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A Featured Transition System (FTS) models the behaviour of all products of a Software Product Line (SPL) in a single compact structure, by associating action-labelled transitions with features that condition their presence in product behaviour. It may however be the case that the resulting featured transitions of an FTS cannot be executed in any product (so called dead transitions) or, on the contrary, can be executed in all products (so called false optional transitions). Moreover, an FTS may contain states from which a transition can be executed only in some products (so called hidden deadlock states). It is useful to detect such ambiguities and signal them to the modeller, because dead transitions indicate an anomaly in the FTS that must be corrected, false optional transitions indicate a redundancy that may be removed, and hidden deadlocks should be made explicit in the FTS to improve the understanding of the model and to enable efficient verification—if the deadlocks in the products should not be remedied in the first place. We provide an algorithm to analyse an FTS for ambiguities and a means to transform an ambiguous FTS into an unambiguous one. The scope is twofold: an ambiguous model is typically undesired as it gives an unclear idea of the SPL and, moreover, an unambiguous FTS can efficiently be model checked. We empirically show the suitability of the algorithm by applying it to a number of benchmark SPL examples from the literature, and we show how this facilitates a kind of family-based model checking of a wide range of properties on FTSs.

FTS4VMC is a publicly available front-end tool for the static analysis and family-based model checking of a Featured Transition System (FTS). It can detect ambiguities in an FTS, disambiguate an ambiguous FTS, transform an FTS into a Modal Transition System (MTS), and interact with the VMC model checker for family-based verification.

A Featured Transition System (FTS) is a formalism for modeling variability in configurable system behavior. The behavior of all variants (products) is modeled in a single compact FTS by associating the possibility to perform an action and transition from one state to another with feature expressions that condition the execution of an action in specific variants. We present a front-end for the research tool VMC. The resulting toolchain allows a modeler to analyze an FTS for ambiguities (dead or false optional transitions and hidden deadlock states), transform an ambiguous FTS into an unambiguous one, and perform an efficient kind of family-based verification of an FTS without hidden deadlock states. We use benchmarks from the literature to demonstrate the novelties offered by the toolchain.

Family-based model checking targets the simultaneous verification of multiple system variants, a technique to handle feature-based variability that is intrinsic to software product lines SPLs. We present an approach for family-based verification based on the feature $$\mu $$-calculus $$\mu L {}_f$$, which combines modalities with feature expressions. This logic is interpreted over featured transition systems, a well-accepted model of SPLs, which allows one to reason over the collective behavior of a number of variants a family of products. Via an embedding into the modal $$\mu $$-calculus with data, underpinned by the general-purpose mCRL2 toolset, off-the-shelf tool support fori¾?$$\mu L {}_f$$ becomes readily available. We illustrate the feasibility of our approach on an SPL benchmark model and show the runtime improvement that family-based model checking with mCRL2 offers with respect to model checking the benchmark product-by-product.

We demonstrate that modal transition systems with variability constraints are equally expressive as featured transition systems, by defining a transformation of the latter into the former, a transformation of the former into the latter, and proving the soundness and completeness of both transformations. Modal transition systems and featured transition systems are widely recognised as fundamental behavioural models for software product lines and our results thus contribute to the expressiveness hierarchy of such basic models studied in other papers published in this journal.

International audience; A Featured Transition System (FTS) is a formal behavioural model for software product lines, which represents the behaviour of all the products of an SPL in a single compact structure by associating transitions with features that condition their existence in products. In general, an FTS may contain featured transitions that are unreach-able in any product (so called dead transitions) or, on the contrary, mandatorily present in all products for which their source state is reachable (so called false optional transitions), as well as states from which only for certain products progress is possible (so called hidden deadlocks). In this paper, we provide algorithms to analyse an FTS for such ambiguities and to transform an ambiguous FTS into an unambiguous FTS. The scope of our approach is twofold. First and foremost, an ambiguous model is typically undesired as it gives an unclear idea of the SPL. Second, an unambiguous FTS paves the way for efficient family-based model checking. We apply our approach to illustrative examples from the literature.

