Mutation Analysis Approach to Develop Reliable Object-Oriented Software

In general, modern programs are large and complex and it is essential that they should be highly reliable in applications. In order to develop highly reliable software, Java programming language developer provides a rich set of exceptions and exception handling mechanisms. Exception handling mechanisms are intended to help developers build robust programs. Given a program with exception handling constructs, for an effective testing, we are to detect whether all possible exceptions are raised and caught or not. However, complex exception handling constructs make it tedious to trace which exceptions are handled and where and which exceptions are passed on. In this paper, we address this problem and propose a mutation analysis approach to develop reliable object-oriented programs. We have applied a number of mutation operators to create a large set of mutant programs with different type of faults. We then generate test cases and test data to uncover exception related faults. The test suite so obtained is applied to the mutant programs measuring the mutation score and hence verifying whether mutant programs are effective or not. We have tested our approach with a number of case studies to substantiate the efficacy of the proposed mutation analysis technique.


Introduction
Of late, computer applications have permeated heavily into every sphere of the daily life of an average person.Many of these applications are large, complex, and safety critical, requiring the software to be extremely reliable.An exception occurrence during a program execution is an abnormal computation state [1] and thus is a threat to the reliability of software.It is advocated that software should be tested adequately to trace if there is any exception in intended behavior [2].To realize this software developers prefer exception handling mechanisms to be embedded inside code so that software can arrest and raise alarm whenever there is any exception and then cause of exception can be eliminated.Many reasons may be attributed to causes of exceptions such as erroneous input, hardware faults, logical errors in the code, semantic violation, linking errors, and limitation of system resources.It is reported that more than 50% of the operational failures that may occur in a system are due to faults in exception handling and recovery [3].To cope with the system failures due to exceptions, most modern programming languages such as Ada, C++ and Java incorporate explicit mechanisms for exception handling.Syntactically, an exception handling mechanism consists of a means to explicitly raise an exceptional condition at a program point and a means of expressing a block of code to handle one or more exceptional conditions.In other words, an exception handling mechanism provides a way to separate code that deals with unusual situations and abnormal program termination.
Exception handling constructs are responsible for the detection and handling of system conditions that could potentially lead to failure.Recent studies of Java programs indicate that exception handling constructs occur frequently and approximately 15%-25% of the classes contained exception handling constructs [4,5].Despite the frequency of their occurrences, the behavior of exception handling constructs is often the least understood and poorly tested part of a program [6].Testing strategy to test object-oriented programs, in general, and exception handling constructs, in particular, is scarcely reported [7].For testing exception handling constructs, some works have been reported [4,6,8].Sinha and Harrold [9] proposed a class of adequacy criteria that can be used to test the behavior of exception handling constructs.Sinha and Harrold [9] described a methodology for applying 2 Advances in Software Engineering the criteria to unit and integration testing of programs that contain exception handling constructs.However, to the best of our literature survey, no approach has been reported so far to generate exception handling related faulty programs and then to test the adequacy of test suites.Adequacy testing is an important issue because a test suite may not locate all exception points.For example, in Java, an exception can be raised implicitly.In that case, it is not possible to draw proper control flow graph [4,10,11].Further, even if all exception paths are known from the control flow graph [4] and satisfy exceptioncoverage criteria [9], it needs to design test data manually for raising all possible potential exceptions.This manual test case generation is not only tedious [6] but raising exceptions is not always guaranteed.As a consequence we need to determine the adequacy of test cases to raise exceptions.In general, determining the path of exceptions is a difficult problem and manual synthesis of test data may not be sufficient to raise all exceptions.In this context, efficiency of a test suite is necessary to be evaluated in order to assure the reliability of a system under test.In summary, given a program, we are to test whether the exception handling constructs are sufficient to throw and catch all possible exceptions or not.
Mutation analysis is a practical method to evaluate the quality of test suites [12][13][14].In this work, we propose a mutation analysis method to evaluate test suites for testing exception handling constructs.We consider a set of mutation operators with which different types of faults can be injected to the original programs.The mutation operators are adopted from the work of Ji et al. [15].The mutant programs are then analyzed with some test suites.We consider test suites generated according to the control flow based structural analysis approach proposed in [4,9] for a given Java program.We also analyzed the program in JUnit 4. 6 [16] and Jumble 1.0 [17] testing environment and their mutant programs.Our experimental results substantiate the efficiency of the proposed mutation analysis approach.
The rest of the paper is organized as follows.We discuss basic concepts, related terminologies, and tools in Section 2. In Section 3, we discuss the mutation operators followed in this work.Mutation analysis is discussed in Section 4. Our experimental results are presented in Section 5. Related work and comparison of our work with others are discussed in Section 6.Finally, Section 7 concludes the paper.

