Truth Table-Based Testing

Generating test cases when the test model is a

truth table

Reading: Binder Chapter 6

Example truth tableVariant Number

Normal Pressure

Call For Heat

Damper Shut Manual Mode Ignition Enable

A B C D Z

0 0 0 0 0 0

1 0 0 0 1 0

2 0 0 1 0 0

3 0 0 1 1 0

4 0 1 0 0 0

5 0 1 0 1 0

6 0 1 1 0 0

7 0 1 1 1 0

8 1 0 0 0 0

9 1 0 0 1 1

10 1 0 1 0 0

11 1 0 1 1 1

12 1 1 0 0 1

13 1 1 0 1 1

14 1 1 1 0 0

15 1 1 1 1 1

Deriving the Logic Function Review boolean algebra

AB = A and B A+B = A or B ~A = not A

A logic function maps n boolean input variables to a boolean output variable

A truth table is an enumeration of all possible input and output values

Logic function The logic function for the example is

Z = AB~C + AD Several techniques to derive it

Karnaugh maps Cause-effect graphs

A compact logic function will produce more powerful test cases

Truth table approaches All-Variants: Every variant is tested once. The number of tests is 2N, infeasible for large tables

All-True: All variants that produce a true outcome are tested Inappropriate if false actions are an important part of the behaviour

All-False: All variants that produce a false outcome are tested Inappropriate if true actions are important

Each-Condition/All-conditions Assumption: For the logic functions X=PQR and Y=P+Q+R, the only relevant cases are:

P Q R X

0 1 1 0

1 0 1 0

1 1 0 0

1 1 1 1

P Q R Y

0 0 1 1

0 1 0 1

1 0 0 1

0 0 0 0

Each-Condition/All-conditions For a logic function such as

Z = AB~C + ADwe apply the heuristic to every termTest cases for

AB~C

A B C D

0 1 0 X

1 0 0 X

1 1 1 X

1 1 0 X

Test cases for AD

A B C D

1 X X 0

0 X X 1

1 X X 1

Each-Condition/All-conditions The number of tests increases linearly with the number of product terms

Values need to be assigned to the Don’t Care variables. Can be done randomly or by suspicion. Try different combinations for different test cases

Binary Decision Diagrams Compact representation of a truth table

Can be used to create test suite A BDD can be generated from the truth table

Start by drawing the full decision tree

A left branch represents False (0) A right branch represents True (1)

Decision tree for boiler example

Reduction process Working from left to right, replace leaf nodes with equivalent constants or variables and prune the branches

This way we can prune the entire left branch of the tree since it only depends on the value of A

First Reduction

Second Reduction

Final Binary Decision Diagram

BDD determinant table A BDD determinant is a root-to-leaf-path in the BDD

The BDD determinant table has one row per path

Variant

A B C D Z

1 0 X X X 0

2 1 0 X D D

3 1 1 1 D D

4 1 1 0 X 1

Test suite generation All combinations of sensitive variables, e.g. D, are createdVariant

A B C D Z

1 0 X X X 0

2 1 0 X 0 0

2 1 0 X 1 1

3 1 1 1 0 0

3 1 1 1 1 1

4 1 1 0 X 1

Variable Negation Strategy Designed to reveal faults that hide in a

don’t care The test suite contains:

Unique true points: A variant per term t, so that t is True and all other terms are False

Near False Points: A variant for each literal in a term. The variant is obtained by negating the literal and is selected only if it makes Z=0

Each variant creates a test candidate set Unique true point candidate sets in

boiler example: {12} {9,11,15}

Example truth tableVariant Number

Normal Pressure

Call For Heat

Damper Shut Manual Mode Ignition Enable

A B C D Z

0 0 0 0 0 0

1 0 0 0 1 0

2 0 0 1 0 0

3 0 0 1 1 0

4 0 1 0 0 0

5 0 1 0 1 0

6 0 1 1 0 0

7 0 1 1 1 0

8 1 0 0 0 0

9 1 0 0 1 1

10 1 0 1 0 0

11 1 0 1 1 1

12 1 1 0 0 1

13 1 1 0 1 1

14 1 1 1 0 0

15 1 1 1 1 1

Negation variants

Candidate set

number

Termnegation

Variants containing this

negation

Variants containing

this negation where Z=0

2 ABC 14,15 14

3 A~B~C 8,9 8

4 ~AB~C 4,5 4,5

6 A~D 8,10,12,14

8,10,14

7 ~AD 1,3,5,7 1,3,5,7

Selecting the test cases At least one variant from each candidate set

Can be done by inspection Random selection is also used Near False Points exercise combinations of don’t care values

6% of all possible tests are created

98% of simulated bugs can be found

Test suite Candidate sets121484,59,11,158,10,141,3,5,7

Minimum Test suite5891214