Patent Publication Number: US-11023368-B1

Title: Reduction of testing space for system testing infrastructure using combinatorics

Description:
BACKGROUND 
     The present invention relates to testing of a computer program and, more specifically, reduction of test case infrastructure. 
     Computerized devices control almost every aspect of our life—from writing documents to controlling traffic lights. However, newly designed computerized devices are often error-prone, and thus require a testing phase in which the errors are discovered and corrected. The testing phase is considered one of the most difficult tasks in designing a computerized device. Thorough testing is important, as the cost of not discovering an error may be enormous depending on how the computerized device is utilized. Coverage tools for checking software provide a measure of how well the software being evaluated has been exercised during testing and thereby give a level of assurance that the software is of high quality. 
     SUMMARY 
     According to one or more embodiments of the present invention, a method for detecting and localizing a fault in a system under test (SUT) includes modeling inputs to the SUT as a collection of attribute-value pairs. The method further includes reducing a Cartesian product space comprising all possible combinations of the attribute-value pairs to a reduced test space at least in part by excluding one or more combinations of attribute-value pairs that are not in a predetermined sequential order of attributes. The method further includes generating an initial set of test vectors that provides complete n-wise coverage of the reduced test space. The method further includes generating an initial set of test cases from the initial set of test vectors. The method further includes executing the initial set of test cases to obtain a first set of execution results. The method further includes determining, based at least in part on the first set of execution results, that one or more test cases failed execution. The method further includes generating a set of new test cases from a selected failing test case, wherein generating the set of new test cases comprises generating, in relation to each attribute in the selected failing test case, a respective subset of new test cases at least in part by changing a respective attribute value for the attribute in the selected failing test case to each other candidate attribute value for the attribute that is not present in any of the one or more test cases that failed execution. The method further includes executing the set of new test cases to obtain a second set of execution results. The method further includes detecting and localizing the fault based at least in part on the second set of execution results. 
     The technical solutions can also be implemented by a system, a computer program product, an apparatus, a machine, a device, or in other practical applications in one or more embodiments of the present invention. 
     Additional technical features and benefits are realized through the techniques of the present invention. Embodiments and aspects of the invention are described in detail herein and are considered a part of the claimed subject matter. For a better understanding, refer to the detailed description and to the drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The specifics of the exclusive rights described herein are particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The foregoing and other features and advantages of the embodiments of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which: 
         FIG. 1  shows a schematic illustration of a computerized environment in accordance with one or more embodiments of the present invention; 
         FIG. 2  is a block diagram representing modules providing a testing infrastructure according to an embodiment of the present invention; 
         FIG. 3  is a schematic hybrid data flow/block diagram illustrating fault detection and localization using combinatorics test design (CTD) and generation of a regression bucket of failing test cases that expose a detected fault in accordance with one or more example embodiments of the present invention; 
         FIG. 4  depicts an example set of CTD vectors according to one or more embodiments of the present invention; 
         FIG. 5  depicts an example CTD vector according to one or more embodiments of the present invention; 
         FIG. 6  is a process flow diagram of an illustrative method for detecting and localizing an n-wise fault using CTD techniques and generating a regression bucket of failing test cases that expose the detected n-wise fault in accordance with one or more example embodiments of the present invention; 
         FIG. 7  depicts a flowchart for providing a deterministic order of tests to run for the system under test in the testing infrastructure according to one or more embodiments of the present invention; and 
         FIG. 8  depicts a computer system according to one or more embodiments of the present invention. 
     
    
    
     The diagrams depicted herein are illustrative. There can be many variations to the diagrams or the operations described therein without departing from the spirit of the invention. For instance, the actions can be performed in a differing order or actions can be added, deleted or modified. Also, the term “coupled” and variations thereof describe having a communications path between two elements and do not imply a direct connection between the elements with no intervening elements/connections between them. All of these variations are considered a part of the specification. 
     DETAILED DESCRIPTION 
     Exemplary embodiments of the present invention relate to, among other things, devices, systems, methods, computer-readable media, techniques, and methodologies for performing fault detection and localization using combinatorial test design (CTD) techniques and for generating a regression bucket of test cases that expose the detected fault. In exemplary embodiments of the present invention, the detected and localized fault occurs in a system under test (SUT). The SUT may be a hardware system or a software system. Further, in exemplary embodiments of the present invention, the fault detection and localization may be performed while adhering to architectural restrictions on the SUT. 
     Additionally, coverage tools for testing the SUT provide a measure of how well the SUT has been exercised during testing and thereby give a level of assurance that the SUT is of high quality. There are a number of types of coverage known in the art, such as statement coverage, line coverage, condition coverage, path coverage, method coverage, and the like. One additional coverage method is functional coverage. Functional coverage is designed to measure an amount, portion or similar metric of tests that examined predetermined functional behaviors. Once functional coverage is measured, quality assurance (QA) personnel may design additional tests to examine untested behaviors. 
     However, test infrastructure can become incredibly expensive and cost per test cycle increases without continuous optimization of products, tests, and environments. As more tests are added, more test suites are run, and the complexity of the supporting services increases along with the cost of each test cycle. Test environments, test dependencies, and test suites need to be managed with the same rigor as the product being shipped (i.e., the SUT). Accordingly, managing the test infrastructure is a technical challenge, and in turn, efficient reduction of the test infrastructure is a technical challenge. It should be noted that the reduction of the test infrastructure does not imply a reduction in quality of testing the SUT. Rather, the technical challenge is that the quality of the tests is to be improved along with the reduction in the test infrastructure. 
     Embodiments of the present invention address such technical challenges. According to one or more embodiments of the present invention, a reduced set of test cases for a SUT are executed on the system. It should be noted that the system is different than the SUT; the SUT is being executed using the system. The reduced set of test cases can be generated using combinatorics test designing (CTD). Errors can be identified based on a subset of tests that fail from that reduced set. Further, according to one or more embodiments of the present invention, inverse CTD is used to localize the fault in the system. 
     According to one or more embodiments of the present invention, CTD is performed with respect to an interaction requirement, such as a pair-wise interaction, n-tuple interaction, or any other. The test plan may provide for sufficient coverage tasks that assure that the interaction requirement is fulfilled. In some exemplary embodiments, test planning is based on a modeling of the test space using a functional coverage model. The test space can represent inputs, scenarios, configurations, the application&#39;s internal state, or any other aspect that might need to be tested. The functional coverage model may include a set of functional attributes. In other embodiments of the present invention, the coverage model can include one from a number of types of coverage known in the art, such as statement coverage, line coverage, condition coverage, path coverage, method coverage, and the like. The type of coverage does not affect reduction of the test infrastructure techniques described herein. 
     Further, with respect to test planning, a test-space may define potential tests that may be executed on the SUT. A test can be associated with exactly one potential test, as opposed to coverage tasks. In some exemplary embodiments of the present invention, several different tests may hold the same potential test. 
     In some exemplary embodiments of the present invention, the motivation for the approach of CTD is that most errors depend on the interaction between a small number of functional attributes. CTD algorithms may also deal with scalability issues. The CTD algorithms may assume that the combinations space is too large to be represented explicitly, and they use various techniques to try to generate an optimized test plan without explicitly enumerating all possible combinations. Examples of such algorithms may be a reduction to the orthogonal arrays or covering array problems. Those techniques are limited in the type of restrictions they allow on the value combinations, or in the type of requested interaction level, and still hit scalability issues as the number of model variables increases. 
