Model based Software Testing Test Assessment and Enhancement

1
Model based Software Testing Test Assessment
and Enhancement

• Aditya P. Mathur
• Purdue University
• Fall 2005

Last update August 18, 2005
2
Learning Objectives

• To understand the relevance and importance of
  test assessment.

• To learn the fundamental principle underlying
  test assessment.

• To learn various methods and tools for test
  assessment.

• To understand the relative strengths/weaknesses
  of test assessment methods.

• To learn how to improve tests based on a test
  assessment procedure.

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What is Test Assessment?

• Once a test set T, a collection of test inputs,
  has been developed, we ask
• How good is T?

• It is the measurement of the goodness of T which
  is known as test assessment.

• Test assessment is carried out based on one or
  more criteria.

4
Test Assessment (contd.)

• These criteria are known as test adequacy
  criteria.

• Test assessment is also known as test adequacy
  assessment.

5
Test assessment (contd.)

• Test assessment provides the following
  information

• A metric, also known as the adequacy score or
  coverage, usually between 0 and 1.

• A list of all the weaknesses found in T, which
  when removed, will raise the score to 1.

• The weaknesses depend on the criteria used for
  assessment.

6
Test assessment (contd.)

• Once the coverage has been computed, and the
  weaknesses identified, one can improve T.

• Improvement of T is done by examining one or more
  weaknesses and constructing new test requirements
  designed to overcome the weakness(es).

• The new test requirements lead to new test
  specifications and to further testing of the
  program.

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Test Assessment (contd.)

• This is continued until all weaknesses are
  overcome, i.e. the adequacy criterion is
  satisfied (coverage1).

• In some instances it may not be possible to
  satisfy the adequacy criteria for one or more of
  the following reasons
• Lack of sufficient manpower

• Weaknesses that cannot be removed because they
  are infeasible.

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Test Assessment (contd.)

• The cost of removing the weaknesses is not
  justified.

• While improving T by removing its weaknesses, one
  usually tests the program more thoroughly than it
  has been tested so far.

• This additional testing is likely to result in
  the discovery of remaining errors.

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Test Assessment (contd.)

• Hence we say that test assessment and improvement
  helps in the improvement of software reliability.

• Test assessment and improvement is applicable
  throughout the testing process and during all
  stages of software development.

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Test Assessment Procedure
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Principle Underlying Test Assessment

• There is a uniform principle that underlies test
  assessment throughout the testing process.

• This principle is referred to as the coverage
  principle.

• It has come about as a result of intensive
  research at Purdue and other research groups in
  software testing.

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The Coverage Principle

• To formulate and understand the coverage
  principle, we need to understand
• coverage domains
• coverage elements

• A coverage domain is a finite domain, related to
  the program under test, that we want to cover.
  Coverage elements are the individual elements of
  this domain

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The Coverage Principle (contd.)
Coverage Domains
Coverage Elements
14
The Coverage Principle (contd.)

• Measuring test adequacy and improving a test set
  against a sequence of well defined, increasingly
  strong, coverage domains leads to improved
  confidence in the reliability of the system under
  test.

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The Coverage Principle (contd.)

• Note the following properties of a coverage
  domain

• It is related to the program under test.

• It is finite.

• It may come from program requirements, related to
  the inputs and outputs.

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The Coverage Principle (contd.)

• It may come from program code. Can you think of a
  coverage domain that comes from the program code?

• It aids in measuring test adequacy as well as the
  progress made in testing. How?

17
The Coverage Principle (contd.)

• Example
• It is required to write a program that takes in
  the name of a person as a string and searches for
  the name in a file of names. The program must
  output the record ID which matches the given
  name. In case of no match a -1 is returned.

What coverage domains can be identified from this
requirement?
18
The Coverage Principle (contd.)

• As we learned earlier, improving coverage
  improves our confidence in the correct
  functioning of the program under test.

• Given a program P and a test T suppose that T is
  adequate w.r.t. a coverage criterion C.

• Does this mean that P is error free?

Obviously???
19
Test Effort

• There are several measures of test effort.

• One measure is the size of T. By this measure a
  test set with a larger number of test cases
  corresponds to higher effort than one with a
  lesser number of test cases.

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Error Detection Effectiveness

• Each coverage criterion has its error detection
  ability. This is also known as the error
  detection effectiveness or simply effectiveness
  of the criterion.

• One measure of the effectiveness of criterion C
  is the fraction of faults guaranteed to be
  revealed by a test T that satisfies C.

