Software Testing - Matthew J. Rutherford

1/12/09 

Class 01 - 2009-01-12

COMP 3705

Advanced Software

Engineering:

Software Testing

Prof. Matt Rutherford

(c) 2009 Matthew J. Rutherford

Hello!

   New professor in the CS department

   Study topics at the intersection of software engineering and distributed systems

   Have 12+ years experience as a software engineer, technical lead, etc… mostly at small companies and startups

   I’m an engineer not a mathematician

Class 01 - 2009-01-12 (c) 2009 Matthew J. Rutherford

1 

How about you?

   Brief intro:

   Name and Job description

   Testing experience?

   Goals for this course?

   Favorite book?

   (Mine is anything by Neal Stephenson: Cryptonomicon, The Big

U, …)


Today

   Brief Introduction

   Administrative / Logistics

   Chapter 1: Introduction to Software Testing

   Section 2.1: Graph Coverage Criteria


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Software Testing Defined

“Software testing consists of the dynamic verification of the behavior of a program on a finite set of test cases, suitably selected from the usually infinite executions domain, against the expected behavior.” - SWEBOK

   Start with the Software Under Test (SUT)

   Execute the software using specific “inputs”

   Look at the “outputs” to determine if the software did the “right thing”


Some Code (Euclid’s Algorithm)

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Some Buggy Code

Class 01 - 2009-01-12 x

3

6

5

3

3 y

6

Result

3

3

3

Precise Imprecise

==3 ✔ >0 ✔

==3 ✔

==1 ✗

>0

>0

✔

✔

(c) 2009 Matthew J. Rutherford

Challenges of Testing

   Input spaces are vast, exhaustive testing is impossible

   Testing proves nothing!

   Move from math to engineering:

   How to reduce the probability of releasing faulty software within constraints imposed by budget?


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Test Case Selection

   Which input values should be used?

   How many?

   When is a set of test cases “adequate”


Test Adequacy Criteria

   A stopping condition on the test-case creation activity

   Help measure progress

   E.g.,:

   white-box: 100% branch coverage

   black-box: all combinations of input space partitions


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This Course

   Is primarily about test adequacy criteria

   Instantiating a test adequacy criterion on an applicable software artifact gives a finite set of “test requirements”

   The requirements create a TODO list for testing


Some Things to Keep in Mind

   The relationship between criteria and bug-finding effectiveness is not really clear

   It is likely that the effectiveness of criteria varies by system

   Selecting the “right” criteria to use for your system is not possible

   Take Home Message:

   Use your brain when testing: add test cases that you think will be valuable, even if they don’t improve the coverage numbers!


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My Relationship to Testing

   I love to study testing techniques:

   Very hands-on and empirical

   Interested in techniques to help reduce the risk of using adequacy criteria

   Clear engineering tradeoff:

   Resources versus quality

   I love to use testing techniques:

   Unit testing my own code

   System-level testing

   Testing other people’s code


OTOH…

   I have, unfortunately, delivered a lot of code without testing it

   Schedule pressure

   Budget constraints

   …

   Have to be realistic:

   There is always a bigger picture than the purely technical in a project

   Systems need to be delivered to be used


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Administrative

   10 classes, including today, 5pm – 7:50pm

   Mix of lecture, discussion and working problems

   Help me out with breaks, etc.

   Office hours

   Before class (starting at 4pm?)

   After class (8pm -?)

   Any other time over the phone (appointments work best)

   Sound reasonable?


Class Website

   http://mjrutherford.org/teaching/2009/winter/COMP3705

   Slides will be available for download

   Homework / reading assignments for each class

   Can you guys access this easily from here?


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Slides

   I’ll bring hard copies to class each week

   They will also be available for download

   (Probably at about 3:30pm on Mondays)

(c) 2009 Matthew J. Rutherford Class 01 - 2009-01-12

Textbook

   Introduction to Software Testing by Paul Ammann and

Jeff Offutt

   Great new book! http://cs.gmu.edu/~offutt/softwaretest/


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Grading

   Homework: 50%

   The lowest 1 grade out of 8 will be dropped

   Will morph into project milestones near the end of the quarter

   Midterm Exam: 25%

   February 16 th – Parts I and II of the textbook

   Final Exam: 25%

   March 16 th - Cumulative


Policies

   Please do the readings before class

   Homework is due at the start of class each week, will not be accepted late unless you make prior arrangements

   Please DO discuss the subject matter and homework problems outside of class. Please DO NOT copy.


