IA169 System Verification and Assurance
Fundaments of Testing
http://www.testingeducation.org/BBST/
Section
Course Organization
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Course Coverage
Topics to be covered ...
Introduction to Formal Verification and Testing
Symbolic Execution
Deductive Verification
LTL (Linear Temporal Logic) Model Checking
CTL (Computation Tree Logic) Model Checking
Bounded Model Checking
CEGAR and Abstract Interpretation
Verification of Real-Time and Hybrid Systems
Verification of Probabilistic Systems
Assurance, Threat Models, Relevant Security Standards
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Prerequisites and Follow-Up
Prerequisites
Formally none, but we expect ...
... capability of basic math reasoning and abstractions.
... some experience with coding.
... you can handle Unix as a user.
Mutual Exclusion with
IV113 and IV101
Possible Follow-Up
IA159 Formal Verification Methods
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Course Structure and Marking
Structure
2/2/2 credits
Lecture, Seminar, Homework
Marking
Final exam 70%
Assignments 30%
50% for E or Colloquy or Credit
60% for D
70% for C
80% for B
90% for A
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Section
Fundaments of Testing
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Testing
Testing is an empirical technical investigation conducted to
provide stakeholders with information about the quality of
the product or service under test.
Empirical Technical
Conduct experimental measurements.
Logic and math.
Modelling.
Employs SW tools.
Investigation
Organised and thorough.
Self-reflecting.
Challenging.
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Testing
Product or Service
Software.
Hardware.
Data.
Documentation and specification.
... other parts that are delivered.
Information
Not know before.
Has some value.
Stakeholders
Who has interest in the success of testing effort.
Who has interest in the success of the product.
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Fundamental Questions of Testing
Mission
Why do we test? What we want to achieve?
Strategy
How to proceed to fulfil the mission efficiently?
Oracle
How to recognise success of the test.
Incompletness
Do we realise that testing cannot prove absence of error?
Measure
How much of of our testing plan has been completed?
How far we are to complete the mission?
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Mission of Testing
Most Typical Mission
Bug hunting.
Identification of factors that reduce quality.
Other Missions
Collect data to support manager decisions, such as: Is the
product good enough to be released?
How much different is the product from product available on
market?
Is the product complete with respect to specification?
Are individual components logically and ergonomically
connected.
. . .
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Other Missions
Other Missions – continued
Support manager decision with empirical results.
Evaluate the cost of support after release.
To check compatibility with other products.
Confirm accordance with the specification.
Find safe scenarios of product usage.
To acquire certification.
Minimise consequences of low quality.
Evaluate the product for third party.
. . .
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Section
Strategy
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Strategy
Strategy is a plan, how to fulfil the mission in the given
context.
Example: Consider spreadsheet computation in four different
contexts.
a) Computer game.
b) Early stage of development of database product.
c) Late stage of development of database product.
d) Driver for medical X-ray scanning device.
Question:
Will you proceed with the same strategy?
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Example – continued
What factors influence strategy selection
What is the mission?
How aggressively we need to detect bugs.
What bugs are less important than others?
How thoroughly testing will be documented?
Discussion
Assume that a program has an enter field that is expecting
numerical values. Is is meaningful to test the product for
situation when we enter non-numeric value? (Not mentioned
in specification at all.)
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Section
Oracle
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Definition of Oracle
Oracle (in the context of testing) is a detection mechanism
or principle to learn that the product passed or failed a test.
Facts
If tester claims that the program passed a test, it does not
mean the program is correct with respect to the tested
property. It depends on the oracle used.
Basically, any test may fail or pass with a suitable oracle.
Example
Does font sizes work properly in OpenOffice, WordPad, and
MS Word text editors?
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Example – OpenOffice 1.0
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Example – WordPad
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Example – WordPad versus MS Word
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Example – WordPad versus MS Word (highlighted)
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Example – Decisions
Questions
Is the observed difference in font sizes a bug in WordPad?
Is the observed difference in font sizes a bug in MS Word?
Is the observed difference in font sizes a bug at all?
Possible Conclusions
We do not know if sizes are correct, but we have tendency to
believe MS Word rather than to WordPad.
