Model Based Software Testing Preliminaries Aditya P. Mathur Purdue University Fall 2005 Last update: August 18, 2005
Dec 20, 2015
Model Based Software Testing Preliminaries
Aditya P. MathurPurdue UniversityFall 2005
Last update: August 18, 2005
Software Testing and Reliability Aditya P. Mathur 2003 2
Learning Objectives: This course
Methods for test assessment The coverage principle and the saturation effect
Tools:
Methods for test generation
Software test process
AETG: Test generation xSUDS: Test assessment , enhancement, minimization,
debugging CodeTest: Test assessment, performance monitoring VisualTest: GUI testing Test RealTime: Test assessment, performance monitoring
Ballista: Robustness testing
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Learning Objectives
How and why does testing improve our confidence in program correctness?
What is coverage and what role does it play in testing?
What are the different types of testing?
What is model-based testing? How does it differ from (formal) verification?
What are the formalisms for specification and design used as source for test and oracle generation?
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Testing: Preliminaries What is testing?
The act of checking if a part or a product performs as expected.
Why test?
Gain confidence in the correctness of a part or a product.
Check if there are any errors in a part or a product.
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What to test? During software lifecycle several products are generated.
Examples:
Requirements document
Design document
Software subsystems
Software system
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Test all! Each of these products needs testing.
Methods for testing various products are different.
Examples:
Test a requirements document using scenario construction and simulation.
Test a design document using simulation. Test a subsystem using functional testing.
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What is our focus? We focus on testing programs using formal models.
Programs may be subsystems or complete systems.
These are written in a formal programming language.
There is a large collection of techniques and tools to test programs.
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Source of Tests
An Abstraction of the MBT Process
Develop/Add Tests
Run Tests
Debug and removedefects
Test adequate?
No Yes Proceed to the next step
Raw requirements
Formal specifications
Finite State Machines
State Charts
Sequence Diagrams
Code, etc.
Tests
Behavior
Modified document
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A Few Terms
Program:
A collection of functions, as in C, or a collection of classes as in java.
Specification:
Description of requirements for a program. This might be formal or informal.
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Few Terms (contd.)
A set of values of input variables of a program. Values of environment variables are also included.
Test case or test input
Test set
Set of test inputs
Program execution
Execution of a program on a test input.
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Few Terms (contd.) Oracle
A function that determines whether or not the results of executing a program under test is as per the program’s specifications.
Verification Human examination of a product, such as design
document, code, user manual, etc., to check for correctness. Inspections an walkthroughs are the generally used methods for verification.
Validation The process of evaluating a system or a subsystem
to determine whether or not it satisfies the specified requirements.
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Correctness
Let P be a program (say, an integer sort program).
For sort let S be:
Let S denote the specification for P.
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Sample Specification
Let K denote any element of this sequence,
. )1(0 somefor eeK −≤≤
P takes as input an integer N>0 and a sequence of N integers called elements of the sequence.
P sorts the input sequence in descending order and prints the sorted sequence.
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Correctness again
P is considered correct with respect to a specification S if and only if:
For each valid input the output of P is in accordance with the specification S.
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Errors, defects, faults
Error: A mistake made by a programmer
Example: Misunderstood the requirements.
Defect/fault: Manifestation of an error in a program.
Example: Incorrect code: if (a<b) {foo(a,b);}Correct code: if (a>b) {foo(a,b);}
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Failure
Incorrect program behavior due to a fault in the program.
Failure can be determined only with respect to a set of requirement specifications.
A necessary condition for a failure to occur is that execution of the program force the erroneous portion of the program to be executed. What is the sufficiency condition?
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Errors and failure
InputsError-revealing inputs cause failure
Program
OutputsErroneous outputs indicatefailure
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Debugging
Suppose that a failure is detected during the testing of P.
The process of finding and removing the cause of this failure is known as debugging.
The word bug is slang for fault.
Testing usually leads to debugging
Testing and debugging usually happen in a cycle.
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Test-debug Cycle
Test
Debug
Yes
Testingcomplete?
No
Done!
Yes No
Failure?
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Testing and Code Inspection
Code inspection is a technique whereby the source code is inspected for possible errors.