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Quick Break?


Introduction to Software Testing

Chapter 1

Introduction

Paul Ammann & Jeff Offutt

www.introsoftwaretesting.com

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Cost of Testing

  

In the real-world, testing is the principle post-design activity

  

Restricting early testing usually increases cost

  

Extensive hardware-software integration requires more testing

Introduction to Software Testing (Ch 1), www.introsoftwaretesting.com © Ammann & Offutt 23

Part 1 : Why Test?

  

Written test objectives and requirements are rare

  

What are your planned coverage levels?

  

How much testing is enough?

  

Common objective – spend the budget …


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Cost of Not Testing

  

Not testing is even more expensive

  

Planning for testing after development is prohibitively expensive

  

A test station for circuit boards costs half a million dollars …

  

Software test tools cost less than $10,000 !!!


Caveat: Impact of New Tools and

Techniques

They’re teaching a new way of plowing over at the Grange tonight - you going?

Naw - I already don’t plow as good as I know how...

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Part 2 : What ?

1.

Types of test activities

2.

Software testing terms

3.

Changing notions of testing

–   test coverage criteria

–   criteria based on structures

Introduction to Software Testing (Ch 1), www.introsoftwaretesting.com © Ammann & Offutt

  

  

Types of Test Activities

Testing can be broken up into four general types of activities

1.

Test Design

2.

Test Automation

3.

Test Execution

4.

Test Evaluation

Each type of activity requires different skills, background knowledge, education and training

  

No reasonable software development organization uses the same people for requirements, design, implementation, integration and configuration control

27

28 Introduction to Software Testing (Ch 1), www.introsoftwaretesting.com © Ammann & Offutt

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Test Design

  

This is the most technical job in software testing

  

Requires knowledge of :

–   Discrete math

–   Programming

–   Testing

  

Requires much of a traditional CS degree

  

This is intellectually stimulating, rewarding, and challenging

  

Test design is analogous to software architecture on the development side

  

Using people who are not qualified to design tests is a sure way to get ineffective tests


Test Automation

  

This is slightly less technical

  

Requires knowledge of programming

–   Fairly straightforward programming – small pieces and simple algorithms

  

Requires very little theory

  

Very boring for test designers

  

Programming is out of reach for many domain experts

  

Who is responsible for determining and embedding the expected outputs ?

–   Test designers may not always know the expected outputs

–   Test evaluators need to get involved early to help with this


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Test Execution

  

This is easy – and trivial if the tests are well automated

  

Requires basic computer skills

–   Interns

–   Employees with no technical background

  

Asking qualified test designers to execute tests is a sure way to convince them to look for a development job

  

If, for example, GUI tests are not well automated, this requires a lot of manual labor

  

Test executors have to be very careful and meticulous with bookkeeping


Test Evaluation

  

This is much harder than it may seem

  

Requires knowledge of :

–   Domain

–   Testing

  

Usually requires almost no traditional CS

–   A background in the domain of the software is essential

–   An empirical background is very helpful (biology, psychology, …)

–   A logic background is very helpful (law, philosophy, math, …)

  

This is intellectually stimulating, rewarding, and challenging

–   But not to typical CS majors – they want to solve problems and build things

  

Domain experts must be free to add new tests


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Types of Test Activities – Summary

1. Test design Design test values to satisfy coverage criteria or other engineering goal

Requires technical knowledge of discrete math, programming and testing

2. Test automation Embed test values into executable scripts

Requires knowledge of scripting

3. Test execution Run tests on the software and record the results

Requires very little knowledge

4. Test evaluation Evaluate results of testing, report to developers

Requires domain knowledge

  

These four general test activities are quite different

  

It is a poor use of resources to use people inappropriately


Types of Activities in the Book

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Software Testing Terms

  

Like any field, software testing comes with a large number of specialized terms that have particular meanings in this context

  

Some of the following terms are standardized, some are used consistently throughout the literature and the industry, but some vary by author, topic, or test organization

  

The definitions here are intended to be the most commonly used


Important Terms

Validation & Verification (

IEEE

)

  

Validation : The process of evaluating software at the end of software development to ensure compliance with intended usage

