Spinal Test Suites for Software Product Lines

A major challenge in testing software product lines is efficiency. In particular, testing a product line should take less effort than testing each and every product individually. We address this issue in the context of input-output conformance testing, which is a formal theory of model-based testing. We extend the notion of conformance testing on input-output featured transition systems with the novel concept of spinal test suites. We show how this concept dispenses with retesting the common behavior among different, but similar, products of a software product line.Comment: In Proceedings MBT 2014, arXiv:1403.704

Design of asynchronous supervisors

One of the main drawbacks while implementing the interaction between a plant and a supervisor, synthesised by the supervisory control theory of \citeauthor{RW:1987}, is the inexact synchronisation. \citeauthor{balemiphdt} was the first to consider this problem, and the solutions given in his PhD thesis were in the domain of automata theory. Our goal is to address the issue of inexact synchronisation in a process algebra setting, because we get concepts like modularity and abstraction for free, which are useful to further analyze the synthesised system. In this paper, we propose four methods to check a closed loop system in an asynchronous setting such that it is branching bisimilar to the modified (asynchronous) closed loop system. We modify a given closed loop system by introducing buffers either in the plant models, the supervisor models, or the output channels of both supervisor and plant models, or in the input channels of both supervisor and plant models. A notion of desynchronisable closed loop system is introduced, which is a class of synchronous closed loop systems such that they are branching bisimilar to their corresponding asynchronous versions. Finally we study different case studies in an asynchronous setting and then try to summarise the observations (or conditions) which will be helpful in order to formulate a theory of desynchronisable closed loop systems

Conditional Transition Systems with Upgrades

We introduce a variant of transition systems, where activation of transitions depends on conditions of the environment and upgrades during runtime potentially create additional transitions. Using a cornerstone result in lattice theory, we show that such transition systems can be modelled in two ways: as conditional transition systems (CTS) with a partial order on conditions, or as lattice transition systems (LaTS), where transitions are labelled with the elements from a distributive lattice. We define equivalent notions of bisimilarity for both variants and characterise them via a bisimulation game. We explain how conditional transition systems are related to featured transition systems for the modelling of software product lines. Furthermore, we show how to compute bisimilarity symbolically via BDDs by defining an operation on BDDs that approximates an element of a Boolean algebra into a lattice. We have implemented our procedure and provide runtime results

Hennessy-Milner Theorems via Galois Connections

We introduce a general and compositional, yet simple, framework that allows to derive soundness and expressiveness results for modal logics characterizing behavioural equivalences or metrics (also known as Hennessy-Milner theorems). It is based on Galois connections between sets of (real-valued) predicates on the one hand and equivalence relations/metrics on the other hand and covers a part of the linear-time-branching-time spectrum, both for the qualitative case (behavioural equivalences) and the quantitative case (behavioural metrics). We derive behaviour functions from a given logic and give a condition, called compatibility, that characterizes under which conditions a logically induced equivalence/metric is induced by a fixpoint equation. In particular, this framework allows to derive a new fixpoint characterization of directed trace metrics

Hennessy-Milner Theorems via Galois Connections

We introduce a general and compositional, yet simple, framework that allows us to derive soundness and expressiveness results for modal logics characterizing behavioural equivalences or metrics (also known as Hennessy-Milner theorems). It is based on Galois connections between sets of (real-valued) predicates on the one hand and equivalence relations/metrics on the other hand and covers a part of the linear-time-branching-time spectrum, both for the qualitative case (behavioural equivalences) and the quantitative case (behavioural metrics). We derive behaviour functions from a given logic and give a condition, called compatibility, that characterizes under which conditions a logically induced equivalence/metric is induced by a fixpoint equation. In particular this framework allows us to derive a new fixpoint characterization of directed trace metrics

Forward and Backward Steps in a Fibration

Distributive laws of various kinds occur widely in the theory of coalgebra, for instance to model automata constructions and trace semantics, and to interpret coalgebraic modal logic. We study steps, which are a general type of distributive law, that allow one to map coalgebras along an adjunction. In this paper, we address the question of what such mappings do to well known notions of equivalence, e.g., bisimilarity, behavioural equivalence, and logical equivalence. We do this using the characterisation of such notions of equivalence as (co)inductive predicates in a fibration. Our main contribution is the identification of conditions on the interaction between the steps and liftings, which guarantees preservation of fixed points by the mapping of coalgebras along the adjunction. We apply these conditions in the context of lax liftings proposed by Bonchi, Silva, Sokolova (2021), and generalise their result on preservation of bisimilarity in the construction of a belief state transformer. Further, we relate our results to properties of coalgebraic modal logics including expressivity and completeness

Bisimulation maps in presheaf categories

The category of presheaves on a (small) category is a suitable semantic universe to study behaviour of various dynamical systems. In particular, presheaves can be used to record the executions of a system and their morphisms correspond to simulation maps for various kinds of state-based systems. In this paper, we introduce a notion of bisimulation maps between presheaves (or executions) to capture well known behavioural equivalences in an abstract way. We demonstrate the versatility of this framework by working out the characterisations for standard bisimulation, ∀-fair bisimulation, and branching bisimulation

Linearization of CIF Through SOS

Linearization is the procedure of rewriting a process term into a linear form, which consist only of basic operators of the process language. This procedure is interesting both from a theoretical and a practical point of view. In particular, a linearization algorithm is needed for the Compositional Interchange Format (CIF), an automaton based modeling language. The problem of devising efficient linearization algorithms is not trivial, and has been already addressed in literature. However, the linearization algorithms obtained are the result of an inventive process, and the proof of correctness comes as an afterthought. Furthermore, the semantic specification of the language does not play an important role on the design of the algorithm. In this work we present a method for obtaining an efficient linearization algorithm, through a step-wise refinement of the SOS rules of CIF. As a result, we show how the semantic specification of the language can guide the implementation of such a procedure, yielding a simple proof of correctness.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

Conditional transition systems with upgrades

We introduce a variant of transition systems, where activation of transitions depends on conditions of the environment and upgrades during runtime potentially create additional transitions. Using a cornerstone result in lattice theory, we show that such transition systems can be modelled in two ways: as conditional transition systems (CTS) with a partial order on conditions, or as lattice transition systems (LaTS), where transitions are labelled with the elements from a distributive lattice. We define equivalent notions of bisimilarity for both variants and characterise them via a bisimulation game. We explain how conditional transition systems are related to featured transition systems for the modelling of software product lines. Furthermore, we show how to compute bisimilarity symbolically via BDDs by defining an operation on BDDs that approximates an element of a Boolean algebra into a lattice. We have implemented our procedure and provide runtime results. This is an extended version of the TASE 2017 paper [1], including all proofs, additional examples, an extension of the formalism to account for deactivation of updates and detailed runtime results