Code inspection is generally considered complementary to testing. Neither is more important than the other.
One is not likely to replace testing by code inspection or by verification.
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Testing for correctness?
Identify the input domain of P.
Execute P against each element of the input domain.
For each execution of P, check if P generates the correct output as per its specification S.
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What is an input domain ? Input domain of a program P is the set of all valid inputs
that P can expect.
The size of an input domain is the number of elements in it.
An input domain could be finite or infinite.
Finite input domains might be very large!
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Identifying the input domain
For the sort program:
N: size of the sequence, K: each element of the sequence.
Example: For N<3, e=3, some sequences in the input domain are:
[0]: A sequence of size 1 (N=1)
[2 1]: A sequence of size 2 (N=2).
[ ]: An empty sequence (N=0).
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Size of an input domain
Suppose that
The size can be computed as:
The size of the input domain is the number of all sequences of size 0, 1, 2, and so on.
6100 ≤≤N
. somefor )1(0 eeK −≤≤
∑=
610
0i
ie Can you derive this formula?
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Testing for correctness? Sorry! To test for correctness P needs to be executed on all inputs.
For our example, it will take an exorbitant amount of time to execute the sort program on all inputs on the most powerful computers of today!
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Exhaustive Testing
This form of testing is also known as exhaustive testing as we execute P on all elements of the input domain.
For most programs exhaustive testing is not feasible.
What is the alternative?
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Formal Verification
Formal verification (for correctness) is different from testing for correctness.
There are techniques for formal verification of programs that we do not plan to discuss.
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Partition Testing
In this form of testing the input domain is partitioned into a finite number of sub-domains.
P is then executed on a few elements of each sub-domain.
Let us return to the sort program.
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Sub-domains
Suppose that 0<=N<=2 and e=3. The size of the partitions is:
We can divide the input domain into three sub-domains as shown.
133333 2102
0=++=∑
=i
i
1
3
9
0=N 2=N
1=N
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Fewer test inputs
Now sort can be tested on one element selected from each domain.
For example, one set of three inputs is:[ ] Empty sequence from sub-domain 1.[2] Sequence from sub-domain 2.[2 0] Sequence from sub-domain 3.
We have thus reduced the number of inputs used for testing from 13 to 3!
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Confidence
Confidence is a measure of one’s belief in the correctness of the program.
Correctness is often not measured in binary terms: a correct or an incorrect program.
Instead, it is measured as the probability of correct operation of a program when used in various scenarios.
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Measures of Confidence
Reliability: Probability that a program will function correctly in a given environment over a certain number of executions.
Test completeness: The extent to which a program has been tested and errors found have been removed.
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Example: Increase in Confidence
We consider a non-programming example to illustrate what is meant by “increase in confidence.”
Example: A rectangular field has been prepared to certain specifications.
One item in the specifications is:
“There should be no stones remaining in the field.”
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Rectangular Field
Search for stones inside a rectangular field.
X
Y
0 L
W
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Testing the Rectangular Field
The field has been prepared and our task is to test it to make sure that it has no stones.
How should we organize our search?
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Partitioning the field
We divide the entire field into smaller search rectangles.
The length and breadth of each search rectangle is one half the expected length and breadth of the smallest stone one expects to find in the field.
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Partitioning into search rectangles
Stone
12345678
Y
Wid
th
1 2 3 4 5 6 7
X Length
Another Stone
Two stones inside one rectangle
A tiny stone
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Input Domain
Input domain is the set of all possible valid inputs to the search process.
In our example this is the set of all points in the field. Thus, the input domain is infinite!
To reduce the size of the input domain we partition the field into finite size rectangles.
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Rectangle size
The length and breadth of each search rectangle is one half that of the smallest stone.
This is an attempt to ensure that each stone covers at least one rectangle. (Is this always true?)
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Constraints
Testing must be completed in less than H hours.
Any stone found during testing is removed.
Upon completion of testing the probability of finding a stone must be less than p.
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Number of search rectangles
LetL: Length of the fieldW: Width of the fieldl: Expected length of the smallest stonew: Expected width of the smallest stone
Size of each rectangle: l/2 x w/2
Number of search rectangles (R)=(L/l)*(W/w)*4
Assume that L/l and W/w are integers.