  

Verification : The process of determining whether the products of a given phase of the software development process fulfill the requirements established during the previous phase

IV&V stands for “ independent verification and validation ”


35

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Test Engineer & Test Managers

  

Test Engineer : An IT professional who is in charge of one or more technical test activities

–   designing test inputs

–   producing test values

–   running test scripts

–   analyzing results

–   reporting results to developers and managers

  

Test Manager : In charge of one or more test engineers

–   sets test policies and processes

–   interacts with other managers on the project

–   otherwise helps the engineers do their work


Test Engineer Activities

Test

Manager design

Test

Designs

Test

Engineer instantiate

Executable

Tests

Test

Engineer

P Computer execute

Output Evaluate


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Static and Dynamic Testing

  

Static Testing : Testing without executing the program

–   This include software inspections and some forms of analyses

–   Very effective at finding certain kinds of problems – especially “potential” faults, that is, problems that could lead to faults when the program is modified

  

Dynamic Testing : Testing by executing the program with real inputs


Software Faults, Errors & Failures

  

Software Fault : A static defect in the software

  

Software Error : An incorrect internal state that is the manifestation of some fault

  

Software Failure : External, incorrect behavior with respect to the requirements or other description of the expected behavior

39


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Testing & Debugging

  

Testing : Finding inputs that cause the software to fail

  

Debugging : The process of finding a fault given a failure


Fault & Failure Model

41

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21 

Test Case

  

Test Case Values : The values that directly satisfy one test requirement

  

Expected Results : The result that will be produced when executing the test if the program satisfies it intended behavior


Observability and Controllability

  

Software Observability : How easy it is to observe the behavior of a program in terms of its outputs, effects on the environment and other hardware and software components

–   Software that affects hardware devices, databases, or remote files have low observability

  

Software Controllability : How easy it is to provide a program with the needed inputs, in terms of values, operations, and behaviors

–   Easy to control software with inputs from keyboards

–   Inputs from hardware sensors or distributed software is harder

–   Data abstraction reduces controllability and observability


43

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  

Inputs to Affect Controllability and

Observability

Prefix Values : Any inputs necessary to put the software into the appropriate state to receive the test case values

  

Postfix Values : Any inputs that need to be sent to the software after the test case values

  

Two types of postfix values

1.

Verification Values : Values necessary to see the results of the test case values

2.

Exit Commands : Values needed to terminate the program or otherwise return it to a stable state

  

Executable Test Script : A test case that is prepared in a form to be executed automatically on the test software and produce a report


Top-Down and Bottom-Up Testing

  

Top-Down Testing : Test the main procedure, then go down through procedures it calls, and so on

  

Bottom-Up Testing : Test the leaves in the tree (procedures that make no calls), and move up to the root.

–   Each procedure is not tested until all of its children have been tested

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White-box and Black-box Testing

  

Black-box testing : Deriving tests from external descriptions of the software, including specifications, requirements, and design

  

White-box testing : Deriving tests from the source code internals of the software, specifically including branches, individual conditions, and statements


Changing Notions of Testing

  

Old view of testing is of testing at specific software development phases

–   Unit, module, integration, system …

  

New view is in terms of structures and criteria

–   Graphs, logical expressions, syntax, input space


47

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Old : Testing at Different Levels

Class A method mA1() method mA2() main Class P

Introduction to Software Testing (Ch 1), www.introsoftwaretesting.com

Class B method mB1()

  

Acceptance testing: Is the software acceptable to the user?

  

System testing: Test the overall functionality of the system

  

Integration testing: Test how modules interact with each other method mB2()

© Ammann & Offutt

  

  

Module testing: Test each class, file, module or component

Unit testing: Test each unit (method) individually

49

Old : Find a Graph and Cover It

  

Tailored to:

–   a particular software artifact

•   code, design, specifications

–   a particular phase of the lifecycle

•   requirements, specification, design, implementation

  

This viewpoint obscures underlying similarities

  

Graphs do not characterize all testing techniques well

  

Four abstract models suffice …


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New : Test Coverage Criteria

A tester’s job is simple : Define a model of the software, then find ways to cover it g  

Test Requirements : Specific things that must be satisfied or covered during testing g  

Test Criterion : A collection of rules and a process that define test requirements


New : Criteria Based on Structures

Structures : Four ways to model software

1.

