We illustrate how to manage variability in a single logical framework consisting of a Modal Transition System (MTS) and an associated set of formulae expressed in the branching-time temporal logic MHML interpreted in a deontic way over such MTSs. We discuss the commonalities and differences with the framework of Classen et al. based on Featured Transition Systems and Linear-time Temporal Logic. I. I Decades after their introduction in [29], Modal Transition Systems (MTSs) and several variants have been recognised as a formal model for behavioural aspects of product families [1], [3]-[7], [18], [19], [21], [28], [30]. An MTS is a Labelled Transition System (LTS) with a distinction among may and must transitions, which can be seen as optional and mandatory for the products of a family. Hence, given a product family, a single MTS allows the definition of both: 1) its underlying behaviour, by means of states and actions, shared among all products, and 2) its variation points, by means of possible and mandatory transitions, differentiating between products. While it can model optional and mandatory features, an MTS alone cannot model constraints regarding alternative features nor those regarding requires and excludes interfeature relations. In [5], we therefore defined a branchingtime temporal logic, MHML, able to express such constraints (and behavioural properties alike) and envisioned an algorithm to derive LTSs describing valid products from an MTS describing a product family and an associated set of MHML formulae expressing further constraints for the family.Our approach is thus to manage variability in product families with a single logical framework consisting of an MTS and a set of MHML formulae (interpreted over MTSs).Also Featured Transition Systems (FTSs) [14] were defined to describe the behaviour of a product family in a single model. An FTS is a Doubly-Labelled Transition System (L 2 TS) with an associated feature diagram, a distinction among transitions by means of a labelling indicating which transitions correspond to which features, and an ordering of the transitions that correspond to alternative features. Both approaches thus model product families in terms of specific transition systems that define a family's behaviour in terms of actions (features). Likewise, both approaches require the addition of further structural relationships between actions to manage (advanced) variability constraints. In this paper, we illustrate their commonalities and differences by applying both approaches to the same running example.As such, we continue the research we initiated in [3]-[5]. In [3], we showed how to finitely characterise a subclass of MTSs by means of deontic logic formulae. In [4], we presented an initial attempt at a logical framework capable of addressing both static and behavioural conformance of products of a product family, by defining a deontic extension of an action-and state-based branching-time temporal logic interpreted over doubly-labelled MTSs. In [5], we introduced MHML and prese...

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Abstract. We present a logical framework that is able to deal with variability in product family descriptions. The temporal logic MHML is based on the classical Hennessy-Milner logic with Until and we interpret it over Modal Transition Systems (MTSs). MTSs extend the classical notion of Labelled Transition Systems by distinguishing possible (may) and required (must) transitions: these two types of transitions are useful to describe variability in behavioural descriptions of product families. This leads to a novel deontic interpretation of the classical modal and temporal operators, which allows the expression of both constraints over the products of a family and constraints over their behaviour in a single logical framework. Finally, we sketch model-checking algorithms to verify MHML formulae as well as a way to derive correct products from a product family description.

The railway sector has seen a large number of successful applications of formal methods and tools. However, up-to-date, structured information about the industrial usage and needs related to formal tools in railways is limited. As a first step to address this, we present the results of a questionnaire submitted to 44 stakeholders with experience in the application of formal tools in railways. The questionnaire was oriented to gather information about industrial projects, and about the functional and quality features that a formal tool should have to be successfully applied in railways. The results show that the most used tools are, as expected, those of the B family, followed by an extensive list of about 40 tools, each one used by few respondents only, indicating a rich, yet scattered, landscape. The most desired features concern formal verification, maturity, learnability, quality of documentation, and ease of integration in a CENELEC process. This paper extends the body of knowledge on formal methods applications in the railway industry, and contributes with a ranked list of tool features considered relevant by railway stakeholders.

Organised to celebrate the 25th anniversary of the FMICS international conference, the present survey addresses 30 questions on the past, present, and future of formal methods in research, industry, and education. Not less than 130 high-profile experts in formal methods (among whom three Turing award winners and many recipients of other prizes and distinctions) accepted to participate in this survey. We analyse their answers and comments, and present a collection of 111 position statements provided by these experts. The survey is both an exercise in collective thinking and a family picture of key actors in formal methods.