Behavioural hybrid process calculus

Process algebra is a theoretical framework for the modelling and analysis of the behaviour of concurrent discrete event systems that has been developed within computer science in past quarter century. It has generated a deeper nderstanding of the nature of concepts such as observable behaviour in the presence of nondeterminism, system composition by interconnection of concurrent component systems, and notions of behavioural equivalence of such systems. It has contributed fundamental concepts such as bisimulation, and has been successfully used in a wide range of problems and practical applications in concurrent systems. We believe that the basic tenets of process algebra are highly compatible with the behavioural approach to dynamical systems. In our contribution we present an extension of classical process algebra that is suitable for the modelling and analysis of continuous and hybrid dynamical systems. It provides a natural framework for the concurrent composition of such systems, and can deal with nondeterministic behaviour that may arise from the occurrence of internal switching events. Standard process algebraic techniques lead to the characterisation of the observable behaviour of such systems as equivalence classes under some suitably adapted notion of bisimulation

Model checking Quantitative Linear Time Logic

This paper considers QLtl, a quantitative analagon of Ltl and presents algorithms for model checking QLtl over quantitative versions of Kripke structures and Markov chains

Bisimulation maps in presheaf categories

The category of presheaves on a (small) category is a suitable semantic universe to study behaviour of various dynamical systems. In particular, presheaves can be used to record the executions of a system and their morphisms correspond to simulation maps for various kinds of state-based systems. In this paper, we introduce a notion of bisimulation maps between presheaves (or executions) to capture well known behavioural equivalences in an abstract way. We demonstrate the versatility of this framework by working out the characterisations for standard bisimulation, ∀-fair bisimulation, and branching bisimulation

Simulation Techniques

In the papers surveyed in this thesis a number of simulation techniques are presented together with their applications to several examples. The papers improve upon existing techniques and introduce new techniques. The improvement of existing techniques is motivated in programming methodology: It is demonstrated that existing techniques often introduce a double proof burden whereas the improved techniques alleviate such a burden. One application is to ensure delay insensitivity in a class of self-timed circuits. A major part of the thesis is concerned with the deduction and use of two simulation techniques to prove the correctness of translations from subsets of occam-2 to transputer code

Analyzing Divergence for Nondeterministic Probabilistic Models

Branching and weak probabilistic bisimilarities are two well-known notions capturing behavioral equivalence between nondeterministic probabilistic systems. For probabilistic systems, divergence is of major concern. Recently several divergence-sensitive refinements of branching and weak probabilistic bisimilarities have been proposed in the literature. Both the definitions of these equivalences and the techniques to investigate them differ significantly. This paper presents a comprehensive comparative study on divergence-sensitive behavioral equivalence relations that refine the branching and weak probabilistic bisimilarities. Additionally, these equivalence relations are shown to have efficient checking algorithms. The techniques of this paper might be of independent interest in a more general setting

Incremental Verification of Component-Based Timed Systems

International audienceWe are interested in the incremental development, by integration of components, of component-based timed systems, and in particular, in the preservation of their properties during such a development process. We model timed components with timed automata. Their composition is achieved with the classic parallel composition operator for timed automata. The specifications of these timed systems are expressed with the timed linear logic Mitl (Metric Interval Temporal Logic). To guarantee the preservation of properties during an incremental development process, we propose to use ? -simulation relations, adapted for timed systems. First, we extend the classic notion of ? -simulation with timed aspects. As in the untimed case, this relation, called timed ? -simulation, preserves safety properties. To preserve more properties, in particular liveness ones, we present another relation, called divergencesensitive and stability-respecting (DS) timed ? -simulation. This last relation preserves all Mitl properties (and thus liveness ones), but also strong non-zenoness and deadlockfreedom. Moreover, as we put ourselves in a component-based framework, we study if the relations are appropriate to the use of the composition operator that we consider. For this purpose, we study if the relations are compatible with this operator, and if composability and compositionality hold. These three properties are a way to reduce the cost of the verification of the preservation, or even to get it for free. It results that the timed ? -simulation is appropriate with the classic operator since the properties hold without any assumption. However, this is not the case for the DS timed ? - simulation. We implemented the algorithmic verification of the simulations in a tool called Vesta (Verification of Simulation for Timed Automata). The structure of the tool was inspired from the one of the Open-Kronos tool. This allows, as additionnal feature, to connect the models considered in Vesta to the modules of the verification platform Open-Caesar. We show the interest of our method by applying it on a case study, concerning a production cell example