Fair testing

Abstract

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.

Towards a Unifying Theory for Choreography Conformance and Contract Compliance

“…In the following we denote with test the should-testing pre-order defined in [RV05] where we consider the set of actions used by terms as being L ∪ {a | a ∈ N } (i.e. we consider located and unlocated input and output actions and √ is included in the set of actions of terms under testing as any other action).…”

“…we consider located and unlocated input and output actions and √ is included in the set of actions of terms under testing as any other action). We denote here with √ the special action for the success of the test (denoted by √ in [RV05]). In the following we consider λ to range over L ∪ {a | a ∈ N }.…”

“…In order to resort to the theory defined in [RV05], we define a normal form for contracts of our calculus that corresponds to terms of the language in [RV05]. The normal form of the system P (denoted with N F(P)) is defined as follows, by using the operator rec X θ (defined in [RV05]) that represents the value of X in the solution of the minimum fixpoint of the finite set of equations θ,…”

“…The normal form of the system P (denoted with N F(P)) is defined as follows, by using the operator rec X θ (defined in [RV05]) that represents the value of X in the solution of the minimum fixpoint of the finite set of equations θ,…”

“…We first consider item In order to prove that also item 2. holds, we start observing that the should testing pre-order is preserved by parallel composition operator [RV05]. Nevertheless, in [RV05] a different parallel operator in the CSP-style is considered:…”