Graphs

2.

Logical Expressions

3.

Input Domain

Characterization

4.

Syntactic Structures


(not X or not Y) and A and B

A: {0, 1, >1}

B: {600, 700, 800}

C: {swe, cs, isa, infs} if (x > y)

z = x - y; else

z = 2 * x;

© Ammann & Offutt 52

51

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1. Graph Coverage – Structural

2

1

3

This graph may represent

•   statements & branches

•   methods & calls

•   components & signals

•   states and transitions


6

5 7

4

Path

Cover every path

•   • •   12567

•   • •   1257

•   • 1357

•   1357

© Ammann & Offutt

•   1343567

•   134357 …

53

1. Graph Coverage – Data Flow

def = {a , m}

2 def = {x, y}

1 use = {x} use = {x} def = {a}

3 def = {m} use = {y}

6

5 use = {a} use = {a} use = {m}

7

This graph contains:

•   defs: nodes & edges where variables get values

•   uses: nodes & edges where values are accessed

4 def = {m} use = {y}

•  

All Uses

Every def “reaches” every use

•   •

•   1, 2, 5, 6, 7

•

3, (5,6)), (a, 3, (5,7)),

•

  •

•

 

 

•

•

 

 

1, 2, 5, 7

1, 3, 5, 6, 7

•   1, 3, 5, 7

•   1, 3, 4, 3, 5,7


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1. Graph - FSM Example

Memory Seats in a Lexus ES 300

Guard (safety constraint) Trigger (input)

[Ignition = off] | Button2

(

Driver 1

Configuration to Modified )

Ignition = off

Driver 2

Configuration

[Ignition = off] | Button1

New

Configuration

Driver 2

Ignition = off

[Ignition = on] | seatBack ()

[Ignition = on] | seatBottom ()

[Ignition = on] | lumbar ()

[Ignition = on] | sideMirrors ()

[Ignition = on] | Reset AND Button2

New

Configuration

Driver 1

Modified

Configuration

[Ignition = on] | Reset AND Button1


2. Logical Expressions

( (a > b) or G ) and (x < y)

Transitions

Program Decision Statements

Software Specifications

Logical

Expressions


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2. Logical Expressions

( (a > b) or G ) and (x < y)

  

Predicate Coverage : Each predicate must be true and false

–   ( (a>b) or G ) and (x < y) = True, False

  

Clause Coverage : Each clause must be true and false

–   (a > b) = True, False

–   G = True, False

–   (x < y) = True, False

  

Combinatorial Coverage : Various combinations of clauses

–   Active Clause Coverage : Each clause must determine the predicate’s result


3. Input Domain Characterization

  

Describe the input domain of the software

–   Identify inputs, parameters, or other categorization

–   Partition each input into finite sets of representative values

–   Choose combinations of values

  

System level

–   Number of students { 0, 1, >1 }

–   Level of course { 600, 700, 800 }

–   Major { swe, cs, isa, infs }

  

Unit level

–   Parameters F (int X, int Y)

–   Possible values X : { <0, 0, 1, 2, >2 }, Y : { 10, 20, 30 }

–   Tests

•   F (-5, 10), F (0, 20), F (1, 30), F (2, 10), F (5, 20)


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4. Syntactic Structures

  

  

  

Based on a grammar, or other syntactic definition

Primary example is mutation testing

1.

Induce small changes to the program: mutants

2.

Find tests that cause the mutant programs to fail: killing mutants

3.

Failure is defined as different output from the original program

4.

Check the output of useful tests on the original program

Example program and mutants if (x > y)

z = x - y; else

z = 2 * x; if (x > y)

Δ if (x >= y)

z = x - y;

Δ z = x + y;

Δ z = x – m; else

z = 2 * x;


Source of Structures

  

These structures can be extracted from lots of software artifacts

–   Graphs can be extracted from UML use cases, finite state machines, source code, …

–   Logical expressions can be extracted from decisions in program source, guards on transitions, conditionals in use cases, …

  

Model-based testing derives tests from a model that describes some aspects of the system under test

–   The model usually describes part of the behavior

–   The source is usually not considered a model


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Coverage Overview

Applied to

Applied to

Applied to


Coverage

61

  

Infeasible test requirements : test requirements that cannot be satisfied

–   No test case values exist that meet the test requirements

–   Dead code

–   Detection of infeasible test requirements is formally undecidable for most test criteria

  

Thus, 100% coverage is impossible in practice


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Two Ways to Use Test Criteria

1.

