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Model checking (MC) for Halpern and Shoham’s interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics (state-based, trace-based and tree-based semantics), all of them assuming homogeneity in the propositional valuation. Here, we focus on the trace-based semantics, where the main semantic entities are the infinite execution paths (traces) of the given Kripke structure. We introduce a quantitative extension of HS over traces, called Difference HS (DHS), allowing one to express timing constraints on the difference among interval lengths (durations). We show that MC and satisfiability of full DHS are in general undecidable, so, we investigate the decidability border for these problems by considering natural syntactical fragments of DHS. In particular, we identify a maximal decidable fragment DHS_{simple} of DHS proving in addition that the considered problems for this fragment are at least 2Expspace-hard. Moreover, by exploiting new results on linear-time hybrid logics, we show that for an equally expressive fragment of DHS_{simple}, the problems are Expspace-complete. Finally, we provide a characterization of HS over traces by means of the one-variable fragment of a novel hybrid logic., LIPIcs, Vol. 247, 29th International Symposium on Temporal Representation and Reasoning (TIME 2022), pages 11:1-11:16

This paper presents our approach to the quantitative modeling and analysis of highly (re)configurable systems, such as software product lines. Different combinations of the optional features of such a system give rise to combinatorially many individual system variants. We use a formal modeling language that allows us to model systems with probabilistic behavior, possibly subject to quantitative feature constraints, and able to dynamically install, remove or replace features. More precisely, our models are defined in the probabilistic feature-oriented language QFLAN, a rich domain specific language (DSL) for systems with variability defined in terms of features. QFLAN specifications are automatically encoded in terms of a process algebra whose operational behavior interacts with a store of constraints, and hence allows to separate system configuration from system behavior. The resulting probabilistic configurations and behavior converge seamlessly in a semantics based on discrete-time Markov chains, thus enabling quantitative analysis. Our analysis is based on statistical model checking techniques, which allow us to scale to larger models with respect to precise probabilistic analysis techniques. The analyses we can conduct range from the likelihood of specific behavior to the expected average cost, in terms of feature attributes, of specific system variants. Our approach is supported by a novel Eclipse-based tool which includes state-of-the-art DSL utilities for QFLAN based on the Xtext framework as well as analysis plug-ins to seamlessly run statistical model checking analyses. We provide a number of case studies that have driven and validated the development of our framework., major revision

QFLan offers modeling and analysis of highly reconfigurable systems, like product lines, which are characterized by combinatorially many system variants (or products) that can be obtained via different combinations of installed features. The tool offers a modern integrated development environment for the homonym probabilistic feature-oriented language. QFLan allows the specification of a family of products in terms of a feature model with quantitative attributes, which defines the valid feature combinations, and probabilistic behavior subject to quantitative constraints. The language's behavioral part enables dynamic installation, removal and replacement of features. QFLan has a discrete-time Markov chain semantics, permitting quantitative analyses. Thanks to a seamless integration with the statistical model checker MultiVeStA, it allows for analyses like the likelihood of specific behavior or the expected average value of non-functional aspects related to feature attributes.

International audience; We report on the suitability of statistical model checking forthe analysis of quantitative properties of product line models by an extendedtreatment of earlier work by the authors. The type of analysis thatcan be performed includes the likelihood of specific product behaviour,the expected average cost of products (in terms of the attributes of theproducts’ features) and the probability of features to be (un)installed atruntime. The product lines must be modelled in QFLan, which extendsthe probabilistic feature-oriented language PFLan with novel quantitativeconstraints among features and on behaviour and with advancedfeature installation options. QFLan is a rich process-algebraic specifi-cation language whose operational behaviour interacts with a store ofconstraints, neatly separating product configuration from product behaviour.The resulting probabilistic configurations and probabilistic behaviourconverge in a discrete-time Markov chain semantics, enablingthe analysis of quantitative properties. Technically, a Maude implementationof QFLan, integrated with Microsoft’s SMT constraint solver Z3,is combined with the distributed statistical model checker MultiVeStA,developed by one of the authors. We illustrate the feasibility of our frameworkby applying it to a case study of a product line of bikes.

We investigate the suitability of statistical model checking for the analysis of probabilistic models of software product lines with complex quantitative constraints and advanced feature installation options. Such models are specified in the feature-oriented language QFLan, a rich process algebra whose operational behaviour interacts with a store of constraints, neatly separating product configuration from product behaviour. The resulting probabilistic configurations and behaviour converge seamlessly in a semantics based on DTMCs, thus enabling quantitative analyses ranging from the likelihood of certain behaviour to the expected average cost of products. This is supported by a Maude implementation of QFLan, integrated with the SMT solver Z3 and the distributed statistical model checker MultiVeStA. Our approach is illustrated with a bikes product line case study.

We investigate the suitability of statistical model checking techniques for the analysis of probabilistic models of software product lines with complex quantitative constraints and advanced feature installation options. Such SPL models are defined in the probabilistic feature-oriented language QFLan. QFLan is a rich process algebra whose operational behaviour interacts with a store of constraints and as such it allows to separate product configuration from product behaviour. The resulting probabilistic configurations and behaviour converge seamlessly in a semantics based on discrete-time Markov chains, thus enabling quantitative analysis. To this aim, we combine a Maude implementation of QFLan, integrated with Microsoft's SMT constraint solver Z3, with the distributed statistical model checker MultiVeStA. This enables analyses that range from the likelihood of specific behaviour to the expected average cost of products, in terms of feature attributes. We illustrate our approach by performing quantitative analyses on a bikes product line case study.