arXiv subjects

Axel Legay

Publications and source records attributed to Axel Legay.

At least 55 records · Page 3Linked to original sources

arXiv2015

Quantitative Analysis of Probabilistic Models of Software Product Lines with Statistical Model Checking

We investigate the suitability of statistical model checking techniques for analysing quantitative properties of software product line models with probabilistic aspects. For this purpose, we enrich the feature-oriented language FLan with action rates, which specify the likelihood of exhibiting particular behaviour or of installing features at a specific moment or in a specific order. The enriched language (called PFLan) allows us to specify models of software product lines with probabilistic configurations and behaviour, e.g. by considering a PFLan semantics based on discrete-time Markov chains. The Maude implementation of PFLan is combined with the distributed statistical model checker MultiVeStA to perform quantitative analyses of a simple product line case study. The presented analyses include the likelihood of certain behaviour of interest (e.g. product malfunctioning) and the expected average cost of products.

cs.SE↗

arXiv2015

Lightweight Monte Carlo Verification of Markov Decision Processes with Rewards

Markov decision processes are useful models of concurrency optimisation problems, but are often intractable for exhaustive verification methods. Recent work has introduced lightweight approximative techniques that sample directly from scheduler space, bringing the prospect of scalable alternatives to standard numerical model checking algorithms. The focus so far has been on optimising the probability of a property, but many problems require quantitative analysis of rewards. In this work we therefore present lightweight statistical model checking algorithms to optimise the rewards of Markov decision processes. We consider the standard definitions of rewards used in model checking, introducing an auxiliary hypothesis test to accommodate reachability rewards. We demonstrate the performance of our approach on a number of standard case studies.

cs.LO↗

arXiv2015

Smart Sampling for Lightweight Verification of Markov Decision Processes

Markov decision processes (MDP) are useful to model optimisation problems in concurrent systems. To verify MDPs with efficient Monte Carlo techniques requires that their nondeterminism be resolved by a scheduler. Recent work has introduced the elements of lightweight techniques to sample directly from scheduler space, but finding optimal schedulers by simple sampling may be inefficient. Here we describe "smart" sampling algorithms that can make substantial improvements in performance.

cs.DS↗

arXiv2015

*-Continuous Kleene $ω$-Algebras

We define and study basic properties of *-continuous Kleene $ω$-algebras that involve a *-continuous Kleene algebra with a *-continuous action on a semimodule and an infinite product operation that is also *-continuous. We show that *-continuous Kleene $ω$-algebras give rise to iteration semiring-semimodule pairs. We show how our work can be applied to solve certain energy problems for hybrid systems.

cs.FL↗

arXiv2014

Stochastic Semantics and Statistical Model Checking for Networks of Priced Timed Automata

This paper offers a natural stochastic semantics of Networks of Priced Timed Automata (NPTA) based on races between components. The semantics provides the basis for satisfaction of probabilistic Weighted CTL properties (PWCTL), conservatively extending the classical satisfaction of timed automata with respect to TCTL. In particular the extension allows for hard real-time properties of timed automata expressible in TCTL to be refined by performance properties, e.g. in terms of probabilistic guarantees of time- and cost-bounded properties. A second contribution of the paper is the application of Statistical Model Checking (SMC) to efficiently estimate the correctness of non-nested PWCTL model checking problems with a desired level of confidence, based on a number of independent runs of the NPTA. In addition to applying classical SMC algorithms, we also offer an extension that allows to efficiently compare performance properties of NPTAs in a parametric setting. The third contribution is an efficient tool implementation of our result and applications to several case studies.

cs.SE↗

arXiv2014

Homotopy Bisimilarity for Higher-Dimensional Automata

We introduce a new category of higher-dimensional automata in which the morphisms are functional homotopy simulations, i.e. functional simulations up to concurrency of independent events. For this, we use unfoldings of higher-dimensional automata into higher-dimensional trees. Using a notion of open maps in this category, we define homotopy bisimilarity. We show that homotopy bisimilarity is equivalent to a straight-forward generalization of standard bisimilarity to higher dimensions, and that it is finer than split bisimilarity and incomparable with history-preserving bisimilarity.