Basic Concepts
In this section, we discuss some basic concepts and terminologies which are referred to in our subsequent discussions.We also briefly introduce the tools used in our work.Java. Java [18] programming language is considered as a model language in this work.In this subsection, we provide an overview of exception handling constructs in Java.Details of exception handling constructs in Java can be found in [19,20].

Exception Handling Constructs in
In Java, exceptions are first-class objects.Each exception is an instance of a class that is derived from the class java.lang.Throwable, which is defined in the standard Java API [19].An exception can be raised at any point in the program through a throw statement.A throw statement is associated with an expression denoting an exception object, which may be a variable (e.g., throw e), a method call (e.g., throw m()) or a new instantiation (e.g., throw new E()), and so forth.A throw statement can appear anywhere in the program.Java exception handling construct includes three blocks: try, catch and finally (see Figure 1(a)).Code can be guarded for exceptions within a try block.Exceptions raised through execution of code (implicitly) or a throw statement (explicitly) within a try block may be caught in one or more catch clause(s) declared immediately following the try block.The finally block is executed independently of what happens in the try block.It may be noted that a try statement consists of a try block and optionally one or more catch blocks and finally block (see Figure 1 A catch block specifies the type of exception it handles and exception handler; that is, it contains a block of code that is executed when an exception of that type is raised in the associated try block.If a finally block is associated with a try block, then the finally block is always executed, irrespective of how control transfers out of the try block.

Java Exception Hierarchy.
Similar to other Java objects, exceptions are typed, and types are organized into a hierarchy.All exceptions inherit from the class type Throwable defined in java.langAPI.The exception type hierarchy defines three different groups of exceptions: errors, runtime exceptions, and checked exception (defined in Java.lang.Exception) (also see Figure 1(b)).Note that errors and runtime exceptions are unchecked exceptions.Unchecked exceptions can be thrown at any point in a Java program and, if uncaught, may propagate back to the program entry point, causing the Java Virtual Machine [20] to terminate.The class Error is responsible for giving errors in some catastrophic failures.The exceptions of type RuntimeException are typically created automatically during runtime in response to some execution errors.The exceptions of the type Exception are checked exceptions and are used for exceptional conditions that user programs can catch.A list of exceptions that a Java programmer can catch in programs is available in [19].There are 11 runtime exceptions, 17 errors, and 7 checked exceptions defined in Java.langAPI [19] as per the release of Java 6. Programmers can define and extend existing exception type in Java API to customize their needs.Some new exception types can also be defined [20].

Call Exception Hierarchy.
In this subsection, we discuss the flow of exceptions within the context of the structure of a given program.This flow of exceptions, we specially term it as call exception hierarchy (CEH), is useful to understand and evaluate how exceptions are handled within a method, which exceptions might arise during the execution of a method, Figure 1: Exception handling constructs and exceptions in Java [19].
which exceptions are handled and where, and which exceptions are passed on.Alternatively, a call exception hierarchy specifies which exceptions may propagate to its caller.In essence, the call exception hierarchy is precisely specifying the behavior of the program as far as the exceptions and handling exceptions are concerned [21].
We identify three basic control flow constructs to obtain the call exception hierarchy in any program.These are method calls, nesting, and multicatch.Any complex and arbitrary call exception hierarchy can be resolved with the help of the above three basic constructs.We discuss the three basic constructs as follows.

Method Calls.
A method say Main can call a method   , which in turn may call another method say   and so on.Any method can throw and catch exceptions.The call exception hierarchy, in this case, implies the parentchild relationship among exceptions.An exception  2 is a child of another exception, say  1 , if  2 occurs in a method that is called by the method where  1 may occur.The call exception hierarchy with method calls is illustrated with an example in Figure 2(a).In Figure 2(a), the method Main calls the method  1 () and is supposed to catch an exception .Now, the method  1 () calls method  2 () and may throw two exceptions, namely,  11 and  12 .The method  2 () in turns may throw exception  21 and  22 .In this case, the exception  should be at the root of the hierarchy because  is supposed to represent all instances of exceptions when the invocation of the method  1 occurs.The exceptions  11 and  12 are 's children because they are instances, which may propagate to .Similarly,  1 is a child of  and  21 ,  22 are the children of  1 .Note that here the exceptions  21 and  22 are supposed to be caught through the exception  1 , if it fails then through .The call exception hierarchy for a situation of method calls in Figures 2(a)(i)-2(a)(iii) is shown in Figure 2(a)(iv).