     In example embodiments of the present invention, inputs to a SUT are modeled as a collection of attribute-value pairs. More specifically, inputs to a SUT can be modeled as a collection of attributes, each of which can take on one or more corresponding attribute values. In example embodiments of the present invention, the entire Cartesian product space that contains all possible combinations of attribute-value pairs can be reduced to a smaller set of test vectors that provides complete n-wise coverage of the entire test space. For instance, if it is assumed that four different attributes A, B, C, and D are modeled, and if it is further assumed that attribute A can take on four distinct values; attribute B can take on three distinct values; attribute C can take on three distinct values; and attribute D can take on two distinct values, then the total number of possible combinations of attribute-value pairs would be 4*3*3*2=72. Thus, in this illustrative example, the entire Cartesian product space would include 72 different combinations of attribute-value pairs. As previously noted, these 72 different combinations of attribute-value pairs can be reduced down to a smaller set of combinations that still provide complete n-wise coverage of the Cartesian product space. For instance, referring to the same example introduced above, if complete pairwise coverage is sought, then the 72 different combinations can be reduced down to 12 distinct combinations that together include every possible pairwise interaction of attribute values. The reduced number of combinations required to provide n-wise coverage may increase logarithmically as n increases. 
     In exemplary embodiments of the present invention, the entire Cartesian product space including all combinations of attribute-value pairs is reduced down to a smaller set of CTD test vectors that provides complete n-wise coverage for a desired n. In complex hardware or software systems, the total number of attributes and corresponding candidate attribute values may be quite large, in which case, the total number of possible combinations of attribute values making up the entire Cartesian product space may be astronomically large, making it practically infeasible to test all possible combinations. Reduction of the entire Cartesian product space down to a substantially smaller number of CTD test vectors that still provide complete n-wise coverage allows for any n-wise (or m-wise where m&lt;n) fault to be detected without having to directly test every possible combination in the test space. 
     In exemplary embodiments of the present invention, a binary decision diagram or the like may be used to perform the reduction and identify the reduced set of CTD vectors that provides complete n-wise coverage. In example embodiments of the present invention, each CTD test vector that is generated includes a unique combination of attribute values, and the set of CTD test vectors together include every possible n-wise interaction of attribute values. In particular, each CTD vector may have a dimension corresponding to the number of attributes that are modeled, where each element of the CTD vector is a respective attribute value for a corresponding attribute. The set of CTD vectors that is generated, however, may not be unique. That is, there may be multiple different sets of CTD vectors, each of which provides complete n-wise coverage. In example embodiments of the present invention, the CTD vectors may be chosen at random while still ensuring complete n-wise coverage. In other example embodiments, the initial set of CTD vectors may be chosen with specific criteria in mind such as, for example, to increase or decrease the representation of particular attribute values within the set of CTD vectors. 
     In exemplary embodiments of the present invention, once the initial set of CTD test vectors are generated, they are used to generate a corresponding set of test cases. For instance, the set of CTD test vectors may be provided as input to a test case generation tool configured to generate a respective corresponding test case for each CTD vector. Each test case may be designed to test the interactions among the particular combination of attribute values contained in the corresponding CTD vector. 
     In exemplary embodiments of the present invention, the test cases are then executed. The execution of each test case results in either a successful execution result, indicating that the combination of attribute values associated with the test case does not contain an n-wise (or m-wise where m&lt;n) error, or a failure execution result, indicating that the combination of attribute values associated with the test case do contain an n-wise (or m-wise where m&lt;n) error. In example embodiments of the present invention, a particular failing test case is then selected and inverse combinatorics is applied to the failing test case to produce a new set of test cases capable of exposing the bug. In exemplary embodiments of the present invention, application of inverse combinatorics to the selected failing test case includes generating a respective new test case with respect to each attribute. Thus, the number of new test cases generated may be equal to the number of attributes. In exemplary embodiments of the present invention, in each new test case, the attribute value of a corresponding attribute in the selected failing test case is changed to an attribute value for that attribute that is not present in any failing test case and the respective attribute value for each other attribute is unchanged from that which is present in the selected failing test case. 
     Those new test case(s) that yield a successful execution result may then be assessed to detect and localize the n-wise (or m-wise where m&lt;n) error. In particular, the specific attribute-value pairs that cause the error may be identified based on those new test cases that successfully execute. A regression bucket of test cases may then be generated based on the error-producing combination of attribute-value pairs. More specifically, every possible combination of attribute values that include the attribute values determined to cause the error may be determined and a regression bucket of corresponding test cases for testing these combinations can be outputted for use by a manual tester, for example. In particular, In example embodiments of the present invention, all test cases contained in the regression bucket will fail when executed until the bug is fixed, after which all regression bucket test cases should pass (i.e., produce a successful execution result). 
     In exemplary embodiments of the present invention, architectural restrictions may apply to the SUT. Architectural restrictions may include any of a variety of restrictions on inputs to the SUT. For instance, an example restriction may be that if a given attribute has a particular attribute value, then one or more other attributes are excluded from having certain attribute value(s). Another example architectural restriction may be that if a given attribute has a particular attribute value, then one or more other attributes must have certain attribute value(s). Yet another example architectural restriction may be that a new attribute is introduced if and only if a particular attribute has a particular attribute value. It should be appreciated that the above examples of architectural restrictions are merely illustrative and not exhaustive. 
     In exemplary embodiments of the present invention, architectural restrictions are taken into account prior to performing the reduction of the entire Cartesian space down to the initial set of CTD vectors that provides the desired complete n-wise coverage. That is, in exemplary embodiments of the present invention, particular combinations of attribute values that violate any architectural restrictions are first excluded from the Cartesian product space, and then the reduction down to the set of CTD vectors that provides complete desired n-wise coverage is performed. In this manner, it can be ensured that no combination of attribute values that violates an architectural restriction is included in the initial set of CTD vectors. Further, In exemplary embodiments of the present invention, when a selected test case corresponding to an initial CTD vector fails and is selected for expansion to obtain a set of new test cases designed to detect and localize an n-wise error, that expansion can be performed first without taking into account any architectural restrictions. Then, any new test cases that violate an architectural restriction can be excluded. In this manner, it can be ensured that the expansion provides as much coverage of the test space in the neighborhood around the failing test case as possible. In addition, in exemplary embodiments of the present invention, the regression bucket of failing test cases may first be generated without regards to architectural restrictions, and then any test cases that violate an architectural restriction can be excluded from the regression bucket. That is, test cases corresponding to all possible combinations in the entire Cartesian product test space that include the particular combination of attribute values causing an n-wise or lesser order error may first be generated and then reduced down to exclude any test case(s) that violate a restriction. Alternatively, the test cases included in the regression bucket may be selected from the reduced Cartesian space from which the initial set of CTD vectors are selected, in which case, the regression bucket is generated to include only those combinations of attribute values that include the subset of attribute values causing the error and that do not violate any architectural restriction. 
     Example embodiments of the invention include various technical features that yield technical effects that provide various improvements to computer technology. For instance, exemplary embodiments of the invention include the technical feature of inverse combinatorics to expand a set of test cases from a selected failing test case. This technical feature allows for an n-wise or lesser order fault to be detected and localized within a single iteration of the expansion. This technical effect represents an improvement to debugging and fault detection computer technology because it automates the creation of additional test cases around a selected failing test case in a manner that is specifically designed to facilitate detection and localization of a fault. Thus, the automated generation of new test cases in accordance with example embodiments of the invention is capable of exposing a fault more efficiently and using a fundamentally different methodology than manual test case generation. Exemplary embodiments of the invention also include the technical feature of generating a regression bucket of test cases that tests every possible combination of attribute values that includes the particular subset of attribute values causing the n-wise fault. Thus, the regression bucket includes only test cases that would all fail prior to correction of the fault and that would all pass after correction of the fault. Thus, the automated generation of a regression bucket of failing test cases in accordance with example embodiments of the invention provides an improvement to computer technology by providing a tester or automated testing algorithm with a set of test cases—each of which is ensured to fail—such that the tester or automated testing algorithm can use the regression bucket of test cases to verify that a fault has been corrected when all test cases ultimately pass after debugging is performed. 
