Software testability

Testability, a property applying to empirical hypothesis, involves two components. The effort and effectiveness of software tests depends on numerous factors including:

• Properties of the software requirements
• Properties of the software itself (such as size, complexity and testability)
• Properties of the test methods used
• Properties of the development- and testing processes
• Qualification and motivation of the persons involved in the test process

The testability of software components (modules, classes) is determined by factors such as:

• Controllability: The degree to which it is possible to control the state of the component under test (CUT) as required for testing.
• Observability: The degree to which it is possible to observe (intermediate and final) test results.
• Isolateability: The degree to which the component under test (CUT) can be tested in isolation.
• Separation of concerns: The degree to which the component under test has a single, well defined responsibility.
• Understandability: The degree to which the component under test is documented or self-explaining.
• Automatability: The degree to which it is possible to automate testing of the component under test.
• Heterogeneity: The degree to which the use of diverse technologies requires to use diverse test methods and tools in parallel.

The testability of software components can be improved by:

• Test-driven development
• Design for testability (similar to design for test in the hardware domain)

Based on the number of test cases required to construct a complete test suite in each context (i.e. a test suite such that, if it is applied to the implementation under test, then we collect enough information to precisely determine whether the system is correct or incorrect according to some specification), a testability hierarchy with the following testability classes has been proposed:[2] [3]

• Class I: there exists a finite complete test suite.
• Class II: any partial distinguishing rate (i.e. any incomplete capability to distinguish correct systems from incorrect systems) can be reached with a finite test suite.
• Class III: there exists a countable complete test suite.
• Class IV: there exists a complete test suite.
• Class V: all cases.

It has been proved that each class is strictly included into the next. For instance, testing when we assume that the behavior of the implementation under test can be denoted by a deterministic finite-state machine for some known finite sets of inputs and outputs and with some known number of states belongs to Class I (and all subsequent classes). However, if the number of states is not known, then it only belongs to all classes from Class II on. If the implementation under test must be a deterministic finite-state machine failing the specification for a single trace (and its continuations), and its number of states is unknown, then it only belongs to classes from Class III on. Testing temporal machines where transitions are triggered if inputs are produced within some real-bounded interval only belongs to classes from Class IV on, whereas testing many non-deterministic systems only belongs to Class V (but not all, and some even belong to Class I). The inclusion into Class I does not require the simplicity of the assumed computation model, as some testing cases involving implementations written in any programming language, and testing implementations defined as machines depending on continuous magnitudes, have been proved to be in Class I. Other elaborated cases, such as the testing framework by Matthew Hennessy under must semantics, and temporal machines with rational timeouts, belong to Class II.

Requirements need to fulfill the following criteria in order to be testable:

• consistent
• complete
• unambiguous
• quantitative (a requirement like "fast response time" can not be verification/verified)
• verification/verifiable in practice (a test is feasible not only in theory but also in practice with limited resources)

Treating the requirement as axioms, testability can be treated via asserting existence of a function ${\displaystyle F_{S}}$ (software) such that input ${\displaystyle I_{k}}$ generates output ${\displaystyle O_{k}}$, therefore ${\displaystyle F_{S}:I\to O}$. Therefore, the ideal software generates the tuple ${\displaystyle (I_{k},O_{k})}$ which is the input-output set ${\displaystyle \Sigma }$, standing for specification.

Now, take a test input ${\displaystyle I_{t}}$, which generates the output ${\displaystyle O_{t}}$, that is the test tuple ${\displaystyle \tau =(I_{t},O_{t})}$. Now, the question is whether or not ${\displaystyle \tau \in \Sigma }$ or ${\displaystyle \tau \not \in \Sigma }$. If it is in the set, the test tuple ${\displaystyle \tau }$ passes, else the system fails the test input. Therefore, it is of imperative importance to figure out : can we or can we not create a function that effectively translates into the notion of the set indicator function for the specification set ${\displaystyle \Sigma }$.

By the notion, ${\displaystyle 1_{\Sigma }}$ is the testability function for the specification ${\displaystyle \Sigma }$. The existence should not merely be asserted, should be proven rigorously. Therefore, obviously without algebraic consistency, no such function can be found, and therefore, the specification cease to be termed as testable.

• Testability

• Robert V. Binder: Testing Object-Oriented Systems: Models, Patterns, and Tools, ISBN 0-201-80938-9
• Stefan Jungmayr: Improving testability of object-oriented systems, ISBN 3-89825-781-9
• Wanderlei Souza: Abstract Testability Patterns, ISSN 1884-0760
• Boris Beizer: , Software Testing Techniques