Nested try Blocks.
In Java, a try block can be nested within another try block and so on.In this case, the call exception hierarchy can be obtained as discussed below.All exceptions at outer try block are at the root.All exceptions at the next inner try blocks are the children of the root.Any exceptions in a try block at the next level are the children of exceptions at its upper try level and so on.We illustrate such a situation with an example.We consider a two-level nested try structure as shown in Figure 2(b).In Figure 2(b)(i) the method Main is supposed to catch the exception , which is at the outermost try block.Now, Main calls method  1 () at the innermost try block.The method  1 () may raise two exceptions, namely,  11 and  12 . 11 and  12 would be the successor of  1 , which is supposed to catch these two exceptions.In turn  1 would be the successor of .The call exception hierarchy of the program structure of Figures 2(b)(i) and 2(b)(ii) is shown in Figure 2(b)(iii).

Multiple catch
Blocks.There may be multiple catch blocks corresponding to a try block [19,20].In this case, all exceptions, which are supposed to be caught, would be placed as a single node and all exceptions, which are raised by a called method inside the try block, would be the children of this node.As an example, let us consider a simple try with multiple catch as shown in Figure 2(c).In Figure 2(c)(i), the method Main contains a try block and this try block is associated with three parallel catch blocks.These three catch blocks are corresponding to handle three different exceptions, namely,  1 ,  2 , and  3 .Further, the method Main() calls the method  1 (), which is supposed to throw the exceptions  11 and  12 (see Figure 2(c)(ii)).In this case, the exceptions  1 ,  2 , and  3 of the caller method Main is at the root and the exceptions  11 and  12 of the called method  1 () are the children of the exceptions  1 ,  2 , and (a) Call exception hierarchy with method calls (b) Call exception hierarchy with nested try blocks   [22] is a widely accepted and practical method to evaluate the quality of a test suite to test programs.Mutation testing is a fault-based testing adequacy criterion proposed by DeMillo et al. [23] initially with the name mutation analysis.Given a program , a set of alternative programs, say (), is considered in order to measure the test adequacy of a test suite .A test set  is adequate to  in relation to () if for each program  ∈ (), either  is equivalent to  or  differs from  on at least one test case  ∈  [24].A mutation testing framework is shown in Figure 3.In the context of mutation analysis some commonly known terminologies are mentioned below.

Mutant. A set of alternative programs 𝜙(𝑃) is called mutants of 𝑃. A mutant program 𝑄 ∈ 𝜙(𝑃) is different from
only on some simple syntactic changes.This is also alternatively called fault injection to .

Mutation
Operator.Mutation operator is a set of rules to decide syntactic changes in the program  to obtain mutants ().

Mutant Dead.
To assess the adequacy of a test set , each mutant  ∈ (), as well as the program , has to be executed against the test cases in .If the observed output of the mutant  is the same as that of  for all test cases in , then  is considered alive; otherwise it is considered dead or distinguished.

Equivalent Mutant.
Let  be the input domain of the test suite .A mutant  is called an equivalent mutant if ∀ ∈ , , and  produce the same results.Note that an equivalent mutant cannot be distinguished and should be discarded from the mutant set as it does not contribute to the adequacy of .

Mutation Score.
Test adequacy is measured by the mutation score (, ) as defined in where DM denotes the number of dead mutants of  for a test suite  and TM and EM are the total number of mutants in () and equivalent mutants, respectively.In summary, a low value of the mutation score implies either test suite unable to cover sufficient faults or there is less faults and vice versa.

Java Program Testing Tools.
Of late, Java programming has been extensively practiced in industries.A number of Java tools are available to support the Java practitioners.Two commonly used tools are JUnit [16,25] and Jumble [17,26].These two tools are used in this work.We introduce these tools briefly in the following.

JUnit. JUnit [16
] is an API framework and is used to automate unit and regression testing.Using JUnit, an entire class, part of a class, that is, a method or some interacting methods and interactions among several objects, can be tested.To test using JUnit, a tester class is required.The tester class contains more than one test case where each test case is written into one test method [25].The tester class also includes a test executor to run the test cases and methods to set up the state(s) of object(s) before and update the state(s) after the execution of each test case.
The advantages with JUnit are that it allows assertions for testing expected results, it has test features for sharing common data, and it helps to isolate and localize errors.The limitation with JUnit is that developers have to write test methods themselves, which requires a substantial amount of coding effort.Further, JUnit is designed to call methods and compare the results they return against expected results.This works for methods that return some results, but many methods instead of returning values have side effects, such as displaying output, modifying states of constituent objects, and modifying attributes' values.Also, JUnit cannot directly test private methods and not suitable for system or integration testing.

