A Mechanized Semantic Framework for Real-Time Systems

International audienceConcurrent systems consist of many components which may execute in parallel and are complex to design, to analyze, to verify, and to implement. The complexity increases if the systems have real-time constraints, which are very useful in avionic, spatial and other kind of embedded applications. In this paper we present a logical framework for defining and validating real-time formalisms as well as reasoning methods over them. For this purpose, we have implemented in the Coq proof assistant well known semantic domains for real-time systems based on labelled transitions systems and timed runs. We experiment our framework by considering the real-time CSP-based language fiacre, which has been defined as a pivot formalism for modeling languages (aadl, sdl, ...) used in the TOPCASED project. Thus, we define an extension to the formal semantic models mentioned above that facilitates the modeling of fine-grained time constraints of fiacre. Finally, we implement this extension in our framework and provide a proof method environment to deal with real-time system in order to achieve their formal certification

On the robustness of temporal properties for stochastic models

Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Automata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity inherent in biological processes. A classical question in formal modelling with clear relevance to biological modelling is the model checking problem. i.e. calculate the probability that a behaviour, expressed for instance in terms of a certain temporal logic formula, may occur in a given stochastic process. However, one may not only be interested in the notion of satisfiability, but also in the capacity of a system to mantain a particular emergent behaviour unaffected by the perturbations, caused e.g. from extrinsic noise, or by possible small changes in the model parameters. To address this issue, researchers from the verification community have recently proposed several notions of robustness for temporal logic providing suitable definitions of distance between a trajectory of a (deterministic) dynamical system and the boundaries of the set of trajectories satisfying the property of interest. The contributions of this paper are twofold. First, we extend the notion of robustness to stochastic systems, showing that this naturally leads to a distribution of robustness scores. By discussing two examples, we show how to approximate the distribution of the robustness score and its key indicators: the average robustness and the conditional average robustness. Secondly, we show how to combine these indicators with the satisfaction probability to address the system design problem, where the goal is to optimize some control parameters of a stochastic model in order to best maximize robustness of the desired specifications

Towards an Efficient Tree Automata Based Technique for Timed Systems

The focus of this paper is the analysis of real-time systems with recursion, through the development of good theoretical techniques which are implementable. Time is modeled using clock variables, and recursion using stacks. Our technique consists of modeling the behaviours of the timed system as graphs, and interpreting these graphs on tree terms by showing a bound on their tree-width. We then build a tree automaton that accepts exactly those tree terms that describe realizable runs of the timed system. The emptiness of the timed system thus boils down to emptiness of a finite tree automaton that accepts these tree terms. This approach helps us in obtaining an optimal complexity, not just in theory (as done in earlier work e.g.[concur16]), but also in going towards an efficient implementation of our technique. To do this, we make several improvements in the theory and exploit these to build a first prototype tool that can analyze timed systems with recursion

Revisiting Robustness in Priced Timed Games

Priced timed games are optimal-cost reachability games played between two players---the controller and the environment---by moving a token along the edges of infinite graphs of configurations of priced timed automata. The goal of the controller is to reach a given set of target locations as cheaply as possible, while the goal of the environment is the opposite. Priced timed games are known to be undecidable for timed automata with $3$ or more clocks, while they are known to be decidable for automata with $1$ clock. In an attempt to recover decidability for priced timed games Bouyer, Markey, and Sankur studied robust priced timed games where the environment has the power to slightly perturb delays proposed by the controller. Unfortunately, however, they showed that the natural problem of deciding the existence of optimal limit-strategy---optimal strategy of the controller where the perturbations tend to vanish in the limit---is undecidable with $10$ or more clocks. In this paper we revisit this problem and improve our understanding of the decidability of these games. We show that the limit-strategy problem is already undecidable for a subclass of robust priced timed games with $5$ or more clocks. On a positive side, we show the decidability of the existence of almost optimal strategies for the same subclass of one-clock robust priced timed games by adapting a classical construction by Bouyer at al. for one-clock priced timed games

Fundamental Approaches to Software Engineering

This open access book constitutes the proceedings of the 24th International Conference on Fundamental Approaches to Software Engineering, FASE 2021, which took place during March 27–April 1, 2021, and was held as part of the Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg but changed to an online format due to the COVID-19 pandemic. The 16 full papers presented in this volume were carefully reviewed and selected from 52 submissions. The book also contains 4 Test-Comp contributions

Current and Future Challenges in Knowledge Representation and Reasoning

Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022 a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade