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Effectiveness (contd.)

• Another measure is the probability that at least
  fraction f of the faults in P will be revealed
  by test T that satisfies C.

• Unfortunately there is no absolute measure of the
  effectiveness of any given coverage criterion for
  a general class of programs and for arbitrary
  test sets.

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Effectiveness (contd.)

• One coverage criterion results in an exception to
  this rule What is it?

• Empirical studies conducted by researchers give
  us an idea of the relative goodness of various
  coverage criteria.

• Thus, for a variety of criteria we can make a
  statement like Criterion C1 is definitely better
  than criterion C2.

23
Effectiveness-continued

• In some cases we may be able to say Criterion C1
  is probably better than criterion C2.

• Such information allows us to construct a
  hierarchy of coverage criteria.

• This hierarchy is helpful in organizing and
  managing testing. How?

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Strength of a coverage criterion

• The effectiveness of a coverage criterion is also
  referred to as its strength.

• Strength is a measure of the criterions ability
  to reveal faults in a program.

• Criterion C1 is considered stronger than
  criterion C2 if C1 is is capable of revealing
  more faults than C2.

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The Saturation Effect

• The rate at which new faults are discovered
  reduces as test adequacy with respect to a finite
  coverage domain increases it reduces to zero
  when the coverage domain has been exhausted.

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Saturation Effect Fault View
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Saturation Effect Reliability View
Functional, Decision, Dataflow, and
Mutation tsting provide various test assessment
criteria.
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Coverage principle-discussion

• Discuss
• How will you use the knowledge of coverage
  principle and the saturation effect in organizing
  and managing testing?

Can you think of any other uses of the coverage
principle and the saturation effect?
29
Control flow graph

• Control flow graph (CFG) of a program is a
  representation of the flow of execution within
  the program.

• More formally, a CFG G is

• G(N,A)
• where N set of nodes and A set of arcs

• There is a unique entry node en in N.

• There is a unique exit node ex in N. A node
  represents a single statement or a block.

• A block is a single-entry-single-exit sequence of
  instructions that are always executed in a
  sequence without any diversion of path except at
  the end of the block.

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Control flow graph (contd.)

• Every statement in a block, except possibly the
  first one, has exactly one predecessor.

• Similarly, every statement in the block, except
  possibly the last one, has exactly one successor.

• An arc a in A is a pair (n,m) of nodes from N
  which represent transfer of control from node n
  to node m.

• A path of length k in G is an ordered sequence of
  arcs, from A such that

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Control flow graph (contd.)

• The first node a1 is en

• The last node ak is ex

• For any two adjacent arcs ai (n,m) and aj
  (p,q), mp.

• A path is considered executable or feasible if
  there exists a test case which causes this path
  to be traversed during program execution,
  otherwise the path is unexecutable or infeasible.

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Control flow graph-example

• Exercise
• Draw a CFG for the following program and identify
  all paths.

1. scanf (x,y) if (ylt0) 2. pow0-y 3. else
powy 4. z1.0 5. while (pow !0) 6. zzx
powpow-1 7. if (ylt0) 8. z1.0/z 9. printf(z)
What does the above program compute?
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Control-flow Graph
34
Structure-based Test Adequacy

• Based on the CFG of a program several test
  adequacy criteria can be defined.

• Some are

• statement coverage criterion
• branch coverage criterion
• condition coverage criterion
• path coverage criterion

35
Statement Coverage

• The coverage domain consists of all statements in
  the program. Restated, in terms of the control
  flow graph, it is the set of all nodes in G.

• A test T satisfies the statement coverage
  criterion if upon execution of P on each element
  of T, each statement of P has been executed at
  least once.

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Statement coverage (contd.)

• Restated in terms of G, T is adequate w.r.t. the
  statement coverage criterion if each node in N is
  on at least one of the paths traversed when P is
  executed on each element of T.

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Statement Coverage (contd.)

• Class exercise
• For the program for which you have drawn the
  control flow graph, develop a test set that
  satisfies the statement coverage criterion.

• Follow the procedure for test assessment and
  improvement suggested earlier.

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Statement Coverage-Weakness

• Consider the following program
• int abs (x)
• int x
• if (xgt0) x0-x
• return x

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Statement coverage-weakness

• Suppose that T (x0).

• Clearly, T satisfies the statement coverage
  criterion.

• But is the program correct and is the error
  revealed by T which is adequate w.r.t. the
  statement coverage criterion?

