Transcript PowerPoint Sunusu

Introduction to Software Testing
Chapter 3.1
Logic Coverage
Paul Ammann & Jeff Offutt
Covering Logic Expressions
 Logic expressions show up in many situations
 Covering logic expressions is required by the US Federal
Aviation Administration for safety critical software
 Logical expressions can come from many sources
– Decisions in programs
– FSMs and statecharts
– Requirements
 Tests are intended to choose some subset of the total
number of truth assignments to the expressions
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Logic Predicates and Clauses
A predicate is an expression that evaluates to a
boolean value
Predicates can contain
– boolean variables
– non-boolean variables that contain >, <, ==, >=, <=, !=
– boolean function calls
Internal structure is created by logical operators
– ¬ – the negation operator
–  – the and operator
–  – the or operator
–  – the implication operator
–  – the exclusive or operator
–  – the equivalence operator
A clause is a predicate with no logical operators
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Example
(a < b)  f (z)  D  (m >= n*o)
Includes four clauses:
(a < b) – relational expression
f (z) – boolean-valued function
D – boolean variable
(m >= n*o) – relational expression
Most predicates have few clauses
– It would be nice to quantify that claim!
Sources of predicates
–
–
–
–
–
Decisions in programs
Guards in finite state machines
Decisions in UML activity graphs
Requirements, both formal and informal
SQL queries
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Problem:
List all the clauses for the predicate below:
((f <= g)  (X > 0))  (M  (e < d + c))
Solution:
There are four: f <= g, X > 0, M, and e < d + c.
Problem: 2 Write the predicate to represent the
requirement:
List all the wireless mice that either retail for more than
$100 or for which the store has more than 20 items.
Also list non-wireless mice that retail for more than $50.
The predicate describing whether to list a given mouse is:
((mouseType = wireless)  ((retail > 100)  (stock > 20)))
((mouseType = wireless)  (retail > 50))
Clause
A clause is a predicate that does not contain any
of the logical operators.
For example, the predicate (a = b) ∨ C ∧ p(x)
contains three clauses:
a relational expression (a = b),
a boolean variable C
the function call p(x).
Because they may contain a structure of their
own, relational expressions require special
treatment.
The Predicate
A predicate may be written in a variety of
logically equivalent ways.
For example, the predicate
((a = b) ∨ C) ∧ ((a = b) ∨ p(x))
is logically equivalent to the predicate given
in the previous slide
but ((a
= b) ∧ p(x)) ∨ (C ∧ p(x))
is not.
The usual rules of boolean algebra may be
used to convert boolean expressions into
equivalent forms.
Testing and Covering Predicates
We use predicates in testing as follows :
– Developing a model of the software as one or more
predicates
– Requiring tests to satisfy some combination of clauses
Abbreviations:
–
–
–
–
–
P is the set of predicates
p is a single predicate in P
C is the set of clauses in P
Cp is the set of clauses in predicate p
c is a single clause in C
Introduction to Software Testing (Ch
3)
© Ammann & Offutt
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Predicate and Clause Coverage
Each predicate and each clause be evaluated to both true
and false
Predicate Coverage (PC) : For each p in P, TR contains two
requirements: p evaluates to true, and p evaluates to false.
Clause Coverage (CC) : For each c in C, TR contains two
requirements: c evaluates to true, and c evaluates to false.
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Predicate Coverage
((a > b) ∨ C) ∧ p(x)
two tests that satisfy predicate coverage are
(a = 5, b = 4, C = true, p(x) = true) and
(a = 5, b = 6, C = false, p(x) = false).
Predicate coverage for the above clause could also
be satisfied with the two tests
 (a = 5, b = 4 , C = true, p(x) = true) and
( a = 5, b = 4, C = true, p(x) = false)
the first two clauses , a = 5, b = 4 , never have the value
false!
Clause Coverage
Predicate ((a > b) ∨ C) ∧ p(x) requires different
values to satisfy Clause Coverage
Clause coverage requires that
(a > b) = true and false,
C = true and false,
p(x) = true and false.
These requirements can be satisfied with two
tests:
((a =5, b = 4), (C = true), p(x) = true) and
((a = 5, b = 6), (C = false), p(x) = false).
Active Clause
Coverage
p= ab
ends up with total four requirements in TR.
Two for clause a and two for clause b.
For clause a, a determines p if and only if b is false.
So we have two test requirements:
(a= true , b= false) , (a= false, b= false)
For clause b, b determines p if and only if a is false.
So we have two requirements
(a = false , b= true), (a= false, b= false))
This is summarized in the partial truth table (bold face)
Clause coverage does not subsume predicate coverage,
Predicate coverage does not subsume clause coverage,
Example: The predicate p = a ∨ b.
The clauses C are {a, b}.
The four test inputs that enumerate the combinations of
logical values for the clauses:
Test set T23 = {2, 3} satisfies clause coverage,
but not predicate coverage, because p is never
false.