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Time to Test
Let t be the time to peek inside one search rectangle. No rectangle is examined more than once.
Let o be the overhead incurred in moving from one search rectangle to another.
Total time to search T=R*t+(R-1)*o
Testing with R rectangles is feasible only if T<H.
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Partitioning the input domain
This set consists of all search rectangles (R).
Number of partitions of the input domain is finite (=R).
However, if T>H then the number of partitions is too large and scanning each rectangle once is infeasible.
What should we do in such a situation?
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Option 1: Do a limited search
Of the R search rectangles we examine only r where r is such that (t*r+o*(r-1)) < H.
This limited search will satisfy the time constraint.
Will it satisfy the probability constraint?
Question:What do the probability and time constraints correspond to in a commercial test ?
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Distribution of Stones
€
si < Ri
To satisfy the probability constraint we must scan enough search rectangles so that the probability of finding a stone, after testing, remains less than p.
Let us assume that there are Si stones remaining after i test cycles.
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Distribution of Stones
There are Ri search rectangles remaining after i test cycles.
Stones are distributed uniformly over the field.
An estimate of the probability of finding a stone in a randomly selected remaining search rectangle is pi = si / Ri .
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Probability Constraint We will stop looking into rectangles if
pi <= p Can we really apply this test method in practice?
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Confidence
Number of stones in the field is not known in advance.
Hence we cannot compute the probability of finding a stone after a certain number of rectangles have been examined.
The best we can do is to scan as many rectangles as we can and remove the stones found.
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Coverage
Suppose that r rectangles have been scanned from a total of R. Then we say that the (rectangle) coverage is r/R.
After a rectangle has been scanned for a stone and any stone found has been removed, we say that the rectangle has been covered.
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Coverage and Confidence
What happens when coverage increases?
As coverage increases (and stones found are removed) so does our confidence in a “stone-free” field.
In this example, when the coverage reaches 100%, (almost) all stones have been found and removed. Can you think of situations when this might not be true?
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Option 2: Reduce number of partitions
If the number of rectangles to scan is too large, we can increase the size of a rectangle. This reduces the number of rectangles.
Increasing the size of a rectangle also implies that there might be more than one stone within a rectangle.
Is this good for a tester?
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Rectangle Size
As a stone may now be smaller than a rectangle, detecting a stone inside a rectangle is not guaranteed.
Despite this fact our confidence in a “stone-free” field increases with coverage.
However, when the coverage reaches 100% we cannot guarantee a “stone-free” field.
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Coverage vs. Confidence
1(=100%)
1
Coverage
Con
fide
nce
0
Does not imply that the fieldis “stone-free”.
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Rectangle Size (again!)
p=Probability of detecting a stone inside a rectangle, given that the stone is there.
t=time to complete a test.
Rectangle sizesmall large
t, p
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Analogy
Field: Program
Stone: ErrorScan a rectangle: Test program on one inputRemove stone: Remove errorPartition: Subset of input domainSize of stone: Size of an errorRectangle size: Size of a partition
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Input domain
Analogy (contd.)
Size of an error is the number of inputs in the input domain each of which will cause a failure due to that error.
Inputs that cause failuredue to Error 1
Inputs that cause failure due to Error 2.
Error 1 is largerthan Error 2.
Does this imply that failures due to error 1 will occur more frequently than those due to error 2?
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Confidence and Probability
It might not increase the probability that the field is “stone-free”.
Increase in coverage increases our confidence in a “stone-free” field.
Important: Increase in confidence is NOT justified if detected stones are not guaranteed to be removed !
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Types of Testing
Basis forclassification
Object under test
All of these methods can be
applied here.
Source of clues fortest input construction
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Testing: Based on Source of Test Inputs
Functional testing/specification testing/black-box testing/conformance testing: Clues for test input generation come from requirements.
White-box testing/coverage testing/code-based testing Clues come from program text.
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Testing: Based on Source of Test Inputs
Stress testing Clues come from “load” requirements. For
example, a telephone system must be able to handle 1000 calls over any 1-minute interval. What happens when the system is loaded or overloaded?
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Testing: Based on Source of Test Inputs
Performance testing Clues come from performance requirements. For
example, each call must be processed in less than 5 seconds. Does the system process each call in less than 5 seconds.