What do you suggest we do to improve T?
40
Branch (or edge) coverage

• In G there may be nodes which correspond to
  conditions in P. Such nodes, also called
  condition nodes, contain branches in P.

• Each such node is considered covered if during
  some execution of P, the condition evaluates to
  true and false these executions of P need not
  be the same.

41
Branch coverage

• The coverage domain consists of all branches in
  G. Restated, in terms of the control flow graph,
  it is the set of all arcs exiting the condition
  nodes.

• A test T satisfies the branch coverage criterion
  if upon execution of P on each element of T, each
  branch of P has been executed at least once.

42
Branch coverage

• Class exercise
• Identify all condition nodes in the flow graph
  you have drawn earlier.
• Does T (x0) satisfy the branch coverage
  criterion?
• If not, then improve it so that it does.

43
Branch Coverage-Weakness

• Consider the following program that is supposed
  to check if the input data item is in the range 0
  to 100, inclusive

int check(x) int x if ((xgt0 ) (xlt200))
checktrue else checkfalse
44
Branch Coverage-Weakness

• Class exercise
• Do you notice the error in this program?
• Find a test set T which is adequate w.r.t.
  statement coverage and does not reveal the error.
• Improve T so that it is adequate w.r.t. branch
  coverage and does not reveal the error.
• What do you conclude about the weakness of the
  branch coverage criterion?

45
Condition Coverage

• Condition nodes in G might have compound
  conditions.

• For example, in the check program the condition
  node contains the condition

((xgt0 ) (xlt200))

• This is a compound condition which consists of
  the elementary conditions xgt0 and xlt200.

46
Condition coverage (contd.)

• A compound condition is considered covered if all
  of its constituent elementary conditions evaluate
  to true and false, respectively, during some
  execution of P.

• A test set T is adequate w.r.t. condition
  coverage if all conditions in P are covered when
  P is executed on elements of T.

47
Condition coverage (contd.)

• Class exercise
• Improve T from the previous exercise so that it
  is adequate w.r.t. the condition coverage
  criterion for the check function and does not
  reveal the error.
• Do you find the above possible?

48
Branch coverage-weakness (contd.)

• Consider the following program

0. int set_z(x,y) 1. int x,y 2. if
(x!0) 3. y5 4. else zz-x 5. if
(zgt1) 6. zz/x 7. else 8. zy
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Branch Coverage-Weakness

• Class exercise
• Construct T for set_z such that (a) T is adequate
  w.r.t. the branch coverage criterion and (b) does
  not reveal the error.
• What do you conclude about the effectiveness of
  the branch and condition coverage criteria?

50
Path coverage

• As mentioned before, a path through a program is
  a sequence of statements such that the entry node
  of the program CFG is the first node on the path
  and the exit node is the last one on the path.

Is this definition equivalent to the one given
earlier?
51
Path coverage (contd.)

• A test set T is considered adequate w.r.t. the
  path coverage criterion if all paths in P are
  executed at least once upon execution on each
  element of T.

• Class exercise
• Construct T for set_z such that T is adequate
  w.r.t. the path coverage criterion and does not
  reveal the error.
• Is the above possible?

52
Path Coverage-Weakness

• The number of paths in a program is usually very
  large.

• How many paths in set_z ?

• How many paths in check ?

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Path Coverage-Weaknesses

• It is the infinite or a prohibitively large
  number of paths that prevent the use of this
  criterion in practice.

• Suppose that a test set T covers all paths. Will
  it guarantee that all errors in P are revealed ?

• Is obtaining 100 path coverage equivalent to
  exhaustive testing?

54
Variants of Path Coverage

• As path coverage is usually impossible to attain,
  other heuristics have been proposed.

• Loop coverage

• Make sure that each loop is executed 0, 1, and 2
  times.

• Try several combinations of if and switch
  statements. The combinations must come from
  requirements.

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Hierarchy in Control flow criteria
Path coverage
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Exercise

• Develop a test set T that is adequate w.r.t. the
  statement, condition, and the loop coverage
  criteria for the exponentiation program.

57
Test strategy

• One can develop a test strategy based on any of
  the criteria discussed.

• Example
• A test strategy based on the statement coverage
  criterion will begin by evaluating a test set T
  against this criterion. Then new tests will be
  added to T until all the statements are covered,
  i.e. T satisfies the criterion.

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Definitions

• Error-sensitive path a path whose execution
  might lead to eventual detection of an error.

• Error revealing path a path whose execution will
  always cause the program to fail and the error to
  be detected.