cs.LO↗

arXiv2014

Scalable Verification of Markov Decision Processes

Markov decision processes (MDP) are useful to model concurrent process optimisation problems, but verifying them with numerical methods is often intractable. Existing approximative approaches do not scale well and are limited to memoryless schedulers. Here we present the basis of scalable verification for MDPSs, using an O(1) memory representation of history-dependent schedulers. We thus facilitate scalable learning techniques and the use of massively parallel verification.

cs.DS↗

arXiv2014

Refinement and Difference for Probabilistic Automata

This paper studies a difference operator for stochastic systems whose specifications are represented by Abstract Probabilistic Automata (APAs). In the case refinement fails between two specifications, the target of this operator is to produce a specification APA that represents all witness PAs of this failure. Our contribution is an algorithm that allows to approximate the difference of two APAs with arbitrary precision. Our technique relies on new quantitative notions of distances between APAs used to assess convergence of the approximations, as well as on an in-depth inspection of the refinement relation for APAs. The procedure is effective and not more complex to implement than refinement checking.

cs.LO↗

arXiv2014

Tropical Fourier-Motzkin elimination, with an application to real-time verification

We introduce a generalization of tropical polyhedra able to express both strict and non-strict inequalities. Such inequalities are handled by means of a semiring of germs (encoding infinitesimal perturbations). We develop a tropical analogue of Fourier-Motzkin elimination from which we derive geometrical properties of these polyhedra. In particular, we show that they coincide with the tropically convex union of (non-necessarily closed) cells that are convex both classically and tropically. We also prove that the redundant inequalities produced when performing successive elimination steps can be dynamically deleted by reduction to mean payoff game problems. As a complement, we provide a coarser (polynomial time) deletion procedure which is enough to arrive at a simply exponential bound for the total execution time. These algorithms are illustrated by an application to real-time systems (reachability analysis of timed automata).

math.CO↗

arXiv2014

Structural Refinement for the Modal nu-Calculus

We introduce a new notion of structural refinement, a sound abstraction of logical implication, for the modal nu-calculus. Using new translations between the modal nu-calculus and disjunctive modal transition systems, we show that these two specification formalisms are structurally equivalent. Using our translations, we also transfer the structural operations of composition and quotient from disjunctive modal transition systems to the modal nu-calculus. This shows that the modal nu-calculus supports composition and decomposition of specifications.

cs.LO↗

arXiv2014

Measuring Global Similarity between Texts

We propose a new similarity measure between texts which, contrary to the current state-of-the-art approaches, takes a global view of the texts to be compared. We have implemented a tool to compute our textual distance and conducted experiments on several corpuses of texts. The experiments show that our methods can reliably identify different global types of texts.

cs.CL↗

arXiv2014

State Machine Flattening: Mapping Study and Assessment

State machine formalisms equipped with hierarchy and parallelism allow to compactly model complex system behaviours. Such models can then be transformed into executable code or inputs for model-based testing and verification techniques. Generated artifacts are mostly flat descriptions of system behaviour. \emph{Flattening} is thus an essential step of these transformations. To assess the importance of flattening, we have defined and applied a systematic mapping process and 30 publications were finally selected. However, it appeared that flattening is rarely the sole focus of the publications and that care devoted to the description and validation of flattening techniques varies greatly. Preliminary assessment of associated tool support indicated limited tool availability and scalability on challenging models. We see this initial investigation as a first step towards generic flattening techniques and scalable tool support, cornerstones of reliable model-based behavioural development.