Fault- or error- based testing Clues come from the faults that are injected into the
program text or are hypothesized to be in the program.
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Testing: Based on Source of Test Inputs
Random testing
Robustness testing
Clues come from requirements. Test are generated randomly using these clues.
Robustness is the degree to which a software component functions correctly in the presence of exceptional inputs or stressful environmental conditions.
Clues come from requirements. The goal is to test a program under scenarios not stipulated in the requirements.
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Testing: Based on Source of Test Inputs
OO testing Clues come from the requirements and the design of
an OO-program.
Protocol testing Clues come from the specification of a protocol. As, for example, when testing for a
communication protocol.
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Testing: Based on Item Under Test
Unit testingTesting of a program unit. A unit is the smallest testable piece of a program. One or more units form a subsystem.
Subsystem testing Testing of a subsystem. A subsystem is a collection
of units that cooperate to provide a part of system functionality
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Testing: Based on Item Under Test
Integration testing Testing of subsystems that are being integrated to
form a larger subsystem or a complete system.
System testing Testing of a complete system.
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Testing: Based on Item Under Test
Regression testing
And the list goes on and on!
Test a subsystem or a system on a subset of the set of existing test inputs to check if it continues to function correctly after changes have been made to an older version.
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Test input construction and objects under test
Test object
Sou
rce
of c
lues
for
te
st in
puts
unit subsystem system
Requirements
Code
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Combinatorial Design
Context: A telephone switch
Problem: Determine what inputs to use to test the switch.
Call Type Billing Access Status
Local Caller Loop Available
Long Dist Collect ISDN Busy
Intl. 800 PBX Blocked
Total parameters: 4 Values for each parameter: 3
Total number of scenarios: 34=81
Parameters:
Sample inputs:
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Reducing the Input Space
Suppose that 81 test is too many for the telephone switch under test.
An alternative is to select a default value for each parameter and then vary each parameter until all values are covered.
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Test Plan with Default Parameter Values
Call Type Billing Access Status
Local Caller Loop Available
Long Dist Caller Loop Available
Intl. Caller Loop Available
Local Collect Loop Available
Local 800 Loop Available
Local Caller ISDN Available
Local Caller PBX Available
Local Caller Loop Busy
Local Caller Loop Blocked
Total inputs: 9
Coverage: 30 of the 54 pair wise interactions.
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Another Test Plan
Call Type Billing Access Status
Local Collect PBX Busy
Long Dist 800 Loop Busy
Intl. Caller ISDN Busy
Local 800 ISDN Blocked
Long Dist Caller PBX Blocked
Intl. Collect Loop Blocked
Local Caller Loop Available
Long Dist Collect ISDN Available
Total inputs: 9
Coverage: All pair wise interactions covered
Intl 800 PBX Available
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Combinatorial Explosion
What if the program under test had 10 parameters each with 3 values?
Total parameter combinations= 310
Number of tests using the default value method= ?
Number of pair-wise combinations = ?
Number of pair-wise combinations covered = ?
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Answers to Questions
Tests with default value method=n+ (n-1) x (k-1)
Pair-wise combinations=(k x (k-1)/2) x n2
For k parameters each with n possible values:
Pair-wise combinations covered=(k-1)+n*(k-1)+(n-1)*(k-1)*(k-1)
Later we shall discuss how to handle the combinatorial explosion.
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Finite State Machines (FSMs)
A state machine is an abstract representation of actions taken by a program or anything else that functions!
It is specified as a quintuple: A: a finite input alphabet Q: a finite set of states q0: initial state which is a member of Q.
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FSMs (contd.) T: state transitions which is a mapping
Q x A--> Q F: A finite set of final states, F is a subset of Q.
Example: Here is a finite state machine that recognizes integers ending with a carriage return character.
A={0,1,2,3,4,5,6,7,8,9, CR} Q={q0,q1,q2} q0: initial state
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FSMs (contd.)
T: {((q0,d),q1),(q1,d),q1), (q1,CR),q2)} F: {q2}
A state diagram is an easier to understand specification of a state machine. For the above machine, the state diagram appears on the next slide.
