2) 2, 4
• Cause Value Combinations for Effect 13:
(5) Л (2) 2, 5
Coverage Matrix (cont’d)
TEST CASES
CAUSES 1 2 3 4 5
Non-Resident (1) T T F F F
Resident (2) F F T T T
$0 Gross Pay $30K (3) T F T F F
$30K Gross Pay $50K (4) F F T F
Gross Pay $50K (5) F F F T
EFFECTS
1% tax (11) T T T F F
5% tax (12) F F F T F
15% tax (13) F F F F T
don’t care, subject to Cause constraint B
Complete Coverage Matrix
TEST CASES
CAUSES 1 2 3 4 5
Non-Resident (1) T T F F F
Resident (2) F F T T T
$0 Gross Pay $30K (3) T F T F F
$30K Gross Pay $50K (4) F F T F
Gross Pay $50K (5) F F F T
EFFECTS
1% tax (11) T T T F F
5% tax (12) F F F T F
15% tax (13) F F F F T
don’t care, subject to Cause constraint B
Comparing Strategy #3 to AFCCV
and AE Coverage
• How does Strategy #3 differ from AFCCV?
– For each Effect, only the connectedCauses are considered.
– It is less conservative:
• Does not ensure that every feasible combination of Cause values will be covered.
• And thus does not ensure that every feasible combination of Effect values will be covered. (Relevant when Effects are not mutually exclusive.)
Complete Coverage Matrix
TEST CASES
CAUSES 1 2 3 4 5
Non-Resident (1) T T F F F
Resident (2) F F T T T
$0 Gross Pay $30K (3) T F T F F
$30K Gross Pay $50K (4) F F T F
Gross Pay $50K (5) F F F T
EFFECTS
1% tax (11) T T T F F
5% tax (12) F F F T F
15% tax (13) F F F F T
don’t care, subject to Cause constraint B
Comparing Strategy #3 to AFCCV
and AE Coverage
• How does Strategy #3 differ from AFCCV?
– For each Effect, only the connectedCauses are considered.
– It is less conservative:
• Does not ensure that every feasible combination of Cause values will be covered.
• And thus does not ensure that every feasible combination of Effect values will be covered. (Relevant when Effects are not mutually exclusive.)
Comparing Strategy #3 to AFCCV
and AE Coverage
• How does it differ from AE?
– It is more conservative (ALL feasible combinations of connected Cause values must be covered for each Effect).
Coming up in “Black-Box Testing
Techniques III”…
• We step-through another (somewhat more complex) example of Cause-Effect Analysis,
• Describe a test case design technique for exploring boundary conditions, and
• Consider a test case design strategy based on intuition and experience.
Black-Box Testing Techniques II
Prepared by
Stephen M. Thebaut, Ph.D.
University of Florida
Software Testing and Verification
Lecture 5