Jumble. Jumble
[17] is a mutation testing tool for Java programs, which interoperates with JUnit.Jumble takes a class to be mutation tested and a set of JUnit test classes as parameters.The output is the overall score of how many mutations are successfully caught as well as details about those mutations which are not.Jumble performs its mutations by directly modifying Java byte code using BCEL package [26].This allows the mutation testing to be done with no compilations.
The advantages with Jumble are that it mutates a program at the byte code level; hence, Jumble is faster and it can be used to test the programs even when the source code is not available.Moreover, Jumble uses a heuristic to improve its performance.Using the heuristic, it determines the order in which to run the test cases so that a test fails at a faster rate.It ensures that the longer test cases run only when there is no shorter test case to cover mutations.
The major limitation with Jumble is that it only provides mutations operators for conditional, arithmetic, initialization and assignment, expressions, return values, and switch statements [26].Jumble cannot discriminate boolean, short, and char data types because all these data types in byte code is represented as 32 bits integer.Further, Jumble uses strong mutation [26].Weak mutation is not possible with Jumble because if JUnit test case uses a value that causes a mutated expression to return a different value, there is no guarantee that the JUnit test case will detect that different value.

Mutation Operators
We consider eight mutation operators to create mutant programs [15].These mutation operators are listed in Table 1.There are two types of mutation operators: related to catch block and try block.These mutation operators are discussed in the following subsections.First, we discuss the proposed mutation operators to change in catch blocks.We then discuss the mutation operators related to alteration in try blocks.We refer to CEH as the call exception hierarchy of a Java program  in our discussions.

BI: Insertion in catch
Block.The purpose of the mutation operator catch block insertion BI is to catch all possible exceptions that might arise at a try block TB.In other words, if CB is the catch block associated with the try block TB, then BI tries to create mutant programs, which hide all exceptions in the try block TB.The mutation operator BI inserts catch blocks  1 ,  2 , . . .,   for all the exception parameter types  1 ,  2 , . . .,   where  1 ,  2 , . . .,   are the callee exceptions in the CEH for the exception at the try block TB.The operation of BI mutation operator is depicted in Figure 6.Since the mutation operator BI hides some exceptions to propagate upward, it may produce equivalent mutants.

RE: Catch and Rethrow Exception.
A situation that may arise in a program is that exception raised in a try block may not be propagated down the exception handling stack.To cover such a fault, the mutation operator called catch and rethrow exception and denoted by RE is proposed.The mutation operator RE for a catch block, say CB, associated with a try block, say TB, catches the exception type E of CB and rethrows the exception E inside the CB (see Figure 7, the operation of RE).
Rethrowing an exception using the mutation operator RE can be formally stated as Let  be the exception type at the catch block CB.Also, let  1 ,  2 , . . .,   be the callee exceptions of the exception E according to call exception hierarchy CEH.The mutation operator RE creates the mutant programs by inserting a throw statement to throw the exception   for each   ∈ ,  1 ,  2 , . . .,   .Note the difference between BI and RE.In BI, a catch block is inserted with an exception, whereas, in RE, it inserts a throw statement in the catch block to throw exception of callee exception type of the exception at catch block including itself.

TD: Deletion in try
Blocks.The mutation operator TD consists of two types of operators: method-level and classlevel mutation operators.Concepts of these operators are taken from [27].These operators are listed in Table 2.
The first three mutation operators in Table 2 are the method-level mutation operators and they modify Java For each e i  {E, E1, E2, E11, E12} expressions by deleting primitive operators in Java programming language [19].The rest of the mutation operators in Table 2 are the class-level mutation operators dealing with object-oriented features such as inheritance, polymorphisms, and dynamic binding.These operators are to modify declarations, modifiers, initializations, and so forth.A detailed description of these mutant operators can be found in [28].
The mutant operator TD can be mathematically stated as follows: where   is an altered statement of  after deleting one or more operator(s) or declaration(s).

TR: Replacement in try
Blocks.Like the mutation operator TD, the mutation operator TR consists of method-level and class-level mutation operators [27,28], which are listed in Table 3.As shown in Table 3, the first six mutation operators are to modify expressions by replacing some compatible Java primitive operators.The remaining mutation operators in Table 3 are to replace modifiers, assignments, initialization, and so forth [28].where   is an altered statement of  after replacing one or more operator(s) or declaration(s).

TI: Insertion in try
Blocks.Different mutation operators belonging to the proposed mutation operator TI are shown in Table 4.In Table 4, the mutation operators in first three rows are to modify expressions by inserting some compatible Java primitive operators.The rest of the operators in Table 4 are related to insertions of modifiers, assignments, initializations, and so forth [28].
The mutant operator TD can be mathematically stated as follows:   statements within try blocks.In the mutation operator TA, we propose to include some statements, which are outside try blocks, or move some statements outside try blocks.Figure 8(ii) shows the working of the mutation operator TA.In Figure 8(i),  1 is a Java program and there is a try block such that a variable, say , is initialized in the try block and it is referenced later outside the try block.Suppose that  is initialized with a null pointer.In that case, it may throw null pointer exception [29].We mutate the program  1 to   1 by including the statement of reference within the try block with the objective that whether the catch block corresponding to try block is able to catch the exception type which might raise due to the reference of .Here, the variable  is initialized and referenced within the try block and exception raised say due to null pointer assignment in statement marked as () may be caught in the catch block.Alternatively, let us consider the case of Java program , where a variable  is initialized and referenced in a try block.We apply the mutation operator TA to  to have a mutant program   such that the reference statement is moved from the try block and place it outside the try-catch block.The objective of this type of mutation is to check whether the exception raised may be propagated and catch in any caller exception or not.In the mutant program, it is now placed outside the try block and which is now beyond the scope of the catch block of the try block.
The mutant operator TA can be mathematically stated as follows: where   is an altered statement of  obtained after either keeping both declaration and reference of an object within the same try block if they were not together or declaration in the try block but its reference outside the try block, when they were originally together within a try block.