     A technical challenge with using tests generated using CTD is in the case of generating test programs that require a particular order of operations of actions to be performed on the SUT. In this case, it is a technical challenge to reduce the testing space using the present CTD technology. For example, consider that the following actions (A, B, and C) can occur in any order on the SUT and that a test requires to have a set of breakpoints within each action to occur before the next action takes place: 
     Action A&lt;runToCompletion, StopBkpt1, StopBkpt2, StopBkpt3&gt; 
     Action B&lt;runToCompletion, StopBkpt4, StopBkpt5&gt; 
     Action C&lt;runToCompletion, StopBkpt6&gt; 
     Here, each of the actions A, B, and C, can be an operation that can be performed by/on the SUT. Each action can be associated with at least one attribute and particular value(s) can be assigned to the attribute(s) for each test. Based on the assigned value(s) a desired result is expected off the test. If the desired result is obtained the test is considered to pass, and otherwise the test is considered to fail. For example, the action A can be associated with an attribute A-a that is assigned a value a1 in a first test, a2 in a second test, and so on. The value assigned to A-a can be different in each test. The values of a1, a2, etc. are specified, for example, a1=runToCompletion, a2=StopBkpt1, a3=StopBkpt2 and a4=StopBkpt3. 
     Now, referring to the actions A, B, and C, above, consider any of the following orders of operations of the actions is what is required for a test of the SUT: ABC, ACB, BAC, BCA, CAB, and CBA. In any of these orders of operations, if the any of the actions does not run to completion, rather stops at a breakpoint, and then runs to completion only after another action(s) has/have taken place, the orders of operations may be like the following four examples: 
     1. A&lt;StopBkpt1&gt;-B&lt;runToCompletion&gt;-A&lt;runToCompletion&gt;-C&lt;runToCompletion&gt;; 
     2. A&lt;StopBkpt1&gt;-B&lt;runToCompletion&gt;-C&lt;runToCompletion&gt;-A&lt;runToCompletion&gt;; 
     3. A&lt;StopBkpt1&gt;-B&lt;runToCompletion&gt;-A&lt;StopBkpt3&gt;-C&lt;runToCompletion&gt;-A&lt;runToCompletion&gt;; and 
     4. A&lt;StopBkpt2&gt;-B&lt;StopBkpt4&gt;-A&lt;runToCompletion&gt;-C&lt;StopBkpt6&gt;-B&lt;runToCompletion&gt;-C&lt;runToCompletion&gt;. 
     Given the present CTD technology of identifying attribute/value pairs to be used in combinatorial reduction, the present CTD based test infrastructure makes multiple models to cover each case of a particular order of operations. Here, one model has to be created for the order of actions themselves and then a separate second model has to represent the execution state of each action (i.e., values assigned to the attributes). Further, the models have to be overlaid in order to identify the testing space that is to be used. Not only is this time consuming, but it is also error prone. 
     Embodiments of the present invention address such technical challenges. According to one or more embodiments of the present invention the technical challenges are addressed by identifying the attributes that require tests with a particular order of operations, and further identifying restrictions (for example, Action A must occur before Action B). Further yet, a full Cartesian product of the unique values of the attributes is determined. A combinatorial reduction and test case abatement is then applied to the set of tests using the Cartesian product to remove any redundant tests. In one or more embodiments of the present invention, identifying the attributes and the restrictions and creating the Cartesian product can be performed in a single step, i.e., using a single model. 
     In one or more embodiments of the present invention, the information about the ordering can be stored using a Markov chain that is used as a payload into the system that is performing CTD reduction and expansion to generate the test programs for the SUT. A Markov chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. 
     Referring now to  FIG. 1 , which shows a schematic illustration of a computerized environment in accordance with embodiments of the present invention. A computerized environment  100  may include one or more computerized tools. It should be noted that the depiction is one possible example of a block diagram and that some components may not be depicted for clarity. 
     In one or more embodiments of the present invention, a user  110 , such as a developer, a QA staff member, a tester, a designer, a verification engineer or the like, may interact with the computerized environment  100 . The user  110  may utilize a man-machine interface (MMI)  112  such as a terminal, a display, a keyboard, an input device or the like. 
     In some exemplary embodiments of the present invention, a coverage model defining tool  102  may be utilized to define the test coverage model, such as a functional coverage model, or the like. In some exemplary embodiments of the present invention, the user  110  may define the attributes that are to be tested, for example, the functional attributes in case a functional coverage is being tested. In some exemplary embodiments of the present invention, a similar tool may be utilized to define a test-space. In some exemplary embodiments, the coverage model may be adapted to be utilized as a test model. 
     In some exemplary embodiments of the present invention, a test execution engine  108  may be utilized to test the SUT. It will be noted that the SUT may be hardware, firmware, software, combination thereof, or any other type of computerized device. The test execution engine  108  may be a simulation-based verification tool, a test-generation platform, or the like. The test execution engine  108  may be operatively coupled to a test planning tool  106  and configured to perform testing in accordance with the test plan. In some exemplary embodiments, the test planning tool  106  may provide the tests for the test execution engine  108  to perform. It will be noted that dynamic verification is a broader concept than testing the SUT, and it further includes test planning, coverage analysis and the like. The test execution engine  108  provides only one aspect of the entire scope of operations that may be performed during dynamic verification and should not be used to construe the term “dynamic verification” narrowly. 
     In some exemplary embodiments of the present invention, a coverage analysis tool  104  is configured to measure coverage of the test space for the SUT based on the dynamic verification performed by the test execution engine  108 . For example, the coverage analysis tool  104  can be a functional coverage analysis tool. The coverage analysis tool  104  provides a coverage measurement, such as a portion of the coverage test-space or of the defined test plan, indicative of coverage tasks that were covered during dynamic verification performed by the test execution engine  108 . The user  110  may review the coverage measurement and/or the list of covered tasks. 
     In some exemplary embodiments of the present invention, a test planning tool  106  may define a test plan to be covered. In some exemplary embodiments of the present invention, the test plan may be a set of coverage tasks to be covered. In some exemplary embodiments of the present invention, the test plan tool  106  may provide tests that are likely to cover the test plan, such as based on a test benchmark stored in a datastore which includes tests that are known/estimated to cover specific aspects of the SUT. As another example, the test plan tool  106  is configured to generate tests so as to cover coverage tasks. The user  110  may review the test plan, the selected test or the like. In some exemplary embodiments of the present invention, the user  110  may provide parameters for the test planning tool  106  to use in determining the objective of the test plan, such as a desired interaction level. Embodiments of the present invention enable the elimination of any redundancy in the generated tests. 
     While the depiction in  FIG. 1  has been described with specific components including the coverage model defining tool  102 , coverage analysis tool  104 , test planning tool  106  and the test execution engine  108 , embodiments of the present invention are not limited to these components or system configurations and can be implemented with other system configuration employing fewer or additional components. 