For WordPad it is not necessary to stick precisely to
typographic standards.
For WordPad it is possibly a bug, but definitely it is not a
problem.
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Example – Risk-Based Testing
Possible (Pragmatic) Position
It is/isn’t a bug? =⇒ It is/isn’t a problem?
It is necessary to know the context, to guess the metrics that
the final consumer will use to judge the issue.
With some risk we can achieve simplification of the decision.
Simplification in Testing Process
Avoid tests that obviously does not reveal any problems.
Avoid tests that obviously reveal only uninteresting problems.
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Example – Judge Criteria
How much do we actually know about typography?
Point definition is unclear.
(http://www.oberonplace.com/dtp/fonts/point.htm)
Absolute sizes are difficult to measure.
(http://www.oberonplace.com/dtp/fonts/fontsize.htm)
From Uncertainty to Heuristics
How precisely must the sizes agree in order to declare that the
sizes are correct?
Obtaining complete information and evaluation of all the facts
is too complicated and costly.
Heuristics are used instead.
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Oracle Problem – Heuristics
Decision Heuristics
Allows for simplification of decision problem.
Advice, recommendation, or procedure to be used within the
given context.
Should not build on any hidden knowledge.
Does not guarantee a good decision.
Various heuristics may lead to contradictory decisions.
Disadvantages
Heuristics might be subjective.
If misused, may cause more harm than good.
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Consistency as Heuristics
Consistency
Good heuristics for decision making.
Consistency with ...
other functions of the product, similar products, history,
producer image, specifications, standards, user expectations,
the purpose of the product, etc.
Advantages
Consistency is objective enough.
Easily described in bug report.
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Imperfection in Decision Making
Unintentional Blindness
Human tester does not consider any test outputs that he/she
does not pay attention to.
Similarly, mechanical tester does not consider test outputs
that it is not told to include into decision.
Uncertainty Principle
The presence of observer may affect what is observed.
Consequence
It is impossible to observe all possible outputs from a single
test.
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Oracle and Automation Process
Motivation
Automation process eliminates human errors.
Automation leads to repeatable procedures.
Automation allows faster test evaluation.
Problems of Automation
It necessary to automate the decision making (oracle)
principle.
Can we do it? Only partially.
Standard Way of Oracle Automation
A file of expected outputs, which is required to match
precisely with the outputs of a test being executed.
Example: MS Word could be used to define a the file of
expected outputs for testing WordPad.
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Problems of Automated Oracle
Amount of Agreement
Assume MS Word to serve as the file of expected outputs for
testing WordPad.
How exactly is the expected output stored?
Is 99% agreement still agreement?
How is the percentage of agreement defined?
False Alarms
Using outdated expected output.
Consequence of simplification of decision making.
Undiscovered Errors
Expected file exhibits the same error as test output.
Unintentional Blindness.
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Section
Measure Methods in Testing
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Coverage as a Measure
Coverage
A set of source code entities that has been checked with at
least one test.
Source-code entities: lines of code, conditions, function calls,
branches, etc.
Used to identify parts that have not been tested yet.
Coverage as a Measure
Possible test plan is to achieve a given percentage of coverage.
The percentage than expresses how much of the final product
has been tested.
Numeric expression for managers to see how much of the
product remains to be tested.
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Coverage as a Measure – Disadvantages
Problems
Could avoid testing of interesting input data.
Does not properly test parts of the product that rely on
external services.
Using Coverage as a Measure
The mission is to test all entities of the product, is that OK?
Complete coverage does not guarantee quality of the product.
Stimulates to prefer quantity rather than quality.
Misleading satisfaction (shouldn’t feel safe).
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Coverage as a Measure – Disadvantages
Example
Input A // program accepts any
Input B // integer into A and B
Print A/B
Observation
Complete coverage is easy achievable.
For example:
input: 2,1
output: 2
There is of course a hidden bug in the program!
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Coverage Criteria for Control-Flow Graphs
y:=y+1
x=y and z>w
x:=x−1
true false
There are various criteria for control-flow graph coverage.