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Definitions Reliable Technique

• Reliable A test technique is reliable for an
  error if it guarantees that the error will always
  be detected.

• This implies that a reliable testing technique
  must lead to the exercising of at least one
  error-revealing path.

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Definitions Weakly Reliable

• Weakly reliable A test technique is weakly
  reliable if it forces the execution of at least
  one error sensitive path.

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Example Error Detection 1

• Let us go over the example in Korel and Laskis
  paper.

• It is a sorting program which uses the bubble
  sort algorithm.

• It sorts an array a0N in descending order.

• There are two, nested, loops in the program.

• The inner loop from i6-i10 finds the largest
  element of aR1N.

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Example Error Detection (contd.)

• The largest element is saved in R0 and R3 points
  to the location of R0 in a.

• The outer loop swaps a(R1) with a(R3).

• The completion of one iteration of the outer loop
  ensures that the sub-array a0R1-1 has been
  sorted and that aR1-1 is greater than or equal
  to any element of aR1N.

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Example Error Detection (contd.)

• There is a missing re-initialization of R3 to R1
  at the beginning of the inner loop.

• In some cases this will cause the program to
  fail.
• What are these cases?

• We will get back to this error later!

64
Data flow graph

• It represents the flow of data in a program.

• The graph is constructed from the control flow
  graph (CFG) of the program.

• A statement that occurs within a node of the CFG
  might contain variables occurrences.

• Each variable occurrence is classified as a def
  or a use.

65
defs and uses

• A def represents the definition of a variable.
  Here are some sample defs of variable x
• xyx
• scanf(x,y)
• int x
• xi-1yx

All defs of x are italicized.

• A use represents the use of a variable in a
  statement. Here a few examples of use of variable
  x

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def-use (contd.)
All uses of x are italicized.

• xx1
• printf (x is d, y is d, x,y)
• cout ltlt x ltlt endl ltlt y
• zxi1
• if (xlty)

• Uses of a variable in input and assignments are
  classified as c-uses. Those in conditions are
  classified as p-uses.

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def-use (contd.)

• c-use stands for computational use and p-use for
  predicate-use.

• Both c- and p-uses affect the flow of control
  p-uses directly as their values are used in
  evaluating conditions and c-uses indirectly as
  their values are used to compute other variables
  which in turn affect the outcome of condition
  evaluation.

68
def-use (contd.)

• A path from node i to node j is said to be
  def-clear w.r.t. a variable x if there is no def
  of x in the nodes along the path from node i to
  node j. Nodes i and j may have a def of x.

• A def-clear path from node i to edge (j,k) is one
  in which no node on the path has a def of x.

69
global-def

• A def of a variable x is considered global to its
  block if it is the last def of x within that
  block.

• A c-use of x in a block is considered global
  c-use if there is no def of x preceding this
  c-use within this block.

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def-use graph definitions

• def(i) set of all variables for which there is a
  global definition at node i.

• c-use(i) set of all variables that have a
  global c-use at node i.

• p-use(i,j) set of all variables for which there
  is a p-use for the edge (i,j).

• dcu(x,i) set of all nodes such that each node
  has x in its c-use and x is in def(i).

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def-use graph definitions

• dpu(x,i) set of all edges such that each edge
  has x in its p-use , x is in def(i).

• The def-use graph of program P is constructed by
  associating defs, c-use, and p-use sets with
  nodes of a flow graph.

72
def-use graph (contd.)
Sample program
1. scanf (x,y) if (ylt0) 2. pow0-y 3. else
powy 4. z1.0 5. while (pow !0) 6. zzx
powpow-1 7. if (ylt0) 8. z1.0/z 9. printf(z)
73
def-use graph (contd.)
Unlabeled edges imply empty p-use set.
defx,y c-use?
1
y
y
defpow c-usey
defpow c-usey
2
3
4
defz c-use?
def? c-use?
5
def? c-use?
pow
pow
defz,pow c-usez,x,pow
7
6
y
y
def? c-usez
defz c-usez
8
9
74
def-use graph exercise
Draw a def-use graph for the following program.
0. int set_z(x,y) 1. int x,y 2. if
(x!0) 3. y5 4. else zz-x 5. if
(zgt1) 6. zz/x 7. else 8. zy
75
def-use graph (contd.)

• Traverse the graph to determine dcu and dpu sets.