Directly generate test values to satisfy the criterion often assumed by the research community most obvious way to use criteria very hard without automated tools

2.

Generate test values externally and measure against the criterion usually favored by industry

–   sometimes misleading

–   if tests do not reach 100% coverage, what does that mean?

Test criteria are sometimes called metrics


Generators and Recognizers

  

Generator : A procedure that automatically generates values to satisfy a criterion

  

Recognizer : A procedure that decides whether a given set of test values satisfies a criterion

  

Both problems are provably undecidable for most criteria

  

It is possible to recognize whether test cases satisfy a criterion far more often than it is possible to generate tests that satisfy the criterion

  

Coverage analysis tools are quite plentiful


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Comparing Criteria with Subsumption

  

Criteria Subsumption : A test criterion C1 subsumes C2 if and only if every set of test cases that satisfies criterion C1 also satisfies C2

  

Must be true for every set of test cases

  

Example : If a test set has covered every branch in a program

(satisfied the branch criterion), then the test set is guaranteed to also have covered every statement


Test Coverage Criteria

  

Traditional software testing is expensive and labor-intensive

  

Formal coverage criteria are used to decide which test inputs to use

  

More likely that the tester will find problems

  

Greater assurance that the software is of high quality and reliability

  

A goal or stopping rule for testing

  

Criteria makes testing more efficient and effective

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1/12/09 

Part 3 : How ?


Testing Levels Based on Test Process

Maturity

   Level 0 : There’s no difference between testing and debugging

   Level 1 : The purpose of testing is to show correctness

   Level 2 : The purpose of testing is to show that the software doesn’t work

   Level 3 : The purpose of testing is not to prove anything specific, but to reduce the risk of using the software

   Level 4 : Testing is a mental discipline that helps all IT professionals develop higher quality software


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34 

Level 0 Thinking

  

Testing is the same as debugging

  

Does not distinguish between incorrect behavior and mistakes in the program

  

Does not help develop software that is reliable or safe



  

Purpose is to show correctness

  

Correctness is impossible to achieve

  

What do we know if no failures?

–   Good software or bad tests?

  

Test engineers have no:

–   Strict goal

–   Real stopping rule

–   Formal test technique

–   Test managers are powerless


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70

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  

Purpose is to show failures

  

Looking for failures is a negative activity

  

Puts testers and developers into an adversarial relationship

  

What if there are no failures?



  

Testing can only show the presence of failures

  

Whenever we use software, we incur some risk

  

Risk may be small and consequences unimportant

  

Risk may be great and the consequences catastrophic

  

Testers and developers work together to reduce risk

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A mental discipline that increases quality

  

Testing is only one way to increase quality

  

Test engineers can become technical leaders of the project

  

Primary responsibility to measure and improve software quality

  

Their expertise should help the developers


Summary

  

More testing saves money

–   Planning for testing saves lots of money

  

Testing is no longer an “art form”

–   Engineers have a tool box of test criteria

  

When testers become engineers, the product gets better

–   The developers get better

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Open Questions

  

Which criteria work best on embedded, highly reliable software?

–   Which software structure to use?

  

How can we best automate this testing with robust tools?

–   Deriving the software structure

–   Constructing the test requirements

–   Creating values from test requirements

–   Creating full test scripts

–   Solution to the “mapping problem”

  

Empirical validation

  

Technology transition

  

Application to new domains


Break + Problem

   Section 1.2, Problem #3 (a), (b), (c)

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Introduction to Software Testing

Chapter 2.1, 2.2

Overview Graph Coverage Criteria

Paul Ammann & Jeff Offutt

www.introsoftwaretesting.com

Ch. 2 : Graph Coverage

Applied to

Applied to

Applied to


39 

Covering Graphs

(2.1)