       FIG. 2  is a block diagram representing modules providing a testing infrastructure according to an embodiment of the invention. More specifically, the infrastructure includes a test generator  208 . The test generator  208  accesses a test infrastructure, such as a repository of test cases  202 , which stores suites of test cases available to verify the correctness of the SUT  214 . Each test case specifies an input to be applied to the SUT  214  and the expected response that should be returned in response to this input (to indicate its correct operation). Typically, the test cases are organized into sets (test suites), for example, each test suite for a different component of the SUT  214 . 
     The test generator  208  creates an execution bucket for each run of the test on the SUT  214 . The bucket specifies the operations to be performed for running the desired test cases in a machine-readable language (such as XML-based). Particularly, in the case of a complete test, all the available test cases are executed on each component of the SUT  214 ; conversely, in the case of a regression test, the execution is limited to a subset of selected test cases. The bucket so obtained can be saved into a file. 
     The test generator  208  receives the event ordering information  220  according to one or more embodiments of the present invention. The event ordering information  220  indicates a particular order for a set of attributes/operations as described herein. For example, the event ordering information  220  indicates a predetermined sequential order in which attributes are to be tested. The event ordering information  220  can be provided in the form of a Markov chain in one or more embodiments of the present invention. The test generator  208  orders the tests in the bucket  212  based on the event ordering information  220 . 
     A test execution engine  108  controls the execution of the bucket read from the file. For each test case of the bucket, this involves the application of the corresponding input to the SUT  214 . In response thereto, the SUT  214  returns a corresponding output to the test execution engine  108 . The test execution engine  108  determines the result of the test case by comparing its output with the corresponding expected response (extracted from the file, for example). The result of the test case (i.e., positive when the two values match and negative otherwise) is saved into a log. For example, this may be achieved by means of a standard Test Tracking Tool (TTT). The results of the (current) run of the test are available in the log for their analysis. 
     For a large, complex SUT  214 , the test case infrastructure  202  can contain a large amount of duplicate test actions/test cases. In accordance with certain embodiments of the present invention, one technique developed to address these challenges incorporates the use of a fingerprint repository  206  with a store of information including a set of fingerprints that correspond to a plurality of regression tests stored in the test repository  202 . In one embodiment, the fingerprints are generated by a fingerprint generator  204 . For instance, the fingerprint repository  206  can include fingerprints of most, if not all, of the tests stored in the test repository  202  and a reference to where copies of the test are located throughout the test infrastructure, similar to an index in a book. Each fingerprint uniquely identifies a specific code path covered by a corresponding test case. In this manner, the system can identify fingerprints (and corresponding tests) that are redundant, and in some cases duplicate. 
     According to embodiments of the present invention, processing of the results  216  of the regression tests generated by the test generator  208  and executed by the test execution engine  108  may include determination of a code path traversed during execution of each generated regression test and generation of a fingerprint for each executed regression test based at least in part on the code path. In some embodiments of the present invention, these steps may be performed by the fingerprint generator  204 . 
     A redundancy analyzer  218  compares fingerprints corresponding to all test cases generated by the test generator  208  to a plurality of fingerprints stored in the fingerprint repository  206 . The redundancy analyzer  218  provides a list of the regression test cases generated by the test generator  208  that have matching fingerprints with one or more fingerprints stored in the fingerprint repository  206 . This information is used to select and discard the duplicate test cases from the test repository  202  (as described below). 
       FIG. 3  is a schematic hybrid data flow/block diagram illustrating fault detection and localization using CTD techniques and generation of a regression bucket of failing test cases that expose a detected fault in accordance with one or more example embodiments of the invention.  FIG. 6  is a process flow diagram of an illustrative method  600  for detecting and localizing an n-wise fault using CTD techniques and generating a regression bucket of failing test cases that expose the detected n-wise fault in accordance with one or more example embodiments of the invention.  FIG. 6  is described in conjunction with  FIGS. 1, 2, and 3 . 
     Illustrative methods in accordance with example embodiments of the invention and corresponding data structures (e.g., modules, units, and other such components) for performing the methods are now described. It should be noted that each operation of the method  600  depicted in  FIG. 6  and/or the method  700  depicted in  FIG. 7  may be performed by one or more of the modules or the like described herein. These modules may be implemented in any combination of hardware, software, and/or firmware as described herein. In certain example embodiments, one or more of these modules may be implemented, at least in part, as software and/or firmware modules that include computer-executable instructions that when executed by a processing circuit cause one or more operations to be performed. A system or device described herein as being configured to implement example embodiments may include one or more processing circuits, each of which may include one or more processing units or nodes. Computer-executable instructions may include computer-executable program code that when executed by a processing unit may cause input data contained in or referenced by the computer-executable program code to be accessed and processed to yield output data. 
     Referring to  FIG. 6  in conjunction with  FIG. 3 , in example embodiments of the present invention, at block  602  of the method  600 , inputs to the SUT  214  are modeled as a collection of attribute value pairs  302 . Any number of attributes may be used to model SUT inputs and each attribute may take on any number of candidate attribute values. At block  604 , computer-executable instructions of one or more n-wise coverage CTD vector generation modules  304  are executed to generate an initial set of CTD vectors  306  that provides n-wise coverage of an entire Cartesian product space associated with the collection of attribute-value pairs  302 . 
     In particular, the entire Cartesian product space that contains all possible combinations of the attribute-value pairs  302  is reduced to a smaller set of CTD test vectors  306  that provides complete n-wise coverage of the entire test space. In example embodiments of the present invention, the complete n-wise coverage provided by the set of CTD vectors  306  may be complete pairwise coverage. For instance, if it is assumed that three attributes are modeled, namely, a “name” attribute, a “color” attribute, and a “shape” attribute as shown in  FIG. 4 , and if it is further assumed that the “name” attribute can take on 4 distinct attributes (Dale, Rachel, Andrew, and Ryan), the “color” attribute can take on 2 distinct attributes (green, blue), and the “shape” attribute can take on 3 distinct attributes (circle, square, triangle), then the total number of possible combinations of attribute-value pairs would be 4*3*2=24. Thus, in this illustrative example, the entire Cartesian product space would include 24 different combinations of attribute-value pairs. 
     The 24 different combinations of attribute-value pairs can be reduced down to a smaller set of combinations (i.e., the set of CTD vectors  306 ) that still provides complete n-wise coverage of the Cartesian product space. For instance, if complete pairwise coverage is sought, then the 24 different combinations can be reduced down to 12 distinct combinations that together include every possible pairwise interaction of attribute values. An example set of CTD vectors  400  is shown in  FIG. 4 . The example set of CTD vectors  400  includes all pairwise interactions between the attribute values of the attributes “name,” “color,” and “shape.” 
     A binary decision diagram or the like may be used to perform the reduction and identify the reduced set of CTD vectors  306  that provides complete n-wise coverage. While each CTD vector in the set of CTD vectors  306  includes a unique combination of attribute values, the set of CTD vectors  306  itself may not be unique. That is, there may be multiple different sets of CTD vectors, each of which provides complete n-wise coverage. For instance, while  FIG. 4  depicts an example set of CTD vectors  400  for the example attributes and attribute values described, it should be appreciated that alternative sets of CTD vectors that include different combinations of attribute values may also independently provide complete n-wise coverage. It should further be appreciated that while the example set of CTD vectors  400  provides complete pairwise coverage and partial three-wise coverage, a greater number of CTD vectors would be needed to provide complete three-wise coverage. Stated more generally, as n increases, the number of CTD vectors needed to provide complete n-wise coverage increases logarithmically with n. 
