Cause-effect graphing

Test and Verification Lecture 4
Cause-effect graphing
& test generation from
predicates
Ulrik Nyman
ulrik@cs.aau.dk
1

Plan for today
Cause-effect graphing
Purpose
Notation
Decision table and test generation
Test generation from predicates
Predicates and Boolean expressions
Fault model
Relation to cause effect graphing
2

Cause-effect graphing
A.k.a. Dependency modeling
Purpose:
Model relationships between
Causes and
Effects
3

Steps
1) Identify causes and effects by reading
requirements.
2) Express relationship between causes
and effects
3) Transform graph to decision table
4) Generate tests from decision table
4

Notation
C implies Ef
C
Ef
Not C implies Ef
C
Ef
Ef when C1 and C2
and C3
C1
C2
^
Ef
C3
5

Notation
Ef when C1 or C2
C1
v
Ef
C2
6

Notation
Exclusive: either
C1 or C2 or C3
E
C1
C2
C3
Inclusive: at least
C1 or C2
I
C1
C2
7

Notation
C1 requires C2
C1
C2
One and only one
of C1 and C2
O
C1
C2
8

Notation
Ef1 masks Ef2
Example:
Ef1: Shipping
invoice
Ef2: Order not
shipped letter
Both effects cannot
occur in the same
test.
Ef1
Ef2
9

Example
Online sales system
Possible configurations
CPU 1, 2, 3
Printer PR 1, 2
Monitor M 20, 23, 30
RAM 256, 512, 1G
Windows: Items, Free and Price
Read requirements
10

Example
Causes
C1: Purchase CPU1
C2: Purchase CPU2
C3: Purchase CPU3
C4: Purchase PR1
C5: Purchase PR2
C6: Purchase M20
C7: Purchase M23
C8: Purchase M30
11

Example
Effects in Free display window
RAM 256
RAM 512 and PR1
RAM 1G and PR2
No giveaway with this item
12

Example
E
C1
C2
Ef1
C3
C4
v
Ef2
C5
^
Ef3
R
C6
C7
1
Ef4
C8
13

Decision table
C1 C2 C3 C4 Ef 1
1 1 1 0 0 1
2 0 0 1 0 1
3 1 0 1 0 0
4 0 1 0 1 0
14

DT from CE graph
CEGDT
Input: Cause effect graph with
C1, C2, ... CP
Ef1, Ef2, ... EfQ
Output:
DT with P + Q rows
Variable number of columns
15

Steps
Process Effects one by one
Find combinations of causes that lead to
the current Effect
Possibly apply heuristics
Update decision table
16

Heuristics
C1
Or node
Desired state: 0
C2
v
Ef
H1: Enumerate all
combinations of inputs to
C1 and C2 such that
C1 = C2 = 0
17

Heuristics
C1
Or node
Desired state: 1
C2
v
Ef
H2: Enumerate all
combinations of inputs to
C1 and C2 other than
those for which
C1 = C2 = 1
18

Heuristics
C1
And node
Desired state: 0
C2
^
Ef
H3: Enumerate one
combination for each of
(0,0)
(1,0)
(0,1)
19

Heuristics
C1
And node
Desired state: 1
C2
^
Ef
H4: Enumerate all
combinations on input of
C1 and C2 such that
C1 = C2 = 1
20

Predicates
Boolean expressions
Bop – Boolean operator
And, Or, Xor, Not
Relop – Relational operator
, =, =, =/=
21

Singular
Singular boolean expression
Each literal only appears once
22

Fault model
Boolean operator fault
Incorrect Boolean operator(s)
Incorrect negation
Incorrect Boolean variable
23

Fault model
Relational operator fault
Incorrect relational operator
Two relational faults
Relational and boolean fault
Arithmetic expression fault
Off-by-* faults
24

Fault model
Not guaranteed to be detected
Missing Boolean variable
Extra Boolean variable
Guaranteed to be detected
Not a real “guarantee”
If we arrive at the test location
25

Testing criteria
BOR: Boolean operator
BRO: Boolean and relational operator
BRE: Boolean and relational expression
26

Generating
We left out this part
Generating BOR, BRO and BRE adequate
test sets
27

Fault propagation
The generation algorithms ensure that
certain types of faults are propagated to
the root node
Does not propagate
N6 v true
N6 v true
N4 ^ true
fault
false
N4 v true
false
28

Fault propagation
The generation algorithms ensure that
certain types of faults are propagated to
the root node
Does propagate
N6 v false
N6 v true
N4 ^ false
fault
false
N4 v false
false
29

CEG and Predicate testing
Relationship among causes can be seen
as predicates
Effects can be used to generate oracle
BOR-CSET vs. CEGDT
BOR-CSET slightly less effective
BOR-CSET significantly smaller test sets
30

White box
Program based predicate test generation
In practice it is hard to find input which
exercises the chosen combinations
31