 Test set T24 = {2, 4} satisfies predicate
coverage, but not clause coverage, because b
is never true.
FINALLY: These two test sets demonstrate that neither
predicate coverage nor clause coverage subsumes the other.
Predicate Coverage
Another Example
((a < b)  D)  (m >= n*o)
predicate coverage
Predicate = true
a = 5, b = 10, D = true, m = 1, n = 1, o = 1
= (5 < 10)  true  (1 >= 1*1)
= true  true  TRUE
= true
Predicate = false
a = 10, b = 5, D = false, m = 1, n = 1, o = 1
= (10 < 5)  false  (1 >= 1*1)
= false  false  TRUE
= false
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((a < b)  D)  (m >= n*o)
Clause coverage
(a < b) = true
(a < b) = false
D = true D = false
a = 5, b = 10
a = 10, b = 5
D = true
m >= n*o = true
D = false
m >= n*o = false
m = 1, n = 1, o = 1 m = 1, n = 2, o = 2
false cases
Two tests
true cases
1) a = 5, b = 10, D = true, m = 1, n = 1, o = 1
2) a = 10, b = 5, D = false, m = 1, n = 2, o = 2
Introduction to Software Testing (Ch 3)
© Ammann & Offutt
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Problems with Predicate and Clause
Coverage
 Predicate Coverage does not fully exercise all the
clauses, especially in the presence of short circuit
evaluation
 Clause Coverage does not always ensure Predicate
Coverage
– That is, we can satisfy Clause Coverage without
causing the predicate to be both true and false
– This is definitely not what we want !
 The simplest solution is to test all combinations
Introduction to Software Testing (Ch 3)
© Ammann & Offutt
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Combinatorial Coverage
Combinatorial Coverage requires every possible combination
• Sometimes called Multiple Condition Coverage
Combinatorial Coverage (CoC) : For each p in P, TR has test
requirements for the clauses in Cp to evaluate to each possible
combination of truth values.
a<b D
1
2
3
4
5
6
7
8
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
m >= n*o
T
F
T
F
T
F
T
F
((a < b)  D)  (m >= n*o)
T
F
T
F
T
F
F
F
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Combinatorial Coverage
A predicate p with n independent clauses has 2n possible
assignments of truth values.

The general idea is simple and
comprehensive
Combinatorial coverage is impractical for predicates
with more than a few clauses.
A powerful collection of test criteria that are based on
the notion of making individual clauses “active”
We check to see that if we vary a clause in a situation
where the clause should affect the predicate. Ifact, the
clause does affect the predicate.
Finally: Getting the details right is hard
What exactly does “independently” mean ?
This idea is simplified as making clauses active19
…
Determination
A clause ci in predicate p, called the major
clause, determines p if and only if the values
of the remaining minor clauses cj are such that
changing ci changes the value of p
This is considered to make the clause active
Determining Predicates
P=A B
if B = true, p is always true.
so if B = false, A determines p.
if A = false, B determines p.
P=A B
if B = false, p is always false.
so if B = true, A determines p.
if A = true, B determines p.
Goal : Find tests for each clause when the
clause determines the value of the predicate
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Active Clause Coverage
Active Clause Coverage (ACC) : For each p in P and each major
clause ci in Cp, choose minor clauses cj, j != i, so that ci
determines p. TR has two requirements for each ci : ci evaluates
to true and ci evaluates to false.
p=ab
1) a = true, b = false
a is major clause
2) a = false, b = false
3) a = false, b = true
4) a = false, b = false
b is major clause
Duplicate
Ambiguity : Do the minor
clauses have to have the same
values when the major clause is
true and false?
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Example : p = (a ∨ b) ∧ c
Finding values for predicate coverage is easy .
Test Requiremet PC = {p = true, p = false}
(a ∨ b)be
∧ c satisfied with the following
and theyp =can
Finding values for predicate coverage is
easythe
and was
already shown in Section
values for
clauses:
3.2. Two test requirements are
TRPC = {p = true, p = false}
Suppose that clauses a, b, and c were defined in terms of Java
program variables as follows
The complete expanded predicate is :
p = (x < y ∨ done) ∧ list.contains(str)
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Test Requirements for
Predicate Coverage.
 The values for the program variables need not be the same
in a particular test case if the goal is to set a clause to a
particular value.
 For example clause a is true in both tests,
even though program variables x and y have different
values.
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The Same Example
.
as Clause Coverage
TR = {a = true, a = false,b = true, b = false, c = true, c = false}
They can be satisfied with the following values for the
clauses (blank cells represent are « don’t-care values»):
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 The test requirements can be satisfied with the following
table for the clauses.
 These can be the same as with clause coverage
 The exception is that the blank cells from
clause coverage are replaced with the values
 Values for major clauses are indicated with upper case
letters in boldface.
The duplication; the first and fifth rows are identical, and
the second and fourth are identical.
Four tests are needed to satisfy General Active Clause Cov.
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