•  

Graphs are the most commonly used structure for testing

•  

Graphs can come from many sources

–   Control flow graphs

–   Design structure

–   FSMs and statecharts

–   Use cases

•  

Tests usually are intended to “cover” the graph in some way


Definition of a Graph

•  

A set N of nodes, N is not empty

•  

A set N

0

of initial nodes, N

0

is not empty

•  

A set N f

of final nodes, N f

is not empty

•  

A set E of edges, each edge from one node to another

–   ( n i

, n j

), i is predecessor, j is successor

79


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0

Three Example Graphs

0 1 2 0

1 2 3 4 5

3 7 8 9

N

N

0 f

= { 0 }

= { 3 }


N

0

= { 0, 1, 2 }

N f

= { 7, 8, 9 }

© Ammann & Offutt

6 1 2

3

N

0

= { }

N f

= { 3 }

81

Paths in Graphs

•  

•  

•  

•  

Path : A sequence of nodes – [n

1

, n

2

, …, n

M

]

–   Each pair of nodes is an edge

Length : The number of edges

–   A single node is a path of length 0

Subpath : A subsequence of nodes in p is a subpath of p

Reach ( n ) : Subgraph that can be reached from n

0 1 2

3 4 5 6

Paths

[ 0, 3, 7 ]

[ 1, 4, 8, 5, 1 ]

[ 2, 6, 9 ]

Reach (0) = { 0, 3, 4, 7,

8, 5, 1, 9 }

Reach ({0, 2}) = G

Reach([2,6]) = {2, 6, 9}

7 8


9


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Test Paths and SESEs

•  

•  

Test Path : A path that starts at an initial node and ends at a final node

Test paths represent execution of test cases

–   Some test paths can be executed by many tests

–   Some test paths cannot be executed by any tests

•  

SESE graphs : All test paths start at a single node and end at another node

–   Single-entry, single-exit

–   N0 and Nf have exactly one node

0

1

2

3

4

5

6

Double-diamond graph

Four test paths

[ 0, 1, 3, 4, 6 ]

[ 0, 1, 3, 5, 6 ]

[ 0, 2, 3, 4, 6 ]

[ 0, 2, 3, 5, 6 ]

© Ammann & Offutt Introduction to Software Testing (Ch 2), www.introsoftwaretesting.com 83

Visiting and Touring

•  

Visit : A test path p visits node n if n is in p

A test path p visits edge e if e is in p

•  

Tour : A test path p tours subpath q if q is a subpath of p

Path [ 0, 1, 3, 4, 6 ]

Visits nodes 0, 1, 3, 4, 6

Visits edges (0, 1), (1, 3), (3, 4), (4, 6)

Tours subpaths (0, 1, 3), (1, 3, 4), (3, 4, 6), (0, 1, 3, 4), (1, 3, 4, 6)


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Tests and Test Paths

•   path ( t ) : The test path executed by test t

•   path ( T ) : The set of test paths executed by the set of tests T

•  

•  

Each test executes one and only one test path

A location in a graph (node or edge) can be reached from another location if there is a sequence of edges from the first location to the second

–   Syntactic reach : A subpath exists in the graph

–   Semantic reach : A test exists that can execute that subpath


Tests and Test Paths

test 1 many-to-one test 2

Test

Path test 3

Deterministic software – a test always executes the same test path many-to-many test 1 Test Path 1 test 2 Test Path 2 test 3 Test Path 3

Non-deterministic software – a test can execute different test paths


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•  

Testing and Covering Graphs

(2.2)

We use graphs in testing as follows :

–   Developing a model of the software as a graph

–   Requiring tests to visit or tour specific sets of nodes, edges or subpaths

•  

•  

•  

Test Requirements (TR) : Describe properties of test paths

Test Criterion : Rules that define test requirements

Satisfaction : Given a set TR of test requirements for a criterion C, a set of tests T satisfies C on a graph if and only if for every test requirement in TR, there is a test path in path(T) that meets the test requirement tr

•  

•  

Structural Coverage Criteria : Defined on a graph just in terms of nodes and edges

Data Flow Coverage Criteria : Requires a graph to be annotated with references to variables

© Ammann & Offutt 87 Introduction to Software Testing (Ch 2), www.introsoftwaretesting.com

Node and Edge Coverage

•  

The first (and simplest) two criteria require that each node and edge in a graph be executed

•  

This statement is a bit cumbersome, so we abbreviate it in terms of the set of test requirements