Mutation Analysis
In the last section, we have discussed the proposed mutation operators to test the effectiveness of test cases for testing exception handling constructs in Java.In this section, we discuss our analysis to evaluate the effectiveness of the proposed mutation operators.To do this, we have considered a number of Java programs.We then apply mutation operators to create a number of mutant programs for each Java program.A number of test cases which are used in our analysis is then discussed.All these steps are discussed in the following subsections.

Subject Programs.
In order to verify the effectiveness of our approach, we have carried out a number of experiments.In our experiments, we have considered five different types of subject programs from different application domains.The Java programs considered are: (i) library information systems (LIS): automating the regular routines in library management, (ii) cell phone system (CPS): designing hand-set services for mobile communications, (iii) trading house automation system (TAS): automating business processes of trading houses, (iv) conference management systems (CMS): automating various activities in conference organization, (v) vending automation system (VAS): automating vending processes.
The designs of LIS and CPS are followed from [30] and [31], respectively.The applications, namely, TAS and CMS, are designed in UML 2.0 by the students of postgraduate course (software engineering) in Computer Science and Engineering Department, Indian Institute of Technology Kharagpur [32,33].The UML models of the application VAS are taken from [34].We follow the designs from the above-mentioned sources and implemented them in Java.The implementation characteristics are summarized in Table 5.
The Java programs we have considered are neither very small nor very large, but of moderate sizes.In column 3 of Variable, say x is initialized in a try-block and later x is referenced in outside the try- block.
Variable, x is initialized and referenced within a try-block TA (i)

Mutant Programs.
In our mutation analysis, we have considered fault-based mutation analysis technique.For this, we have generated the mutant programs of the considered programs (in Table 5).The mutant programs are generated by seeding faults randomly to the programs based on a fault model.The fault model we have followed in our work is stated below.
(1) Catch block misses exception: the exception thrown in a try block does not match with the exception parameter type of the catch block associated with the try block.
(2) Catch block handles exceptions incorrectly: the body of a catch block, that is, the exception handling routine, is not proper to handle the exceptions.
(3) Catch block rethrows exceptions: catch block handles an exception and rethrows the same or another exception(s).
(4) Catch block catches exceptions: exception thrown matches with the exception parameter type in a catch block and does not perform any routine but avoids abnormal exit.
(5) Try block throws exceptions implicitly: due to faults in expression, keyword, declaration, initialization, and assignment, some exceptions may be generated implicitly.
(6) Try block misses or throws explicit exceptions: some exceptions are missed and thrown outside try block; some exceptions are thrown deliberately inside try block.
Based on the above fault model, we have applied the mutation operators as discussed in Section 3, and the number of mutant programs created for each programs is shown in Table 6.
We have also generated a number of mutant programs with Jumble [17,26].The mutant programs with Jumble for each sample program is shown in the last row of Table 6.According to the proposed mutation operators we create 149 mutant programs for LIS (see column 2, Table 6), 152 mutant programs for TAS (column 3, Table 6), 163 mutant programs for CPS (column 4, Table 6), 162 mutant programs for CMS (column 5, Table 6), and 131 mutant programs for VAS (column 6, Table 6).