       FIG. 5  depicts an example CTD vector  500  of the type that may be included in the set of CTD vectors  306 . The example CTD vector  500  includes multiple attributes  502 . As previously described, the attributes  502  may be used to model inputs to the SUT  214 . The attributes  502  may be associated with attribute values  504 . In particular, each attribute  502  may have a corresponding attribute value  504 , which may be one of one or more candidate attribute values that the attribute is allowed to take on. 
     Further, according to one or more embodiments of the present invention, the n-wise coverage CTD vector generation module  104  reduces the entire Cartesian product space associated with the collection of attribute-value pairs  302  down by identifying and excluding those combinations that do not adhere to the event ordering information  220 . In one or more embodiments of the present invention, the event ordering information  220  is used to generate architectural restrictions associated with the SUT  214 . After the entire Cartesian product space is reduced to exclude combinations that do not satisfy architectural restrictions on the SUT  214 , the n-wise coverage CTD vector generation module  304 , generates a further reduced initial set of CTD vectors  306 . In example embodiments of the present invention, each CTD vector  306  is selected only from the reduced test space that excludes invalid combinations of attribute values that violate architectural restrictions on the SUT  214 . Here, the invalid combination includes a sequence of the attributes that does not match the event ordering information  220 . 
     Accordingly, an architectural restriction is created on the Cartesian product space that a particular first attribute has to be used before a particular second attribute according to the event ordering information  220 . For example, Action A has to be performed prior to Action B no matter what. Architectural restrictions may additionally include any of a variety of restrictions on inputs to the SUT  214 . For instance, an example restriction may be that if a given attribute has a particular attribute value, then one or more other attributes are excluded from having certain attribute value(s). Another example architectural restriction may be that if a given attribute has a particular attribute value, then one or more other attributes must have certain attribute value(s). Yet another example architectural restriction may be that a new attribute is introduced if and only if a particular attribute has a particular attribute value. It should be appreciated that the above examples of architectural restrictions are merely illustrative and not exhaustive. 
     In example embodiments of the present invention, architectural restrictions are taken into account in method  600  prior to performing the reduction of the entire Cartesian space down to the initial set of CTD vectors  306  that provides desired complete n-wise coverage. That is, particular combinations of attribute values that violate any architectural restrictions are first excluded from the Cartesian product space, and then the reduction down to the set of CTD vectors  306  that provides complete desired n-wise coverage is performed. In this manner, it can be ensured that no combination of attribute values that violates an architectural restriction is included in the initial set of CTD vectors  306 . 
     Referring again to  FIG. 6 , at block  606  of the method  600 , in example embodiments of the present invention, the test case generation modules  208  may be executed to generate, from the initial set of CTD test vectors  306 , a corresponding set of test cases  202 , which are then executed by the test case execution module(s)  108  to yield an execution result (pass or fail) for each test case. 
     For instance, the set of CTD test vectors  306  may be provided as input to a test case generation tool  208  that generates a respective corresponding test case for each CTD vector. Each test case in the set of test cases  202  tests the interactions among the particular combination of attribute values contained in a corresponding CTD vector of the set of CTD vectors  306 . It should be appreciated that a set of CTD vectors and their corresponding test cases may, at times herein, be described and/or depicted interchangeably. For instance, the example set of CTD vectors  400  depicted in  FIG. 4  may be interchangeably thought of as the corresponding set of test cases that test the particular combinations of attribute values represented by the set of CTD vectors  400 . 
     In addition, the test generator  208  receives the event ordering information  220  according to one or more embodiments of the present invention. The event ordering information  220  indicates a particular order for a set of attributes/operations as described herein. The event ordering information  220  can be provided in the form of a Markov chain in one or more embodiments of the present invention. The test generator  208  orders the tests in the bucket  212  based on the event ordering information  220 . 
     At block  608  of the method  600 , computer-executable instructions of the test case execution module(s)  108  are executed to determine whether any test cases in the set of test cases  202  failed. In example embodiments of the present invention, execution of each test case  202  results in either a successful execution result, indicating that the combination of attribute values contained in the corresponding CTD vector  306  does not contain an n-wise (or m-wise where m&lt;n) error, or a failure execution result, indicating that the combination of attribute values in the corresponding CTD vector  306  does contain an n-wise (or m-wise where m&lt;n) error. 
     Referring to the example depicted in  FIG. 4 , test cases corresponding to the example set of CTD vectors  400  are executed at block  606  to yield a respective execution result for each test case. In particular, two test cases  402  and  404  are illustratively depicted in  FIG. 4  as resulting in failure. Failing test case  402  tests the following combination of attribute values: Dale; blue; triangle, which respectively correspond to the attributes name, color, and shape. Failing test case  404  tests the following combination of attribute values: Dale; blue; circle, which respectively correspond to the attributes name, color, and shape. Although “Dale” and “blue” are present both in the CTD vector corresponding to failing test case  402  and in the CTD vector corresponding to failing test case  404 , it is unclear at this stage in the process as to whether “Dale” and “blue” are generating a pairwise error; whether “Dale” and (“triangle” or “circle”) are generating the pairwise errors; or whether “blue” and (“triangle” or “circle”) are generating the pairwise errors. Subsequent operations of method  600  can utilize inverse combinatorics to expand the test space around a selected failing test case to detect and localize the particular combination of attribute values that are causing the n-wise error (pairwise error in the case of the example depicted in  FIG. 4 ). 
     Responsive to a negative determination at block  608 , the method  600  may end because none of the initial set of test cases  202  has failed. Because the initial set of CTD vectors  306  (based on which the set of test cases  202  are generated) provided complete n-wise coverage, it can be ensured that an n-wise or lesser order error is not present. However, successful execution of all of the test cases in the initial set of test cases  202  does not ensure that a higher order error (k-wise where k&gt;n) is not present. 
     On the other hand, in response to a positive determination at block  608  indicating that execution of the set of test cases  202  results in one or more failing test cases  314 , the method  600  includes using an inverse CTD test case generation module  316  to execute and to select a particular failing test case  314  and apply inverse combinatorics to the selected failing test case  314  to produce a new set of test cases  318  capable of being used to detect and localize the combination of attribute values that are causing the n-wise or lesser order error. 
     In example embodiments of the present invention, application of inverse combinatorics to the selected failing test case  314  includes generating a respective new test case  318  with respect to each attribute. Thus, the number of new test cases generated may be equal to the number of attributes. In example embodiments, in each new test case  318 , the attribute value in the selected failing test case  314  of a corresponding attribute is changed to an attribute value for that attribute that is not present in any other failing test case and the respective attribute value for each other attribute is unchanged from that which is present in the selected failing test case  314 . 
     Referring again to the example depicted in  FIG. 4 , assuming that failing test case  402  is selected at block  610 , then the example set of new test cases  406  may be generated. In example embodiments of the present invention, each example new test case  406  may be generated by changing the attribute value of a corresponding attribute in the selected failing test case  402  to a different value that is not present in any other failing test case. For instance, a first new test case corresponding to the CTD vector &lt;Andrew, blue, triangle&gt; is obtained by changing the attribute value of the “name” attribute in the failing test case  402  from “Dale” to “Andrew” while keeping the attribute values for the other attributes the same as in the failing test case  402 . Similarly, a second new test case corresponding to the CTD vector &lt;Dale, green, triangle&gt; is obtained by changing the attribute value of the “color” attribute in the failing test case  402  from “Blue” to “Green” while keeping the attribute values for the other attributes the same as in the failing test case  402 . Lastly, a third new test case corresponding to the CTD vector &lt;Dale, blue, square&gt; is obtained by changing the attribute value of the “shape” attribute in the failing test case  402  from “triangle” to “square” while keeping the attribute values for the other attributes the same as in the failing test case  402 . 
