We investigate the notion of fair testing, a formal testing theory in the style of De Nicola and Hennessy, where divergences are disregarded as long as there axe visible outgoing transitions. The usual testing theories, such as the standard model of failure pre-order, do not allow such fair interpretations because of the way in which they ensure their compositionality with respect to abstraction from observable actions. This feature is usually present in the form of a hiding-operator (CSP, ACP, LOTOS) or part of parallel composition (CCS). Its application can introduce new divergences causing semantic complications. In this paper we present a testing scenario that captures the intended notion of fairness and induces a pre-congruence for abstraction. In the presence of a sufficiently strong synchronisation feature it is shown to be the coarsest pre-congruence contained in the (non-congruent) fair version of failure preorder. We also give a denotational characterisation.
Compositional testing concerns the testing of systems that consist of communicating components which can also be tested in isolation. Examples are component based testing and interoperability testing. We show that, with certain restrictions, the ioco-test theory for conformance testing is suitable for compo sitional testing, in the sense that the integration of fully conformant components is guaranteed to be correct. As a consequence, there is no need to re-test the inte grated system for conformance. This result is also relevant for testing in context, since it implies that every failure of a system embedded in a test context can be reduced to a fault of the system itself. * This research was supported by Ordina Finance and by the dutch research programme PROGRESS under project: TES5417: Atomyste-ATOm splitting in eMbedded sYStems TEsting. Another scenario, with similar characteristics, is testing in context. This refers to the situation that a tester can only access the implementation under test through a test context [7,8,9]. The test context interfaces between the implementation under test and the tester. As a consequence the tester can only indirectly observe and control the iu t via the test context. This makes testing weaker, in the sense that there are fewer pos sibilities for observation and control of the iu t. With testing in context, the question is whether faults in the iu t can be detected by testing the composition of iu t and test context, and whether a failure of this composition always indicates a fault of the iut. This question is the converse of compositional testing: when testing in context we wish to detect errors in the iu t-a component-by testing it in composition with the test context, whereas in compositional testing we wish to infer correctness of the integrated system from conformance of the individual components. This paper studies the above mentioned compositionality properties of ioco for two operations on labeled transition systems: parallel composition and hiding. if ioco has this compositionality property for these operations, it follows that correctness of the parts (the components) implies correctness of the whole (the integrated system), or that a fault in the whole (iut and test context) implies a fault in the component (iut). This compositionality property is formally called a pre-congruence. We show that ioco is a pre-congruence for parallel composition and hiding in the absence of underspecification of input actions. One way to satisfy this condition is to only allow specifications which are input enabled. Another way is to make the under specification explicit by completion. We show that, in particular, demonic completion is suitable for this purpose. As a final result we show how to use the original (uncom pleted) specifications and still satisfy the pre-congruence property. This leads to a new implementation relation, baptized ioco v which is slightly weaker than ioco. This paper has two main results. First we show a way to handle underspecifica tion of input actions wh...
In this paper we present case studies that describe how the graph transformation tool GROOVE has been used to model problems from a wide variety of domains. These case studies highlight the wide applicability of GROOVE in particular, and of graph transformation in general. They also give concrete templates for using GROOVE in practice. Furthermore, we use the case studies to analyse the main strong and weak points of GROOVE.
Abstract. We show how edge-labelled graphs can be used to represent first-order logic formulae. This gives rise to recursively nested structures, in which each level of nesting corresponds to the negation of a set of existentials. The model is a direct generalisation of the negative application conditions used in graph rewriting, which count a single level of nesting and are thereby shown to correspond to the fragment ∃¬∃ of first-order logic. Vice versa, this generalisation may be used to strengthen the notion of application conditions. We then proceed to show how these nested models may be flattened to (sets of) plain graphs, by allowing some structure on the labels. The resulting formulae-as-graphs may form the basis of a unification of the theories of graph transformation and predicate transformation.
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