cs.SE↗

arXiv2014

Towards Statistical Prioritization for Software Product Lines Testing

Software Product Lines (SPL) are inherently difficult to test due to the combinatorial explosion of the number of products to consider. To reduce the number of products to test, sampling techniques such as combinatorial interaction testing have been proposed. They usually start from a feature model and apply a coverage criterion (e.g. pairwise feature interaction or dissimilarity) to generate tractable, fault-finding, lists of configurations to be tested. Prioritization can also be used to sort/generate such lists, optimizing coverage criteria or weights assigned to features. However, current sampling/prioritization techniques barely take product behavior into account. We explore how ideas of statistical testing, based on a usage model (a Markov chain), can be used to extract configurations of interest according to the likelihood of their executions. These executions are gathered in featured transition systems, compact representation of SPL behavior. We discuss possible scenarios and give a prioritization procedure illustrated on an example.

cs.SE↗

arXiv2013

Contracts and Behavioral Patterns for SoS: The EU IP DANSE approach

This paper presents some of the results of the first year of DANSE, one of the first EU IP projects dedicated to SoS. Concretely, we offer a tool chain that allows to specify SoS and SoS requirements at high level, and analyse them using powerful toolsets coming from the formal verification area. At the high level, we use UPDM, the system model provided by the british army as well as a new type of contract based on behavioral patterns. At low level, we rely on a powerful simulation toolset combined with recent advances from the area of statistical model checking. The approach has been applied to a case study developed at EADS Innovation Works.

cs.SE↗

arXiv2013

SoS contract verification using statistical model checking

Exhaustive formal verification for systems of systems (SoS) is impractical and cannot be applied on a large scale. In this paper we propose to use statistical model checking for efficient verification of SoS. We address three relevant aspects for systems of systems: 1) the model of the SoS, which includes stochastic aspects; 2) the formalization of the SoS requirements in the form of contracts; 3) the tool-chain to support statistical model checking for SoS. We adapt the SMC technique for application to heterogeneous SoS. We extend the UPDM/SysML specification language to express the SoS requirements that the implemented strategies over the SoS must satisfy. The requirements are specified with a new contract language specifically designed for SoS, targeting a high-level English- pattern language, but relying on an accurate semantics given by the standard temporal logics. The contracts are verified against the UPDM/SysML specification using the Statistical Model Checker (SMC) PLASMA combined with the simulation engine DESYRE, which integrates heterogeneous behavioral models through the functional mock-up interface (FMI) standard. The tool-chain allows computing an estimation of the satisfiability of the contracts by the SoS. The results help the system architect to trade-off different solutions to guide the evolution of the SoS.

cs.SE↗

arXiv2013

Proceedings 1st Workshop on Advances in Systems of Systems

This volume contains the proceedings of the first workshop on Advances in Systems of Systems (AISOS'13), held in Roma, Italy, March 16. System-of-Systems describes the large scale integration of many independent self-contained systems to satisfy global needs or multi-system requests. Examples are smart grid, intelligent buildings, smart cities, transport systems, etc. There is a need for new modeling formalisms, analysis methods and tools to help make trade-off decisions during design and evolution avoiding leading to sub-optimal design and rework during integration and in service. The workshop should focus on the modeling and analysis of System of Systems. AISOS'13 aims to gather people from different communities in order to encourage exchange of methods and views.

cs.SE↗

arXiv2013

Verification for Reliable Product Lines

Many product lines are critical, and therefore reliability is a vital part of their requirements. Reliability is a probabilistic property. We therefore propose a model for feature-aware discrete-time Markov chains as a basis for verifying probabilistic properties of product lines, including reliability. We compare three verification techniques: The enumerative technique uses PRISM, a state-of-the-art symbolic probabilistic model checker, on each product. The parametric technique exploits our recent advances in parametric model checking. Finally, we propose a new bounded technique that performs a single bounded verification for the whole product line, and thus takes advantage of the common behaviours of the product line. Experimental results confirm the advantages of the last two techniques.

cs.SE↗

arXiv2013

Kleene Algebras and Semimodules for Energy Problems

With the purpose of unifying a number of approaches to energy problems found in the literature, we introduce generalized energy automata. These are finite automata whose edges are labeled with energy functions that define how energy levels evolve during transitions. Uncovering a close connection between energy problems and reachability and Büchi acceptance for semiring-weighted automata, we show that these generalized energy problems are decidable. We also provide complexity results for important special cases.

cs.FL↗