     It should be appreciated that the respective attribute value that is changed to obtain each new test case  406  is obviously not present in the selected failing test case  402 . Moreover, each changed attribute value is not present in any other failing test case as well (e.g., failing test case  404 ). Specifically, the changed attribute value “Andrew” for the first new test case is not present in any failing test case; the changed attribute value “green” for the second new test case is not present in any failing test case; and the changed attribute value “square” for the third new test case is not present in any failing test case. 
     After generating the set of new test cases  318  by performing inverse combinatorics on a selected failing test case  314 , the test case execution module(s)  108  is used for executing the new test cases  318 , at block  612  of the method  600 . Further, at block  614 , one or more n-wise error localization modules  322  detect and localize an n-wise or lesser order error based on the attributes and their corresponding original failing attribute values in the selected failing test case  314  that when changed resulted in new test cases that pass. In particular, computer-executable instructions of the n-wise error localization module(s)  322  are executed to assess execution results  320  for the set of new test cases  318  to detect and localize an n-wise or lesser order error based on those new test cases that yield a successful execution result. As used herein, a lesser order error refers to an m-wise error where m&lt;n, assuming complete n-wise coverage by the set of CTD vectors  306 . 
     Referring again to the example depicted in  FIG. 4  which assumes detection and localization of a pairwise error, execution of the set of new test cases  406  results in the first new test case corresponding to the CTD vector &lt;Andrew, blue, triangle&gt;passing; the second new test case corresponding to the CTD vector &lt;Dale, green, triangle&gt;passing; and the third new test case corresponding the CTD vector &lt;Dale, blue, square&gt;failing. In example embodiments, the n-wise error localization module(s)  322  determine, based on the failing execution result for the third new test case, that the “shape” attribute is not contributing to a pairwise error because changing the attribute value from “triangle” in the failing test  402  to “square” in the third new test case continues to result in failure. 
     On the other hand, the n-wise error localization module(s)  322  may determine that the attributes whose attribute values were changed to obtain the new test cases that passed execution do contribute to the pairwise error. Specifically, in example embodiments of the present invention, based on the successful execution result for the first new test case corresponding to the CTD vector &lt;Andrew, blue, triangle&gt;, the n-wise error localization module(s)  322  determines that the “name” attribute and the original failing attribute value “Dale” are contributing to the pairwise error. Similarly, in example embodiments, based on the successful execution result for the second new test case corresponding to the CTD vector &lt;Dale, green, triangle&gt;, the n-wise error localization module(s)  322  determines that the “color” attribute and the original failing attribute value “blue” are also contributing to the pairwise error. 
     Thus, based on the execution results  320  for the set of new test cases  318 , the n-wise error localization module(s)  322  can determine, in the example depicted in  FIG. 4 , that the attributes “name” and “color” having the attribute values “Dale” and “blue,” respectively, are responsible for the pairwise error. Stated more generally, the n-wise error localization module(s)  322  can determine the specific attribute-value pairs that cause an n-wise or lesser order error based on an assessment of the execution results  320  for the set of new cases  318 , and more specifically, the original attribute values that were changed in the selected failing test case to obtain passing new test cases. 
     The example depicted in  FIG. 4  assumes an initial set of CTD vectors  400  that provides complete pairwise coverage, in which case, a pairwise or lesser order error (e.g., a single attribute value that causes an error) can be detected and localized in a single pass of applying inverse combinatorics on a selected failing test case to obtain the set of new test cases  318 . In general, if the initial set of CTD vectors  306  provides n-wise coverage, then a single pass of applying inverse combinatorics on a selected failing test case reveals an n-wise or lesser order error. While a k-wise error where k&gt;n may be detectable using an initial set of CTD vectors that provides complete n-wise coverage, this is not a guarantee because the initial set of CTD vectors  306  would not include all k-wise interactions. However, an initial set of CTD vectors  306  that provides complete n-wise coverage (e.g., complete pairwise coverage) may provide some degree of k-wise coverage where k&gt;n (e.g., three-wise coverage), and thus, based on the particular CTD vectors that are chosen, the method  600  can reveal a k-wise error at a single pass or after multiple passes of applying inverse combinatorics to selected failing test cases. 
     Referring again to  FIG. 6 , at block  616  of the method  600 , computer-executable instructions of one or more regression bucket generation module(s)  326  are executed to generate and output a regression bucket  212  of failing test cases that includes all possible combinations in the Cartesian product space that include the original failing attribute-value pairs. The regression bucket generation module  326 , in example embodiments of the present invention, receives an indication of the error-producing subset of attribute-value pairs  324  as input and determines and outputs the regression bucket  212  that includes only those test cases that correspond to all possible combinations in the Cartesian product space that include the particular attribute values that are causing the detected error. 
     Referring again to the example of  FIG. 4 , the regression bucket generation module  326  receives as input the attributes “name” and “color” and the corresponding attribute values “Dale” and “blue” that are causing the pairwise error, determines all attribute-value combinations in the Cartesian product space that include “Dale” and “blue,” and populates the regression bucket  212  with test cases corresponding to all of these combinations. In this example, the regression bucket  212  includes the following test cases: (Dale, blue, triangle); (Dale, blue, circle); and (Dale, blue, square). Because each of the test cases in the regression bucket  212  includes the attribute values “Dale” and “blue” for the attributes “name” and “color,” respectively, which together are contributing to the detected pairwise error, each test case in the regression bucket  212  is ensured to fail. In example embodiments of the present invention, the regression bucket  212  can be outputted for use by a manual tester or another automated debugging algorithm. The regression bucket  212  of failing test cases can be used to verify whether the detected error has been corrected because all test cases contained in the regression bucket  212  will pass only when the error is fixed. Thus, if any test case in the regression bucket  212  continues to fail despite modifications made to the SUT  214  in an attempt to correct the error, then this indicates that the error has not been completely resolved. 
     Another technical challenge with the testing infrastructure is that when verifying the quality of the SUT  214 , a diverse and robust sequence of tests has to be used to adequately cover as many scenarios the SUT  214  may be subjected to as possible. Certain scenarios require a specific order of events to occur to guarantee that a given service or path is exercised, as described herein. Some scenarios may not necessitate that a specific order of events occur. For these scenarios to be tested, the technical challenge is to introduce more randomness into the test system to represent a production environment where the SUT  214  will likely operate. 
     One or more embodiments of the present invention address such technical challenges by using Markov chains. A Markov chain is a mathematical construct used to model state changes in the SUT  214  based on random probabilities of a specific event occurring while the SUT  214  is in a given state. The probability of an event occurring to any given state can be tuned to control how much order or randomness the SUT  214  will be subjected to by the test cases executed by the testing infrastructure. 
       FIG. 7  depicts a flowchart for providing a deterministic order of tests to run for the SUT  214  in the testing infrastructure according to one or more embodiments of the present invention. The method  700  that is depicted includes modeling the attribute-value pairs for the testing, at block  702 . The modeling is similar to that performed in the method  600 . The method further includes assigning a probability factor to an attribute-value pair, at block  704 . In one or more embodiments of the present invention, each attribute-value pair is assigned a respective probability value. 
     The probability value indicates a probability of the attribute-value being selected for generating a test case. Alternatively, or in addition, the probability value indicates a probability of a test case associated with that attribute-value being selected to be executed in the bucket  212  of tests. The probability value can be manually configured by a test engineer to facilitate higher (or lower) chance that a particular attribute-value is tested. In an example, setting the probability value to ‘1’ ensures that the attribute-value pair is tested. Conversely, setting the probability value to ‘0’ ensures that the attribute-value pair is not tested. 