The modal mu-calculus mu-L is a well-known fixpoint logic to express and model check properties interpreted over labeled transition systems. In this paper, we propose two variants of the mu-calculus, mu-Lf and mu-Lf', for feature transition systems. For this, we explicitly incorporate feature expressions into the logics, allowing operators to select transitions and behavior restricted to specific products and subfamilies. We provide semantics for mu-Lf and mu-Lf' and relate the two new mu-calculi and mu-L to each other. Next, we focus on the analysis of SPL behavior and show how our formalism can be applied for product-based verification with mu-Lf as well as family-based verification with mu-Lf'. We illustrate by means of a toy example how properties can be model checked, exploiting an embedding of mu-Lf' into the mu-calculus with data., Comment: In Proceedings FMSPLE 2016, arXiv:1603.08577

International audience; Model-based mutation analysis is a powerful but expensive testing technique. We tackle its high computation cost by proposing an optimization technique that drastically speeds up the mutant execution process. Central to this approach is the Featured Mutant Model, a modelling framework for mutation analysis inspired by the software product line paradigm. It uses behavioural variability models, viz., Featured Transition Systems, which enable the optimized generation, configuration and execution of mutants. We provide results, based on models with thousands of transitions, suggesting that our technique is fast and scalable. We found that it outperforms previous approaches by several orders of magnitude and that it makes higher-order mutation practically applicable.

In order to provide a rigorous foundation for Software Product Lines (SPLs), several fundamental approaches have been proposed to their formal behavioral modeling. In this paper, we provide a structured overview of those formalisms based on labeled transition systems and compare their expressiveness in terms of the set of products they can specify. Moreover, we define the notion of tests for each of these formalisms and show that our notions of testing precisely capture product derivation, i.e., all valid products will pass the set of test cases of the product line and each invalid product fails at least one test case of the product line. Comparing three fundamental models of Software Product Lines.Proving modal transition systems less expressive than product line labeled transition systems.Proving product line labeled transition systems less expressive than featured transition systems.Using Abramsky's test expressions to characterize product derivation.

Mutation testing is an established technique used to evaluate the quality of a set of test cases. As model-based testing took momentum, mutation techniques were lifted to the model level. However, as for code mutation analysis, assessing test cases on a large set of mutants can be costly. In this paper, we introduce the Variability-Intensive Behavioural teSting (VIBeS) framework. Relying on Featured Transition Systems (FTSs), we represent all possible mutants in a single model constrained by a feature model for mutant (in)activation. This allow to assess all mutants in a single test case execution. We present VIBeS implementation steps and the DSL we defined to ease model-based mutation analysis.

We show how the FMC model checker can successfully be used to model and analyze behavioural variability in Software Product Lines. FMC accepts parameterized specifications in a process-algebraic input language and allows the verification of properties of such models by means of efficient on-the-fly model checking. The properties can be expressed in a logic that allows to correlate the parameters of different actions within the same formula. We show how this feature can be used to tailor formulas to the verification of only a specific subset of products of a Software Product Line, thus allowing for scalable family-based analyses with FMC. We present a proof-of-concept that shows the application of FMC to an illustrative Featured Transition System from the literature.

We present an automatic technique to transform a subclass of featured transition systems into modal transition systems with additional sets of variability constraints in the specific format accepted by the variability model checker VMC. Both formal models are widely used in the field of software product line engineering and both come with a dedicated model checker. The transformation serves two purposes. First, it contributes to a better understanding of the fundamental differences between the two approaches, basically concerning the way in which variability constraints are represented (in terms of features and actions, respectively). Second, it paves the way to compare the modelling and analysis of product line behaviour in two different settings.

International audience; Mutation testing is an effective technique for either improving or generating fault-finding test suites. It creates defective or incorrect program artifacts of the program under test and evaluates the ability of test suites to reveal them. Despite being effective, mutation is costly since it requires assessing the test cases with a large number of defective artifacts. Even worse, some of these artifacts are behaviourally "equivalent" to the original one and hence, they unnecessarily increase the testing effort. We adopt a variability perspective on mutation analysis. We model a defective artifact as a transition system with a specific feature selected and consider it as a member of a mutant family. The mutant family is encoded as a Featured Transition System, a compact formalism initially dedicated to model-checking of software product lines. We show how to evaluate a test suite against the set of all candidate defects by using mutant families. We can evaluate all the considered defects at the same time and isolate some equivalent mutants. We can also assist the test generation process and efficiently consider higher-order mutants.