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Coverage Criteria for Control-Flow Graphs
y:=y+1
x=y and z>w
x:=x−1
true false
Statement coverage
Every statement (assignment, input, output, condition) is
executed in at least one test.
Set of tests to achieve full coverage:
(x = 2, y = 1, z = 4, w = 3)
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Coverage Criteria for Control-Flow Graphs
y:=y+1
x=y and z>w
x:=x−1
true false
Edge coverage
Every edge of CFG is executed in at least one test.
Set of tests to achieve full coverage:
(x = 2, y = 1, z = 4, w = 3), (x = 3, y = 3, z = 5, w = 7)
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Coverage Criteria for Control-Flow Graphs
y:=y+1
x=y and z>w
x:=x−1
true false
Condition coverage
Every condition is a Boolean combination of elementary
conditions, for example x < y or even(x).
If it is possible, every elementary condition is evaluated in at
least one test to TRUE and in at least one test to FALSE.
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Coverage Criteria for Control-Flow Graphs
y:=y+1
x=y and z>w
x:=x−1
true false
Condition coverage
Set of tests to achieve full coverage:
(x = 3, y = 2, z = 5, w = 7), (x = 3, y = 3, z = 7, w = 5)
In both cases, only the FALSE branch of IF statement is taken.
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Coverage Criteria for Control-Flow Graphs
y:=y+1
x=y and z>w
x:=x−1
true false
Edge/Condition coverage
Edge and Condition coverage at the same time.
Set of tests to achieve full coverage:
(x = 2, y = 1, z = 4, w = 3), (x = 3, y = 2, z = 5, w = 7),
(x = 3, y = 3, z = 7, w = 5)
Is the set the smallest possible one?
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Coverage Criteria for Control-Flow Graphs
y:=y+1
x=y and z>w
x:=x−1
true false
Multiple condition coverage
Every Boolean combination of TRUE/FALSE values that may
appear in some decision condition must occur in at least one
test.
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Coverage Criteria for Control-Flow Graphs
y:=y+1
x=y and z>w
x:=x−1
true false
Multiple condition coverage
Set of tests to achieve full coverage:
(x = 2, y = 1, z = 4, w = 3), (x = 3, y = 2, z = 5, w = 7),
(x = 3, y = 3, z = 7, w = 5), (x = 3, y = 3, z = 5, w = 6)
Exponential grow in the number of tests.
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Coverage Criteria for Control-Flow Graphs
y:=y+1
x=y and z>w
x:=x−1
true false
Path coverage
Every executable path is executed in at least one test.
The number of paths is big, even infinite in case there is an
unbounded cycle in the control-flow graph.
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Hierarchy of Coverage Criteria
Criterion A includes criterion B, denoted with A → B, if after
full coverage of type A we guarantee full coverage of type B.
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Hierarchy of Coverage Criteria
Criterion A includes criterion B, denoted with A → B, if after
full coverage of type A we guarantee full coverage of type B.
path
coverage

multiple condition
coverage

edge/condition
coverage
uu

edge
coverage

condition
coverage
statement
coverage
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Cycle Coverage
Coverage and Number of Cycle Iterations
All criteria except the path criterion does not reflect the
number of iterations over a cycle body.
In case of nested cycles, systematic testing of all possible
executable paths become complicated.
Ad hoc Strategy for Testing Cycles
Check the case when the cycle is completely skipped.
Check the case when the cycle is executed exactly once.
Check the case when the cycle is executed the expected
number of times.
If a boundary n is known for the number of cycle executions,
try to design tests where the cycle is executed n − 1, n, and
n + 1 times.
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Coverage for Data-Flow Graphs
Motivation
Detect usage of undefined variables.
On some paths, a variable may be set for a specific purpose
and later on its value misused for other purpose.
Control Flow criteria do not guarantee inclusion of tests for
above mentioned or likewise situations.
Data Flow Coverage
Cover paths through control flow graph that go through a
location where a variable is used but it is not defined along all
incoming paths through control-flow graph.
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Support for Code Coverage
C/C++, Linux
Tools gcov and lcov.