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Node and Edge Coverage

•  

Edge coverage is slightly stronger than node coverage

•  

The “length up to 1” allows for graphs with one node and no edges

•  

NC and EC are only different when there is an edge and another subpath between a pair of nodes (as in an “ if-else ” statement)

0

Node Coverage : TR = { 0, 1, 2 }

Test Path = [ 0, 1, 2 ]

1

2


Edge Coverage : TR = { (0,1), (0, 2), (1, 2) }

Test Paths = [ 0, 1, 2 ]

[ 0, 2 ]


Paths of Length 1 and 0

•  

A graph with only one node will not have any edges

0

•  

It may be boring, but formally, Edge Coverage needs to require

Node Coverage on this graph

•  

Otherwise, Edge Coverage will not subsume Node Coverage

–   So we define “length up to 1” instead of simply “length 1”

•  

We have the same issue with graphs that only have one edge – for Edge Pair Coverage …

0

1


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Covering Multiple Edges

•  

Edge-pair coverage requires pairs of edges, or subpaths of length 2

•  

The “length up to 2” is used to include graphs that have less than 2 edges

•  

The logical extension is to require all paths …

•  

Unfortunately, this is impossible if the graph has a loop, so a weak compromise is to make the tester decide which paths:


1

3

2

6

0

Structural Coverage Example

Node Coverage

TR = { 0, 1, 2, 3, 4, 5, 6 }

Test Paths: [ 0, 1, 2, 3, 6 ] [ 0, 1, 2, 4, 5, 4, 6 ]

4

Edge Coverage

TR = { (0,1), (0,2), (1,2), (2,3), (2,4), (3,6), (4,5), (4,6), (5,4) }

Test Paths: [ 0, 1, 2, 3, 6 ] [ 0, 2, 4, 5, 4, 6 ]

Edge-Pair Coverage

TR = { [0,1,2], [0,2,3], [0,2,4], [1,2,3], [1,2,4], [2,3,6],

[2,4,5], [2,4,6], [4,5,4], [5,4,5], [5,4,6] }

Test Paths: [ 0, 1, 2, 3, 6 ] [ 0, 1, 2, 4, 6 ] [ 0, 2, 3, 6 ]

[ 0, 2, 4, 5, 4, 5, 4, 6 ]

5

Complete Path Coverage

Test Paths: [ 0, 1, 2, 3, 6 ] [ 0, 1, 2, 4, 6 ] [ 0, 1, 2, 4, 5, 4, 6 ] [ 0, 1, 2,

4, 5, 4, 5, 4, 6 ] [ 0, 1, 2, 4, 5, 4, 5, 4, 5, 4, 6 ] …


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Loops in Graphs

•  

If a graph contains a loop, it has an infinite number of paths

•  

Thus, CPC is not feasible

•  

SPC is not satisfactory because the results are subjective and vary with the tester

•  

Attempts to “deal with” loops:

–   1970s : Execute cycles once ([4, 5, 4] in previous example, informal)

–   1980s : Execute each loop, exactly once (formalized)

–   1990s : Execute loops 0 times, once, more than once (informal description)

–   2000s : Prime paths


Simple Paths and Prime Paths

•  

•  

Simple Path : A path from node ni to nj is simple if no node appears more than once, except possibly the first and last nodes are the same

–   No internal loops

–   Includes all other subpaths

–   A loop is a simple path

Prime Path : A simple path that does not appear as a proper subpath of any other simple path

1

0

2

Simple Paths : [ 0, 1, 3, 0 ], [ 0, 2, 3, 0], [ 1, 3, 0, 1 ],

[ 2, 3, 0, 2 ], [ 3, 0, 1, 3 ], [ 3, 0, 2, 3 ], [ 1, 3, 0, 2 ],

[ 2, 3, 0, 1 ], [ 0, 1, 3 ], [ 0, 2, 3 ], [ 1, 3, 0 ], [ 2, 3, 0 ],

[ 3, 0, 1 ], [3, 0, 2 ], [ 0, 1], [ 0, 2 ], [ 1, 3 ], [ 2, 3 ], [ 3, 0 ], [0],

[1], [2], [3]

3

Prime Paths : [ 0, 1, 3, 0 ], [ 0, 2, 3, 0], [ 1, 3, 0, 1 ],

[ 2, 3, 0, 2 ], [ 3, 0, 1, 3 ], [ 3, 0, 2, 3 ], [ 1, 3, 0, 2 ],

[ 2, 3, 0, 1 ]