     In one or more embodiments of the present invention, the selected attribute-value pairs and their respective assigned probability value is stored in the form of a hash value, at block  706 . In other words, a hash represents an attribute-value pair and a probability value assigned to that pair. In one or more embodiments of the present invention, unique hashes are generated for each of the attribute-value pairs and its probability value. In one or more embodiments of the present invention, to ensure unique hashes prime number modulus, multiplication, etc. operations may be used. The attribute-value pairs and corresponding probability values are accordingly stored has a hash table, facilitating a processor to use techniques such as binary decision diagram or the like to perform a reduction to identify the reduced set of CTD vectors  306  that provides complete n-wise coverage. Binary decision diagram can be applied as described elsewhere herein. 
     At block  708  of the method  700 , the n-wise coverage CTD vector generation module  304  reduces the entire Cartesian product space associated with the collection of attribute-value pairs  302  down by identifying and excluding those combinations that do not adhere to architectural restrictions associated with the SUT  214 . For example, an event ordering information  220 , a restriction about a particular value of the attribute, and other types of architectural restrictions can be associated with one or more of the attribute-value pairs. 
     After the entire Cartesian product space is reduced to exclude combinations that do not satisfy architectural restrictions on the SUT  214 , the n-wise coverage CTD vector generation module  304  generates the further reduced initial set of CTD vectors  306 , at block  710  of the method  700 . In example embodiments, each CTD vector  306  is selected only from the reduced test space that excludes invalid combinations of attribute values that violate architectural restrictions on the SUT  214 . The CTD vector  306  is selected based on the probability value assigned with the attribute-value pair. To facilitate the probability value to have effect in selection of the attribute-value pair, a Markov chain is used to represent each selection as a state. The mathematical construct of the Markov chain then models state changes based on the probabilities of a specific event occurring (i.e., selection of a particular attribute-value pair) while the system is in a given state (i.e., presently selected attribute-value pair). 
     At block  712  of the method  700 , the initial set of test cases  202  is generated from the initial set of CTD vectors  306  and executed similar to block  606  of the method  600 . At block  714 , a determination is made as to whether any of test cases  202  failed similar to the determination at block  608  of the method  600 . In response to a negative determination at block  714 , the method  700  ends because none of test cases  202  produce a failing execution result. On the other hand, in response to a positive determination at block  714 , the method  700  proceeds to block  716 , where the inverse CTD test case generation module  316  generates the new test cases  318  from a selected failing test case. 
     In one or more embodiments of the present invention, a respective set of new test cases is generated for each attribute by changing the attribute value for that attribute in the selected failing test case to each other candidate attribute value for that attribute that is not present in any of the failing test cases. For example, a single new test case is generated with respect to each attribute in a selected failing test case by changing the attribute value for the attribute to another attribute value that the attribute is eligible to have and that is not present in any failing test case. While there may be multiple attribute values for an attribute that are not present in any failing test case, each new test case generated only tests one such attribute value, and thus, in this technique of creating new tests, each new test case can be generated simply by oscillating a corresponding attribute value in the selected failing test case to one other attribute value that is not present in any failing test case. 
     Alternatively, in one or more embodiments of the present invention, for each attribute in a selected failing test case, a new test case is generated for each possible attribute value for that attribute that is not present in any failing test case. Thus, according to the this second technique, if there are multiple attribute values for an attribute that are not present in any failing test case, a new test case is generated for each such attribute value. 
     In the example depicted in  FIG. 4 , for instance, inverse combinatorics are applied to the failing test case  402  to obtain the set of new test cases  406  according to the first technique above. That is, a single new test case is shown as being generated with respect to each attribute in the selected failing test case  402  by changing the corresponding attribute value for that attribute in the selected failing test case  402  to another candidate attribute value that is not present in any failing test case. If, on the other hand, the set of new test cases  406  was instead generated according to the second technique above, the set of new test cases  406  includes the following additional test cases: (Ryan, blue, triangle) and (Rachel, blue, triangle) because the attribute values “Ryan” and “Rachel” are also not present in any failing test case. 
     Further, the inverse CTD test case generation module  316  excludes any of the new test cases that violate an architectural restriction on the SUT  214 . The set of new test cases  318  obtained via the inverse combinatorics expansion is accordingly reduced to a smaller set by excluding (and not executing) one or more new test cases that violate one or more architectural restrictions. In particular, when a selected test case corresponding to an initial CTD vector  306  fails and is selected for expansion to obtain the set of new test cases  318  designed to detect and localize an n-wise error, the expansion may be performed first without taking into account any architectural restrictions. Then, any new test cases generated from the expansion that violate an architectural restriction can be excluded from the set of new test cases  318 . In this manner, it can be ensured that the expansion provides as much coverage of the test space in the neighborhood around the failing test case as possible. 
     Further, the method  700  includes executing the reduced set of new tests  318 , at block  718 , similar to block  612  of the method  600 . At block  720  of the method  700 , an n-wise error is detected and localized based at least in part on the attributes and their corresponding attribute values in the selected failing test case that when changed produce a new test case that passes, similar to block  614  of the method  600 . Further, at block  722 , the regression bucket  212  of failing test cases is generated similar to block  616  of the method  600 . Each test case in the regression bucket  212  corresponds to a particular combination of attribute values that includes the failure-producing subset of attribute value pairs  324  such that the regression bucket  212  covers all possible combinations of attribute-value pairs that adhere to architectural restrictions on the SUT  214  and that include the failure-producing attribute values. Further yet, at block  724 , any failing test case that violates an architectural restriction can be excluded from the regression bucket  212 . 
     Accordingly, the method  700  facilitates the regression bucket  212  of failing test cases to be generated without regards to architectural restrictions, and then any test case that violates an architectural restriction can be excluded from the regression bucket  212 . That is, test cases corresponding to all possible combinations in the entire Cartesian product test space that include the particular combination of attribute values causing an n-wise or lesser order error may first be generated and included in the regression bucket  212 , and then the regression bucket  212  may be reduced to exclude any test case(s) that violate a restriction. In alternative example embodiments, the test cases included in the regression bucket  212  may be selected from the reduced Cartesian space from which the initial set of CTD vectors are selected, in which case, the regression bucket  212  would be generated to include only those combinations of attribute values that include the subset of attribute values causing the error and that do not violate any architectural restriction. 
     In addition, the tests that are selected are based on the probability values that are tuned for each attribute-value pair. Therefore, a first attribute-value pair with a higher probability value has a higher chance of being tested than a second attribute-value pair with a probability value that is lower than that of the first attribute-value pair. A test engineer can accordingly control the selection of tests in the CTD based test infrastructure. 
     Turning now to  FIG. 8 , a computer system  800  is generally shown in accordance with an embodiment of the present invention. The computer system  800  can be an electronic, computer framework comprising and/or employing any number and combination of computing devices and networks utilizing various communication technologies, as described herein. The computer system  800  can be easily scalable, extensible, and modular, with the ability to change to different services or reconfigure some features independently of others. The computer system  800  may be, for example, a server, desktop computer, laptop computer, tablet computer, or smartphone. In some examples, computer system  800  may be a cloud computing node. Computer system  800  may be described in the general context of computer system executable instructions, such as program modules, being executed by a computer system. Generally, program modules may include routines, programs, objects, components, logic, data structures, and so on that perform particular tasks or implement particular abstract data types. Computer system  800  may be practiced in distributed cloud computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed cloud computing environment, program modules may be located in both local and remote computer system storage media including memory storage devices. 
