 # Deriving Tests Algorithmically

The effectiveness of model-based testing is primarily due to the potential for automation it offers. If the model is machine-readable and formal to the extent that it has a well-defined behavioral interpretation, test cases can in principle be derived mechanically.

Often the model is translated to or interpreted as a finite state automaton or a state transition system. This automaton represents the possible configurations of the system under test. To find test cases, the automaton is searched for executable paths. A possible execution path can serve as a test case. This method works if the model is deterministic or can be transformed into a deterministic one. Valuable off-nominal test cases may be obtained by leveraging unspecified transitions in these models.

Depending on the complexity of the system under test and the corresponding model the number of paths can be very large, because of the huge amount of possible configurations of the system. For finding appropriate test cases, i.e. paths that refer to a certain requirement to proof, the search of the paths has to be guided. For test case generation, multiple techniques have been applied and are surveyed in.

Test case generation by theorem proving
Theorem proving has been originally used for automated proving of logical formulas. For model-based testing approaches the system is modeled by a set of logical expressions (predicates) specifying the system's behavior. For selecting test cases the model is partitioned into equivalence classes over the valid interpretation of the set of the logical expressions describing the system under test. Each class is representing a certain system behavior and can therefore serve as a test case. The simplest partitioning is done by the disjunctive normal form approach. The logical expressions describing the system's behavior are transformed into the disjunctive normal form.

Test case generation by constraint logic programming and symbolic execution
Constraint programming can be used to select test cases satisfying specific constraints by solving a set of constraints over a set of variables. The system is described by the means of constraints. Solving the set of constraints can be done by Boolean solvers (e.g. SAT-solvers based on the Boolean satisfiability problem) or by numerical analysis, like the Gaussian elimination. A solution found by solving the set of constraints formulas can serve as a test cases for the corresponding system.

Constraint programming can be combined with symbolic execution. In this approach a system model is executed symbolically, i.e. collecting data constraints over different control paths, and then using the constraint programming method for solving the constraints and producing test cases.

Test case generation by model checking
Model checkers can also be used for test case generation. Originally model checking was developed as a technique to check if a property of a specification is valid in a model. When used for testing, a model of the system under test, and a property to test is provided to the model checker. Within the procedure of proofing, if this property is valid in the model, the model checker detects witnesses and counterexamples. A witness is a path, where the property is satisfied, whereas a counterexample is a path in the execution of the model, where the property is violated. These paths can again be used as test cases.

Test case generation by using an event-flow model
A popular model that has recently been used extensively for testing software with a graphical user-interface (GUI) front-end is called the event-flow model that represents events and event interactions. In much the same way as a control-flow model represents all possible execution paths in a program, and a data-flow model represents all possible definitions and uses of a memory location, the event-flow model represents all possible sequences of events that can be executed on the GUI. More specifically, a GUI is decomposed into a hierarchy of modal dialogs; this hierarchy is represented as an integration tree; each modal dialog is represented as an event-flow graph that shows all possible event execution paths in the dialog; individual events are represented using their preconditions and effects. An overview of the event-flow model with associated algorithms to semi-automatically reverse engineer the model from an executing GUI software is presented inthis 2007 paper. Because the event-flow model is not tied to a specific aspect of the GUI testing process, it may be used to perform a wide variety of testing tasks by defining specialized model-based techniques called event-space exploration strategies (ESES). These ESES use the event-flow model in a number of ways to develop an end-to-end GUI testing process, namely by checking the model, test-case generation, and test oracle creation.

Test case generation by using a Markov chains model
Markov chains are an efficient way to handle Model-based Testing. Test model realized with Markov chains model can be understood as a usage model: we spoke of Usage/Statistical Model Based Testing. Usage models, so Markov chains, are mainly constructed by 2 artifacts : the Finite State Machine (FSM) which represents all possible usage scenario of the system and the Operational Profiles (OP) which qualify the FSM to represent how the system will statically will be used. The first (FSM) helps to know what can be or has been tested and the second (OP) helps to derive operational test cases. Usage/Statistical Model-based Testing starts from the facts that is not not possible to exhaustively test a system and that failure can appear with a very low rate.This approach offers a pragmatic way to statically derive test cases focused on: improving as prompt as possible the system under test reliability. The company ALL4TEC provides an implementation of this approach with the tool MaTeLo (Markov Test Logic). MaTeLo allows to model the test with Markov chains, derive executables test cases w.r.t the usage testing approach, and assess the system under test reliability with the help of the so called Test Campaign Analysis module.

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