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Test generation

• Exercises
• For the above graph generate a test set that
  satisfies
• the branch coverage criterion
• the all-defs criterion - for definitions of all
  variables at least one use (c- or p- use) must be
  exercised.
• the all-uses criterion- all p-uses and all c-uses
  of all variable definitions be covered.

• Develop the tests incrementally, i.e. by
  modifying the previous test set!

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?SUDS processing Phase I
P, Program under test
78
?ATAC processing phase II
coverage analyzer
79
Mutation Testing

• What is mutation testing?

• Mutation testing is a code-based test assessment
  and improvement technique.

• It relies on the competent programmer hypothesis
  which is the following assumption

• Given a specification a programmer develops a
  program that is either correct or differs from
  the correct program by a combination of simple
  errors.

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Mutation testing (contd.)

• The process of program development is considered
  as iterative whereby an initial version of the
  program is refined by making simple, or a
  combination of simple changes, towards the final
  version.

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Mutant

• Given a program P, a mutant of P is obtained by
  making a simple change in P.

What is zpush?
82
Another mutant
83
Mutant

• A mutant M is considered distinguished by a test
  case t ?T iff
• P(t)?M(t)
• where P(t) and M(t) denote, respectively, the
  observed behavior of P and M when executed on
  test input t.

• A mutant M is considered equivalent to P iff
• P(t)?M(t) ?t ? T.

84
Mutation score

• During testing a mutant is considered live if it
  has not been distinguished or proven equivalent.

• Suppose that a total of M mutants are generated
  for program P.

• The mutation score of a test set T, designed to
  test P, is computed as
• number of live mutants/(M-number of equivalent
  mutants)

85
Test adequacy criterion

• A test T is considered adequate w.r.t. the
  mutation criterion if its mutation score is 1.

• The number of mutants generated depends on P and
  the mutant operators applied on P.

• A mutant operator is a rule that when applied to
  the program under test generates zero or more
  mutants.

86
Mutant Operators

• Consider the following program
• int abs (x)
• int x
• if (xgt0) x0-x
• return x

87
Mutation operator

• Consider the following rule
• Replace each relational operator in P by all
  possible relational operators excluding the one
  that is being replaced.

• Assuming the set of relational operators to be
  lt, gt, lt, gt, , !, the above mutant
  operator will generate a total of 5 mutants of P.

88
Mutation Operators

• Mutation operators are language dependent.

• For Fortran a total of 22 operators were proposed.

• For C a total of 77 operators were proposed. None
  have been proposed for C though most of the
  operators for C are applicable to C programs.

89
Equivalent mutant

• Consider the following program P

• int x,y,z
• scanf(x,y)
• if (xgt0)
• xx1 zx(y-1)
• else
• xx-1 zx(y-1)

• Here z is considered the output of P.

90
Equivalent mutant (contd.)

• Now suppose that a mutant of P is obtained by
  changing xx1 to xabs(x)1.

• This mutant is equivalent to P as no test case
  can distinguish it from P.

91
Mutation Testing Procedure
Given P and a test set T
1. Generate mutants
2. Compile P and the mutants
3. Execute P and the mutants on each test case.
4. Determine equivalent mutants..
5. Determine mutation score.
6. If mutation score is not 1 then improve the
test set and repeat from step 3.
92
Mutation Testing Procedure (contd.)

• In practice the above procedure is implemented
  incrementally.

• One applies a few selected mutant operators to P
  and computes the mutation score w.r.t. to the
  mutants generated.

• Once these mutants have been distinguished or
  proven equivalent, another set of mutant
  operators is applied.

93
Mutation Testing Procedure

• This procedure is repeated until either all the
  mutants have been exhausted or some external
  condition forces testing to stop.

• We will not discuss the details of practical
  application of mutation testing.

94
Tools for Mutation Testing

• Mothra for Fortran, developed at Purdue, 1990

• Proteum for C, developed at the University of
  Saõ Paulo at Saõ Carlos in Brazil.

95
Uses of Mutation Testing

• Mutation testing is useful during integration
  testing to check for integration errors.

• Only the variables that are in the interfaces of
  the components being integrated are mutated. This
  reduces the complexity of mutation testing.

96
Summary

• Test adequacy criterion

• Test improvement

• Coverage principle

• Saturation effect

• Control flow criteria

• Data flow criteria
• def, use, p-use, c-use, all-uses

97
Summary (contd.)

• xSUDS, data flow testing tool.

• Mutation testing
• mutant, distinguishing a mutant, live mutant,
  mutant score, competent programmer hypothesis.