     As shown in  FIG. 8 , the computer system  800  has one or more central processing units (CPU(s))  801   a ,  801   b ,  801   c , etc. (collectively or generically referred to as processor(s)  801 ). The processors  801  can be a single-core processor, multi-core processor, computing cluster, or any number of other configurations. The processors  801 , also referred to as processing circuits, are coupled via a system bus  802  to a system memory  803  and various other components. The system memory  803  can include a read only memory (ROM)  804  and a random access memory (RAM)  805 . The ROM  804  is coupled to the system bus  802  and may include a basic input/output system (BIOS), which controls certain basic functions of the computer system  800 . The RAM is read-write memory coupled to the system bus  802  for use by the processors  801 . The system memory  803  provides temporary memory space for operations of said instructions during operation. The system memory  803  can include random access memory (RAM), read only memory, flash memory, or any other suitable memory systems. 
     The computer system  800  comprises an input/output (I/O) adapter  806  and a communications adapter  807  coupled to the system bus  802 . The I/O adapter  806  may be a small computer system interface (SCSI) adapter that communicates with a hard disk  808  and/or any other similar component. The I/O adapter  806  and the hard disk  808  are collectively referred to herein as a mass storage  810 . 
     Software  811  for execution on the computer system  800  may be stored in the mass storage  810 . The mass storage  810  is an example of a tangible storage medium readable by the processors  801 , where the software  811  is stored as instructions for execution by the processors  801  to cause the computer system  800  to operate, such as is described herein below with respect to the various Figures. Examples of computer program product and the execution of such instruction is discussed herein in more detail. The communications adapter  807  interconnects the system bus  802  with a network  812 , which may be an outside network, enabling the computer system  800  to communicate with other such systems. In one embodiment, a portion of the system memory  803  and the mass storage  810  collectively store an operating system, which may be any appropriate operating system, such as the z/OS or AIX operating system from IBM Corporation, to coordinate the functions of the various components shown in  FIG. 8 . 
     Additional input/output devices are shown as connected to the system bus  802  via a display adapter  815  and an interface adapter  816  and. In one embodiment, the adapters  806 ,  807 ,  815 , and  816  may be connected to one or more I/O buses that are connected to the system bus  802  via an intermediate bus bridge (not shown). A display  819  (e.g., a screen or a display monitor) is connected to the system bus  802  by a display adapter  815 , which may include a graphics controller to improve the performance of graphics intensive applications and a video controller. A keyboard  821 , a mouse  822 , a speaker  823 , etc. can be interconnected to the system bus  802  via the interface adapter  816 , which may include, for example, a Super I/O chip integrating multiple device adapters into a single integrated circuit. Suitable I/O buses for connecting peripheral devices such as hard disk controllers, network adapters, and graphics adapters typically include common protocols, such as the Peripheral Component Interconnect (PCI). Thus, as configured in  FIG. 8 , the computer system  800  includes processing capability in the form of the processors  801 , and, storage capability including the system memory  803  and the mass storage  810 , input means such as the keyboard  821  and the mouse  822 , and output capability including the speaker  823  and the display  819 . 
     In some embodiments, the communications adapter  807  can transmit data using any suitable interface or protocol, such as the internet small computer system interface, among others. The network  812  may be a cellular network, a radio network, a wide area network (WAN), a local area network (LAN), or the Internet, among others. An external computing device may connect to the computer system  800  through the network  812 . In some examples, an external computing device may be an external webserver or a cloud computing node. 
     It is to be understood that the block diagram of  FIG. 8  is not intended to indicate that the computer system  800  is to include all of the components shown in  FIG. 8 . Rather, the computer system  800  can include any appropriate fewer or additional components not illustrated in  FIG. 8  (e.g., additional memory components, embedded controllers, modules, additional network interfaces, etc.). Further, the embodiments described herein with respect to computer system  800  may be implemented with any appropriate logic, wherein the logic, as referred to herein, can include any suitable hardware (e.g., a processor, an embedded controller, or an application specific integrated circuit, among others), software (e.g., an application, among others), firmware, or any suitable combination of hardware, software, and firmware, in various embodiments. 
     In one or more embodiments of the present invention, the computer system  800  can be the environment  100  with the SUT being a computer program or a hardware component being used by the computer system  800 . In one or more embodiments of the present invention, the computer system  800  can be the SUT  214 , which is part of a server cluster. 
     The present invention may be a system, a method, and/or a computer program product at any possible technical detail level of integration. The computer program product may include a computer-readable storage medium (or media) having computer-readable program instructions thereon for causing a processor to carry out aspects of the present invention. 
     The computer-readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer-readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer-readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer-readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire. 
     Computer-readable program instructions described herein can be downloaded to respective computing/processing devices from a computer-readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in a computer-readable storage medium within the respective computing/processing device. 
     Computer-readable program instructions for carrying out operations of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuitry, or either source-code or object code written in any combination of one or more programming languages, including an object-oriented programming language such as Smalltalk, C++, or the like, and procedural programming languages, such as the “C” programming language or similar programming languages. The computer-readable program instructions may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer-readable program instruction by utilizing state information of the computer-readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention. 
     Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer-readable program instructions. 
     These computer-readable program instructions may be provided to a processor of a general-purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer-readable program instructions may also be stored in a computer-readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer-readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer-implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the Figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions. 
     The descriptions of the various embodiments of the present invention have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments described herein. 
     Various embodiments of the invention are described herein with reference to the related drawings. Alternative embodiments of the invention can be devised without departing from the scope of this invention. Various connections and positional relationships (e.g., over, below, adjacent, etc.) are set forth between elements in the following description and in the drawings. These connections and/or positional relationships, unless specified otherwise, can be direct or indirect, and the present invention is not intended to be limiting in this respect. Accordingly, a coupling of entities can refer to either a direct or an indirect coupling, and a positional relationship between entities can be a direct or indirect positional relationship. Moreover, the various tasks and process steps described herein can be incorporated into a more comprehensive procedure or process having additional steps or functionality not described in detail herein. 
     The following definitions and abbreviations are to be used for the interpretation of the claims and the specification. As used herein, the terms “comprises,” “comprising,” “includes,” “including,” “has,” “having,” “contains” or “containing,” or any other variation thereof, are intended to cover a non-exclusive inclusion. For example, a composition, a mixture, process, method, article, or apparatus that comprises a list of elements is not necessarily limited to only those elements but can include other elements not expressly listed or inherent to such composition, mixture, process, method, article, or apparatus. 
     Additionally, the term “exemplary” is used herein to mean “serving as an example, instance or illustration.” Any embodiment or design described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments or designs. The terms “at least one” and “one or more” may be understood to include any integer number greater than or equal to one, i.e. one, two, three, four, etc. The terms “a plurality” may be understood to include any integer number greater than or equal to two, i.e. two, three, four, five, etc. The term “connection” may include both an indirect “connection” and a direct “connection.” 
     The terms “about,” “substantially,” “approximately,” and variations thereof, are intended to include the degree of error associated with measurement of the particular quantity based upon the equipment available at the time of filing the application. For example, “about” can include a range of ±8% or 5%, or 2% of a given value. 
     For the sake of brevity, conventional techniques related to making and using aspects of the invention may or may not be described in detail herein. In particular, various aspects of computing systems and specific computer programs to implement the various technical features described herein are well known. Accordingly, in the interest of brevity, many conventional implementation details are only mentioned briefly herein or are omitted entirely without providing the well-known system and/or process details.