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State diagram
q0 q1d
d
CRq2
Final state indicatedby concentric circles.
States indicated by circles.
State transitions indicatedby labeled arrows from one statethe another (which could be the same). Each label must be from the alphabet. It is also known asan event.
d: denotes a digit
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State Diagram-Actions
q0 q1 q2d/set i to d
d/add 10*d to i
CR/output i
Can you describe what this machine computes?Can you construct a regular expression that describes all strings recognized by this state machine?
x/y: x is an element ofthe alphabet and y is an action.
i is initialized to d when the machine moves from state q0 to q1.i is incremented by 10*d when the machine moves from q1 to q1.The current value of i is output when a CR is encountered.
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State Machine: Languages
Each state machine recognizes a language.
The language recognized by a state machine is the set S of all strings such that: when any string s in S is input to the state machine
the machine goes through a sequence of transitions and ends up in the final state after having scanned all elements of s.
Testing state machines? Later!
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The Unified Modeling Language
Unified Modeling Language (UML) is a notation to express requirements and designs of software systems.
Requirements are represented using:
a collection of use cases, each use case being a representative of a collection of scenarios.
a collection of system sequence diagrams that explain the interaction between a user and the application for each use case.
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UML: Design Representation
Design of an application is represented in UML by a collection of diagrams of the following types (not an exhaustive list):
Sequence (or collaboration) diagrams depict the sequence of actions initiated due to an external event. This sequence is depicted in terms of messages sent from one object to another.
Statecharts depict the relationship amongst various states of an object.
Class diagrams capture the relationships amongst classes.
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ECG Monitor
Use Case Diagram (partial)
Physician
Remote Display
Display waveforms
Capture waveform
Processalarms
Calibratesensors
<<uses>>
Service Personnel
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A Sequence Diagram (partial)
Passenger 1 is on floor 6 and 2 on floor 2.
Passenger 1Elevator Controller Passenger 2
Request UP elevator
Light UP indicator
Request DN elevatorDoor closes, E moves, passes floor 2.
Door opensArrives at floor 6.
Queue request
Request floor 8
Light DN indicator
Light floor buttonOne sequence diagram for each use case.
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What else can one indicate on a sequence diagram?
Broadcast messages sent by one object and received by more than one.
Timing marks to show timing constraints m between two events.
Event identifiers can be attached to an event; an ID can be referenced in other parts of the diagram.
State marks are placed on the object timing line to indicate state changes for that object.
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A State Diagram
Idle
Transmitting
Waiting
Message Ready/Trans-count=0
[Trans-count<=limit]
tm (wait-time)
[else]/inform sender of failure
ACK
Behavior of a Message Transaction Object
Invalid ACK
Done/Start-timerTrans-count++
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UML State Charts
Similar to state diagrams.
States can be nested within states. Inner states are known as substates.
History connector allows the specification of default initial state in a super state.
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S1
UML State Charts
entry: f1()
exit: f3()do: f2()
entry: g1()
exit: g3()do: g2()
S2
Y2
SS1
SS2
Y1
S3P
R Q
X1
X2
X3
T1
T2
T3
T4/C1 C2T5H
[G1][G1]
History connector: SS2 is the default initial state in the absence of history, else the last active state is the default.Each state may have entry and exit actions as well as activities.
Entry (exit) actions are executed in the (reverse) order of nesting.
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Transitions in UML Statecharts
event name (parameters) [guard] / action list^ event list
event name: name of the event triggering the transition
parameters: List of parameters passed with the event signal.
guard: Boolean expression that must evaluate to true for the transition to take place.
action list: List of actions to be executed when the transition is taken.
event list: List of events generated, and propagated to other state machines, when the transition is taken.
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Summary
Testing and debugging
Specification
Correctness versus confidence
Input domain
Exhaustive testing and combinatorial explosion
UML artifacts: Use cases, FSM, State Charts, Sequence diagrams
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Summary: Terms
Reliability Coverage Error, defect, fault, failure Debugging, test-debug cycle Types of testing, basis for
classification
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Summary: Questions
What is the effect of reducing the partition size on probability of finding errors?
How does coverage effect our confidence in program correctness?
Does 100% coverage imply that a program is fault-free?
What decides the type of testing?