Generating Test Cases.
To test the subject programs and their mutant versions, we have considered several test cases for each subject program.Generation of test cases is not the focus of this work.We have studied the existing test case generation approaches and followed an appropriate approach as discussed in the following.Structural testing techniques [35] develop test cases to cover various structural elements of a program such as control-flow, data-flow, branch, and path.Control-flow based structural testing criteria [36] use the flow of control in a program to generate test cases.Data-flow-based testing criteria [37][38][39][40] use the data-flow relationships to select the test cases.In branch testing [36,41], test cases are developed by considering inputs that cause certain branches in the program under test to be executed.Similarly, in path testing [42,43], test cases are generated to execute certain paths in programs.All the existing structural testing techniques, however, not necessarily cover new structural element such as exception handling constructs, all statements that raise exceptions, and those that catch exceptions.Please note that these criteria may be similar to the traditional coverage criteria [36] that require the coverage of statements or branches.Nevertheless, the criteria such as branch testing [41] have weak fault detection capabilities [44].As a consequence, all-throw, all-catch coverage criteria are not necessarily strong coverage criteria.In fact, this coverage criterion does not cover the various exceptional control flow paths [4].Sinha and Harrold [9] proposed a family of exception testing criteria to adequately test the behavior of exception handling constructs.Based on the proposed criteria [9], Sinha and Harrold [4] proposed a testing mechanism dealing with exception handling constructs.In [4], a technique has been proposed to construct control-flow graph representation of programs with explicit exception occurrences, that is, exceptions that are raised explicitly through throw statements and exception handling constructs.This control-flow representation is useful to trace various exceptional control flow paths and cover different types of exception that can be raised at a statement or the complex control and data interactions, both intra-and intermethods, that may have in the presence of exception handling constructs.In our work, we propose the test case generation scheme following the control flow representation of programs proposed in [4,9].From the control-flow representation, we can specify the paths to be tested; however, test data to exercise a path is a challenging task, particularly, for complex and large number of paths.The existing approaches of test data generation can be divided into three classes: random, static, and dynamic.Random test data generation is easy to automate but problematic [45].First, it produces a statistically insignificant sample of the possible paths through the program under test.Second, it may be expensive to generate the expected output data for the large amount of input data produced.Finally, given that exceptions occur only rarely, the input domain which causes an exception is likely to be small.Random test data generations may never hit on this small area of the input domain.
Static approaches to test data generation generally use symbolic execution.Many test data generation approaches presented in the literature use symbolic execution to obtain structural test data [46][47][48][49][50]. Symbolic execution works by traversing a control flow graph of the program under test and building up symbolic representations of the internal variables in terms of the input variables for the desired path.Branches within the code introduce constraints on the variables.Solutions to these constraints represent the desired test data.A number of problems exist with this approach.Using symbolic execution it is difficult to analyze recursion, array, and indices which depend on input data and some loop structures.Also, the problem of solving arbitrary constructs is known to be undecidable.
Dynamic test-data generation involves execution of the program under test and a directed search for test data that meets the desired criterion [51].Local search techniques only work effectively for linear continuous functions.Consequently, these techniques are likely to become stuck at a local optimum [52].DeMillo and Offutt [53] and Offutt et al. [54] proposed approaches for test data generation for mutation testing.The technique proposed in [53] is based on mutation analysis to create test data approximating the test adequacy.The technique is to automatically generate constraints and solve them to create test cases for unit testing.Another technique proposed in [54] is an extension of previous research [53] in constraint-based testing.This later method takes an initial set of values for each input and then refine the values through the control-flow graph of the program and resolve the path constraint dynamically.In this work, to generate the test data for test cases we follow the approach proposed in [54].

Results and Discussion
Test suites for each program considered in our work were generated as discussed in Section 4. Mutant programs for each program is also developed using the mutation operators discussed in Section 3. In this section, we discuss our experiments and result is obtained.Let  be the test suite for a program  and () its set of mutant programs.For each test case  ∈ , we execute the program  and all mutant programs  ∈ ().If the observed output of the mutant  is different than that of , then we increase the count of the number of mutants killed.This way, we calculate the total numbers of mutants killed by a given test suite .Further, we also calculate the equivalent mutants, such that two mutant programs  1 ∈ () and  2 ∈ () are not distinguishable as far as the output of the two is concerned.We determine whether a mutant  ∈ () is an equivalent mutant or not.To do this, we look through the semantic exception hierarchy (as discussed in Section 2.2).If the exception parameter type in any original catch block is a super class of all the derived types (according to Java exception hierarchy) in the mutant catch block, then we judge the mutant  to be an equivalent mutant.This is because the base type of exception can also accommodate all its subclass types.We also check if some mutants due to the mutation operators BD, BI, TD, TR, and TI are equivalent or not.
Our experimental results of mutation analysis with five considered subject programs are presented in Table 7.The number of mutants killed, equivalent mutants detected, and mutation score for each program and its number of test cases in test suite are shown in Table 7.It is observed that the number of mutants killed by Jumble with the mutant programs created by Jumble is on average 21.On the other hand, the number of mutants killed with mutant programs created by our proposed mutant operators is on average 87.It is also observed that mutant killed by Jumble is mainly related to logical, arithmetic, and conditional expression, whereas Advances in Software Engineering mutant killed with our approach is largely related to exception handling constructs.The performance of our mutation analysis is attributed in Figure 9. Figure 9 compares the mutant programs created, mutant killed, mutation points with exception handling constructs, and mutation score according to Jumble and our approach.
It may be noted that JUnit considers one module at a time.In contrast, we have followed the system testing approach.This is because the unit testing approach is not so effective to test an object-oriented program as multiple objects are in collaboration to solve a problem [55].Moreover, our hierarchy of call exception is not necessarily limited to a single class but rather distributed across several classes.As a consequence, we need to have access to all the relevant modules so that from the callee class we can determine the actual location from where an exception has been thrown and caught.With modular approach it cannot be determined.Hence, in our approach, we have considered the whole program, that is, a nonmodular analysis technique.We admit that modular approach is faster but the nonmodular analysis at the use case level is quite practical and usually followed in object-oriented software engineering development environment [56].Time Complexity.The running time complexities of both Jumble and our approach are (), where  is the number of exceptional handling constructs in a program.