Example: lcov
gcc -fprofile-arcs -ftest-coverage foo.c -o foo
lcov -d . -z
lcov -c -i -d . -o base.info
./foo
lcov -c -d . -o collect.info
lcov -d . -a base.info -a collect.info -o result.info
genhtml result.info
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Statistics on Found/Fixed Bugs per Time Unit
Week statistics
The number of newly discovered errors.
The number of fixed errors.
The ratio of found versus fixed errors.
Visualisation
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Weibull Distribution
Observation
The number of discovered errors per time unit exhibits
Weibull Distribution.
Can be used as a measure for the remaining amount of testing.
Software Engineering Method to set the release date.
Using Weibull Distribution
At the moment the curve reaches the peak, the remaining
part of the curve may be predicted, hence, a moment in time
may be set, when expected number of errors discovered per
week drops below a given threshold.
Parameters of Weibull distribution influence the “width” and
“height/slope” of the peak.
F(x) = 1 − e−ax−b
for x > 0
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Weibull Distribution – Imperfections
Vague Precision
Testing does not follow the typical usage of the product.
The probability of error discovery is different for different
errors.
Fix may cause other new errors.
Bugs are dependent.
The number of errors in the product changes over time.
Error insertion exhibits Weibull distribution itself.
Testing epochs (various testing procedures) are independent.
...
Conclusions
Weibull Distribution is not very reliable.
Can be used only with large projects for very rough estimation.
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Impact of following Weibull Distribution
Assumption
Software developers are aware of being measured.
Phase one
Reach the peak as quickly as possible.
Double reporting of errors.
Avoid fixing known errors.
...
Phase two
Stick to expected shape of the curve.
Delay reporting of errors.
Reporting outside bug-tracking system.
...
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Section
Incompleteness of Testing
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Definition
Observation
The amount of tests to be run is extremely large.
Resources for testing are always limited.
What Is Not Complete Testing
Complete Coverage
Every line of code.
Every branching point.
...
When testers do not find more errors.
Testing plan is finished.
What Is Complete Testing
There are no hidden or unknown errors in the product.
If new issue is reported, testing could not be complete.
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Reasons for Incompletness of Testing
The number of tests is too large (infinitely many).
To perform all tests means:
To test all possible input values of every input variable.
To test all combinations of input variables.
To test every possible run of a system.
To test every combination of HW and SW, including future
technology.
To test every way a user may use the product.
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Impossibility to Test All Possible Inputs
Data Bus-Width
The number of tests grows exponentially with respect to bit
used for data representation.
n-bits requires 2n tests.
Other Reasons
Timing of actions.
Invalid or unexpected inputs (buffer overflow).
Edited inputs
Easter egg [http://j-walk.com/ss/excel/eastereg.htm]
Common Argumentation
“This is not what the customer would do with our product.”
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Incapability to Test All Runs
Assume the following system
Questions
How many different ways it is possible to reach EXIT ?
How many different ways it is possible to reach EXIT , if A
can be visited at most n-times?
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Incapability to Test All Runs
Example
In [F] is a memory leak, in [B] garbage collector.
System will reach an invalid state, if [B] is avoided long
enough.
Observation
Simplified testing of paths may not discover the error.
The error manifests in circumstances that cannot be achieved
with a simple test.
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Summary for Measure and Incompleteness
Incompleteness
Testing cannot prove absence of error.
It is impossible to test all valid inputs.
Existence of testing plan inhibits testing creativity.
Measure
There are methods to measure progress in testing phase.
but they are unreliable.
Focusing strongly on a selected measure may influence the
effectiveness of testing.
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Section
Practicals and Homework
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Practicals and Homework
Practicals
Analyse a simple triangle.cpp program and develop a test suit
fulfilling given criterion of coverage.
Automate regression testing (make test), include
Hand-written functional tests
Coverage of code (LCOV/GCOV)
Homework
Reading on MC/DC:
http://www.faa.gov/aircraft/air_cert/design_approvals/air_
software/cast/cast_papers/media/cast-10.pdf
List, and briefly describe as many black-box testing approaches as
you can find or are aware of.
http://www.testingeducation.org/BBST/
Optional: Look at CMAKE and CTEST systems.
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