Finite horizon analysis of Markov automata

Markov automata constitute an expressive continuous-time compositional modelling formalism, featuring stochastic timing and nondeterministic as well as probabilistic branching, all supported in one model. They span as special cases, the models of discrete and continuous-time Markov chains, as well as interactive Markov chains and probabilistic automata. Moreover, they might be equipped with reward and resource structures in order to be used for analysing quantitative aspects of systems, like performance metrics, energy consumption, repair and maintenance costs. Due to their expressive nature, they serve as semantic backbones of engineering frameworks, control applications and safety critical systems. The Architecture Analysis and Design Language (AADL), Dynamic Fault Trees (DFT) and Generalised Stochastic Petri Nets (GSPN) are just some examples. Their expressiveness thus far prevents them from efficient analysis by stochastic solvers and probabilistic model checkers. A major problem context of this thesis lies in their analysis under some budget constraints, i.e. when only a finite budget of resources can be spent by the model. We study mathematical foundations of Markov automata since these are essential for the analysis addressed in this thesis. This includes, in particular, understanding their measurability and establishing their probability measure. Furthermore, we address the analysis of Markov automata in the presence of both reward acquisition and resource consumption within a finite budget of resources. More specifically, we put the problem of computing the optimal expected resource-bounded reward in our focus. In our general setting, we support transient, instantaneous and final reward collection as well as transient resource consumption. Our general formulation of the problem encompasses in particular the optimal time-bound reward and reachability as well as resource-bounded reachability. We develop a sound theory together with a stable approximation scheme with a strict error bound to solve the problem in an efficient way. We report on an implementation of our approach in a supporting tool and also demonstrate its effectiveness and usability over an extensive collection of industrial and academic case studies.Markov-Automaten bilden einen mächtigen Formalismus zur kompositionellen Modellierung mit kontinuierlicher stochastischer Zeit und nichtdeterministischer sowie probabilistischer Verzweigung, welche alle in einem Modell unterstützt werden. Sie enthalten als Spezialfälle die Modelle diskreter und kontinuierlicher Markov-Ketten sowie interaktive Markov-Ketten und probabilistischer Automaten. Darüber hinaus können sie mit Belohnungs- und Ressourcenstrukturen ausgestattet werden, um quantitative Aspekte von Systemen wie Leistungsfähigkeit, Energieverbrauch, Reparatur- und Wartungskosten zu analysieren. Sie dienen aufgrund ihrer Ausdruckskraft als semantisches Rückgrat von Engineering Frameworks, Steuerungsanwendungen und sicherheitskritischen Systemen. Die Architekturanalyse und Designsprache (AADL), Dynamic Fault Trees (DFT) und Generalized Stochastic Petri Nets (GSPN) sind nur einige Beispiele dafür. Ihre Aussagekraft verhindert jedoch bisher eine effiziente Analyse durch stochastische Löser und probabilistische Modellprüfer. Ein wichtiger Problemzusammenhang dieser Arbeit liegt in ihrer Analyse unter Budgetbeschränkungen, das heisst wenn nur ein begrenztes Budget an Ressourcen vom Modell aufgewendet werden kann. Wir studieren mathematische Grundlagen von Markov-Automaten, da diese für die in dieser Arbeit angesprochene Analyse von wesentlicher Bedeutung sind. Dazu gehört insbesondere das Verständnis ihrer Messbarkeit und die Festlegung ihrer Wahrscheinlichkeitsmaßes. Darüber hinaus befassen wir uns mit der Analyse von Markov-Automaten in Bezug auf Belohnungserwerb sowie Ressourcenverbrauch innerhalb eines begrenzten Ressourcenbudgets. Genauer gesagt stellen wir das Problem der Berechnung der optimalen erwarteten Ressourcen-begrenzte Belohnung in unserem Fokus. Dieser Fokus umfasst transiente, sofortige und endgültige Belohnungssammlung sowie transienten Ressourcenverbrauch. Unsere allgemeine Formulierung des Problems beinhalet insbesondere die optimale zeitgebundene Belohnung und Erreichbarkeit sowie ressourcenbeschränkte Erreichbarkeit. Wir entwickeln die grundlegende Theorie dazu. Zur effizienten Lösung des Problems entwerfen wir ein stabilen Approximationsschema mit einer strikten Fehlerschranke. Wir berichten über eine Umsetzung unseres Ansatzes in einem Software-Werkzeug und zeigen seine Wirksamkeit und Verwendbarkeit anhand einer umfangreichen Sammlung von industriellen und akademischen Fallstudien