Related Work and Comparison
Gallagher and Narasimhan [8] proposed an approach for testing exception handling constructs.They proposed structural analysis to select the effective test cases from a given set of test cases to test exception handling constructs in Java programs.In their structural analysis, the whole structure of a program under test is analyzed to retrieve all possible execution paths.They define a fitness function to measure the performances of test cases.All test cases are executed and then evaluated one by one and the high quality test cases are selected based on their fitness measures.
Ji et al. [15] proposed four mutation operators for Java exception handling constructs.They aimed to develop effective mutant programs based on those mutation operators.The major difference with the work of Ji et al. [15] and our work is that they proposed the mutation operators to test whether the Java exceptional handling constructs will be able to catch the exceptions or not whereas objective of our work is to test the adequacy of test suites through mutation analysis on Java exceptions.Further, in Ji et al. [15] work, they considered exceptions, which are raised implicitly, that is, calling Java library routines.On the other hand, in addition to implicit raise of exceptions, we consider the generation of exceptions explicitly using arithmetic and logical control statements.That is why we consider many more conventional mutation operators other than the mutation operators as proposed by Ji et al. [15].Moreover, to ensure that there is a sufficient number of exceptions raised, we have given extra effort to develop test cases accordingly, which is grossly ignored in the work of Ji et al. [15].More significantly, Ji et al. [15] adopted a trivial experiment with JUnit to test the effectiveness of their proposed mutation operators, that is, whether their proposed mutation operators really capable of causing mutant programs or not.It may be noted that JUnit tests a program at a unit level (i.e., one class at a time), which in fact can catch exceptions raised by the methods in that class only.But, in general, an exception can be raised from method(s) located not necessarily in the same class it is actually caught.Indeed, it is a difficult task to catch the exceptions unless we have a full tracking of all paths of exceptions from the point of cause of exception to the caller routine (and hence main class).This requires entire program to be taken into account rather than only a particular unit.Furthermore, in our approach, emphasize has been given to locate the cause of exception at any point on a path of execution.
Sinha and Harrold [9] described a class of test adequacy criteria that can be used to test the behavior of exception handling constructs.They present a subsumption hierarchy of the criteria and point out the relationship of the criteria to those found in traditional subsumption hierarchies.They also proposed techniques for generating the testing requirements for the criteria using some control flow representations.
Buhr [21] proposed some exception handling mechanisms in the context of developing rich language features for developing robust programs.They also discussed the exception propagation mechanism and proposed propagation models such as static, dynamic, and propagation.
Sinha and Harrold [4] extended their work reported in [9] to analyze and test programs with exception handling constructs.They proposed techniques to construct control-flow representations for Java programs with explicit exceptions occurrences.They used these representation to perform some analysis such as static and dynamic slicing, structural and regression testing, and dynamic execution profiling.
Tracey et al. [6] proposed an optimization technique for automatically generating test data to test exceptions.They considered Ada as the model language in their approach.The proposed approach is based on the application of a dynamic global optimization based search for the required test data.
Adamopoulos et al. [57] reported on the cause of equivalent mutants.Offutt and Pan [58] proposed a technique to detect equivalent mutants and infeasible paths.
Andrews et al. [14] made a thorough investigation of a fundamental assumption that has been underlying much of experimental software testing research that whether faults generated by hand or from mutation operators is representative of real faults.They observed that the use of mutation operators is able to yield trustworthy results; that is, generated mutants are similar to real faults.Mutants appear, however, to be different from hand seeded faults that seem to be harder to detect than real faults.
Ma et al. [27] introduced a number of mutation operators to create mutant programs in the context of Java programming language.They propose a tool for entire mutation process and testing [28].The mutant operators proposed in [27] only modify expressions by replacing, deleting, and inserting primitive features of Java programming language at methodlevel and object-oriented specific features such as inheritance, polymorphisms, and dynamic binding at class-level.However, Ma et al. did not consider any mutation operators to handle exceptions related faults.
Work of Gallagher and Narasimhan [8] and Sinha and Harrold [4] followed static analysis and their approaches not necessarily locate all exception points, particularly those exceptions raised implicitly.For example, an exception can be raised implicitly from calling Java library routine.As a consequence, it is very difficult to draw control flow representations or path identification to cover all problems.Hence, test case selection according to these approach may not be adequate.The proposed method, on the other hand, does not determine exception paths explicitly.We attempt to change exception propagation path according to the characteristic of Java exception handling constructs.
Jumble provides mutation operators for arithmetic expression, conditional predicate, initialization, assignment, return values, and control constructs such as if-then, if-thenelse, switch, and loop.It is to be noted that the mutation operators according to Jumble are not sufficient enough for exception handling constructs.