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Prime Path Coverage

•  

A simple, elegant and finite criterion that requires loops to be executed as well as skipped

•  

•  

Will tour all paths of length 0, 1, …

That is, it subsumes node, edge, and edge-pair coverage


Round Trips

•  

Round-Trip Path : A prime path that starts and ends at the same node

95

1/12/09 

•  

•  

These criteria omit nodes and edges that are not in round trips

That is, they do not subsume edge-pair, edge, or node coverage


48 

Prime Path Example

•  

•  

The previous example has 38 simple paths

Only nine prime paths

0

1

3

2

6

4

5


Prime Paths

[ 0, 1, 2, 3, 6 ]

[ 0, 1, 2, 4, 5 ]

[ 0, 1, 2, 4, 6 ]

[ 0, 2, 3, 6 ]

[ 0, 2, 4, 5]

[ 0, 2, 4, 6 ]

[ 5, 4, 6 ]

[ 4, 5, 4 ]

[ 5, 4, 5 ]

© Ammann & Offutt

Execute loop 0 times

Execute loop once

Execute loop more than once

97

Touring, Sidetrips and Detours

•  

Prime paths do not have internal loops … test paths might

•  

Tour : A test path p tours subpath q if q is a subpath of p

•  

Tour With Sidetrips : A test path p tours subpath q with sidetrips iff every edge in q is also in p in the same order

•  

The tour can include a sidetrip, as long as it comes back to the same node

•  

Tour With Detours : A test path p tours subpath q with detours iff every node in q is also in p in the same order

•  

The tour can include a detour from node ni , as long as it comes back to the prime path at a successor of ni


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Sidetrips and Detours Example

1 2 3 4

0 1 2 4 5

Touring without sidetrips or detours

3

1 6

0

Touring with a sidetrip

0

1

Touring with a detour

1

1

2

3

2

4

5

3

2

2

3

4

3

4

4

5

5

5


Infeasible Test Requirements

•  

An infeasible test requirement cannot be satisfied

–   Unreachable statement (dead code)

–   A subpath that can only be executed if a contradiction occurs ( X > 0 and X < 0 )

•  

•  

•  

•  

Most test criteria have some infeasible test requirements

It is usually undecidable whether all test requirements are feasible

When sidetrips are not allowed, many structural criteria have more infeasible test requirements

However, always allowing sidetrips weakens the test criteria

Practical recommendation – Best Effort Touring

–   Satisfy as many test requirements as possible without sidetrips

–   Allow sidetrips to try to satisfy unsatisfied test requirements


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1

3

0

2

6

Simple & Prime Path Example

4

Simple paths

Len 0

[0]

[1]

[2]

[3]

[4]

[5]

[6] !

‘!’ means path terminates

Len 1

[0, 1]

[0, 2]

[1, 2]

[2, 3]

[2, 4]

[3, 6] !

[4, 6] !

[4, 5]

[5, 4]

5

Len 4

[0, 1, 2, 3, 6] !

[0, 1, 2, 4, 6] !

[0, 1, 2, 4, 5] !

Len 2

[0, 1, 2]

[0, 2, 3]

[0, 2, 4]

[1, 2, 3]

[1, 2, 4]

[2, 3, 6] !

[2, 4, 6] !

[2, 4, 5] !

[4, 5, 4] *

[5, 4, 6] !

[5, 4, 5] *

Len 3

[0, 1, 2, 3]

[0, 1, 2, 4]

[0, 2, 3, 6] !

[0, 2, 4, 6] !

[0, 2, 4, 5] !

[1, 2, 3, 6] !

[1, 2, 4, 5] !

[1, 2, 4, 6] !

‘*’ means path cycles

Prime Paths

© Ammann & Offutt 101 Introduction to Software Testing (Ch 2), www.introsoftwaretesting.com

Problem

Section 2.2.1, Exercise #4

(b) List test paths that achieve node coverage, but not edge coverage

(c) List test paths that achieve edge coverage, but not edge-pair coverage

(d) List test paths that achieve edge-pair coverage


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For Next Class

   Read Chapters 1 and 2

   Homework #1

   Due January 19 th at the start of class

   Section 1.1 Exercise #2

   Section 2.1 Exercise #1, #2


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