Model-based testing is an application of

model-based design Model-based design (MBD) is a mathematical and visual method of addressing problems associated with designing complex control, signal processing and communication systems. It is used in many motion control, industrial equipment, aerospace, and a ...

for designing and optionally also executing artifacts to perform

software testing Software testing is the act of checking whether software satisfies expectations. Software testing can provide objective, independent information about the Quality (business), quality of software and the risk of its failure to a User (computin ...

system testing System testing, a.k.a. end-to-end (E2E) testing, is testing conducted on a complete software system. System testing describes testing at the system level to contrast to testing at the system integration, integration or unit level. System t ...

. Models can be used to represent the desired behavior of a system under test (SUT), or to represent testing strategies and a test environment. The picture on the right depicts the former approach. A model describing a SUT is usually an abstract, partial presentation of the SUT's desired behavior. Test cases derived from such a model are functional tests on the same level of abstraction as the model. These test cases are collectively known as an abstract test suite. An abstract test suite cannot be directly executed against an SUT because the suite is on the wrong level of abstraction. An executable test suite needs to be derived from a corresponding abstract test suite. The executable test suite can communicate directly with the system under test. This is achieved by mapping the abstract test cases to concrete test cases suitable for execution. In some model-based testing environments, models contain enough information to generate executable test suites directly. In others, elements in the abstract test suite must be mapped to specific statements or method calls in the software to create a concrete test suite. This is called solving the "mapping problem".Paul Ammann and Jeff Offutt. Introduction to Software Testing, 2nd edition. Cambridge University Press, 2016. In the case of online testing (see below), abstract test suites exist only conceptually but not as explicit artifacts. Tests can be derived from models in different ways. Because testing is usually experimental and based on heuristics, there is no known single best approach for test derivation. It is common to consolidate all test derivation related parameters into a package that is often known as "test requirements", "test purpose" or even "use case(s)". This package can contain information about those parts of a model that should be focused on, or the conditions for finishing testing (test stopping criteria). Because test suites are derived from models and not from source code, model-based testing is usually seen as one form of

black-box testing Black-box testing, sometimes referred to as specification-based testing, is a method of software testing that examines the functionality of an application without peering into its internal structures or workings. This method of test can be applie ...

. Model-based testing for complex software systems is still an evolving field.

Models

Especially in Model Driven Engineering or in Object Management Group's ( OMG's) model-driven architecture, models are built before or parallel with the corresponding systems. Models can also be constructed from completed systems. Typical modeling languages for test generation include UML, SysML, mainstream programming languages, finite machine notations, and mathematical formalisms such as Z, B ( Event-B),

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Coq Coenzyme Q10 (CoQ10 ), also known as ubiquinone, is a naturally occurring biochemical cofactor (coenzyme) and an antioxidant produced by the human body. It can also be obtained from dietary sources, such as meat, fish, seed oils, vegetables, ...

Deploying model-based testing

There are various known ways to deploy model-based testing, which include online testing, offline generation of executable tests, and offline generation of manually deployable tests.''Practical Model-Based Testing: A Tools Approach''
, Mark Utting and Bruno Legeard, , Morgan-Kaufmann 2007 Online testing means that a model-based testing tool connects directly to an SUT and tests it dynamically. Offline generation of executable tests means that a model-based testing tool generates test cases as computer-readable assets that can be later run automatically; for example, a collection of Python classes that embodies the generated testing logic. Offline generation of manually deployable tests means that a model-based testing tool generates test cases as human-readable assets that can later assist in manual testing; for instance, a PDF document in a human language describing the generated test steps.

Deriving tests algorithmically

The effectiveness of model-based testing is primarily due to the potential for automation it offers. If a 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.

From finite-state machines

Often the model is translated to or interpreted as a

finite-state automaton A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number o ...

or a

state transition system In theoretical computer science, a transition system is a concept used in the study of computation. It is used to describe the potential behavior of discrete systems. It consists of states and transitions between states, which may be labeled wi ...

. 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

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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. To find test cases that can cover an appropriate, but finite, number of paths, test criteria are needed to guide the selection. This technique was first proposed by Offutt and Abdurazik in the paper that started model-based testing. Multiple techniques for test case generation have been developed and are surveyed by Rushby. Test criteria are described in terms of general graphs in the testing textbook.

Theorem proving

Theorem proving Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a majo ...

was originally used for automated proving of logical formulas. For model-based testing approaches, the system is modeled by a set of predicates, specifying the system's behavior. To derive test cases, the model is partitioned into

equivalence classes In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set S into equivalence classes. These equivalence classes are constructed so that elements a ...

over the valid interpretation of the set of the predicates describing the system under test. Each class describes a certain system behavior, and, therefore, can serve as a test case. The simplest partitioning is with the disjunctive normal form approach wherein the logical expressions describing the system's behavior are transformed into the

disjunctive normal form In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or in philosophical logic a ''cluster c ...

Constraint logic programming and symbolic execution

Constraint programming Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state t ...

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 In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) asks whether there exists an Interpretation (logic), interpretation that Satisf ...

) or by

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

, like the

Gaussian elimination In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can a ...

. 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.

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 a Markov chain test model

Markov chains are an efficient way to handle Model-based Testing. Test models realized with Markov chains can be understood as a usage model: it is referred to as Usage/Statistical Model Based Testing. Usage models, so Markov chains, are mainly constructed of 2 artifacts : the

finite-state machine A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number o ...

(FSM) which represents all possible usage scenario of the tested system and the Operational Profiles (OP) which qualify the FSM to represent how the system is or will be used statistically. 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 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 which are focused on improving the reliability of the system under test. Usage/Statistical Model Based Testing was recently extended to be applicable to embedded software systems.