Conclusions
Exception handling is an important mechanism to develop robust and reliable programs.It is a difficult task to test whether all exception points are covered and all exception handler routines are arranged appropriately or not.It is also not possible to identify all exception paths precisely because there are some exceptions which can be raised implicitly.This paper proposes a number of mutation operators to create mutant programs.With these mutant programs, we verify the effectiveness of a given test suite, particularly to verify the exception handling constructs.In other words, mutation operators used in this paper can generate effective mutant programs which can raise and handle different type of exceptions.The test suite which can kill more mutant programs is with a higher mutation score.Effectiveness of the proposed mutation operators is comparable to that of Jumble.Jumble also reports the quantity of mutants killed as the score of a test suite.Jumble provides mutations operators, which are mainly limited to arithmetic expressions, conditions, return values, and control statements such as decision and loop.The main limitation in Jumble is that there is no explicit mutation operators in Jumble that can take care exception handling constructs.Our experiments with five different programs substantiate that the proposed mutation operators are 69% (on average, mutation score in Jumble and our approach is 27 and 87, resp.)more effective to build mutants and then kill the mutant programs than the mutation analysis technique in Jumble.Nevertheless, this result is based on experiments with moderate sized Java programs from different application domains and can be taken as indicative.To have conclusive decision we should go for more experiments with more subjects.
Using the proposed mutation operators and mutation analysis method, our work can be further extended to guide automatic synthesis of test cases for testing exception handling constructs.Further, the mutation operators are proposed considering Java as the model language.We can extend the approach for other advanced programming languages.

Figure 4
Figure 4  explains the operation of the mutation operator BD.If there are more than one catch block, then it can delete in an arbitrary way one or more catch block(s).The objective of this mutation operator is to alter the exception propagation path.When an exception, say , is thrown in TB, the mutant program with BD should not handle the exception  appropriately because of the absence of CB.As
. . .//Guarded block, . . .//where exception can . . .//be raised In other words, all exceptions except the exception(s) at the root of a call exception hierarchy are callee exceptions.Direct Caller Exception.In CEH, if an exception   is the immediate predecessor of another exception   , then the exception   is called the direct caller exception.Direct Callee Exception.In CEH, if an exception   is the immediate successor of another exception   , then the exception   is called the direct callee exception.
Caller Exception.An exception  in a CEH for a program  is called the caller exception if it is a parent of any other exception   ∈ .In other words, all exceptions except at the leaf of call exception hierarchy are the caller exceptions.Callee Exception.An exception  in a CEH for a program  is called the callee exception if it is a child of any other exception   ∈ .

Table 1 :
Exception handling related mutation operators.
If the CB is at the root node in the CEH, then BR replaces the exception parameter type of CB with that of DCE, where DCE denotes the direct callee exception of the exception of CB.
• • }Figure 4: Mutation operator BD.a consequence, the exception raised at TB should be back propagated to the caller exception, if any in the CEH.The exception  then may be handled at an upper level if the exception type of  matches with some other exception at upper level.It may be noted that the original program and a mutant version may cause same exception meeting some reachability at the try block TB.In that case, deleting the whole catch block CB would not produce any distinctions between the two programs for a test case.Hence, this operator may produce equivalent mutants.3.2.BR:Replacement of catch Block.The mutation operator BR is proposed to cover faults such that a program does not handle exception correctly.Let CB be the catch block to be altered.The mutation operator BR attempts to deviate from the exception propagation path.The mutation operator BR creates mutant program(s) depending on the level of the occurrence of the catch block CB.Also, see Figure5, which states the three different levels of CBs and their possible mutants.Three rules are to be followed.Rule 1. Rule 2. If the CB is at any leaf node in the CEH, then BR replaces the exception parameter type of CB with that of DPE, where DPE denotes the direct caller exception of the exception of CB.Rule 3. If the CB is at an intermediate level, that is, neither at the root nor at leaf of the CEH, then CBR replicates the catch block CB into two blocks CB1 and CB2, such that BR replaces

Table 5 ,
the numerator indicates the number of entity and boundary classes and the denominator indicates the number of modal classes also called controller classes (classes which exhibit distinct behavior in different states).The numbers of total try blocks, catch blocks are shown in columns 4 and 5 of Table5, respectively.The number of exceptions thrown in Java methods, which are not within the scope of try block, is shown in column 6 of Table5.

Table 5 :
Characteristics of subject programs.

Table 7 :
Results of mutation analysis.