Section: New Results

Component-Based Design

Participants : Eric Badouel, Albert Benveniste, Benoît Caillaud, Benoît Delahaye, Sophie Pinchinat.

The Modal Interface Theory

In [18] , we present the modal interface theory, a unification of interface automata and modal specifications, two radically dissimilar models for interface theories. Interface automata is a game-based model, which allows the designer to express assumptions on the environment and which uses an optimistic view of composition: two components can be composed if there is an environment where they can work together. Modal specifications are a language theoretic account of a fragment of the modal mu-calculus logic with a rich composition algebra which meets certain methodological requirements but which does not allow the environment and the component to be distinguished. The present paper contributes a more thorough unification of the two theories by correcting a first attempt in this direction by Larsen et al., drawing a complete picture of the modal interface algebra, and pushing the comparison between interface automata, modal automata and modal interfaces even further.

A Stochastic Interface Theory

Notions of specification, implementation, satisfaction, and refinement, together with operators supporting stepwise design, constitute a specification theory. In [16] , we construct such a theory for Markov Chains (MCs) employing a new abstraction of a Constraint MC. Constraint MCs permit rich constraints on probability distributions and thus generalize prior abstractions such as Interval MCs. Linear (polynomial) constraints suffice for closure under conjunction (respectively parallel composition). This is the first specification theory for MCs with such closure properties. We discuss its relation to simpler operators for known languages such as probabilistic process algebra. Despite the generality, all operators and relations are computable.

Contract-Based Compositional Analysis of Stochastic Systems

A contract allows to distinguish hypotheses made on a system (the guarantees) from those made on its environment (the assumptions). In [17] , we focus on models of Assume/Guarantee contracts for (stochastic) systems. We consider contracts capable of capturing reliability and availability properties of such systems. We also show that classi- cal notions of Satisfaction and Refinement can be checked by effective methods thanks to a reduction to classical verification problems. Finally, theorems supporting compositional reasoning and enabling the scalable analysis of complex systems are also studied.

Modal event-clock specifications for timed component-based design

On the one hand, modal specifications are classic, convenient, and expressive mathematical objects to represent interfaces of component-based systems. On the other hand, time is a crucial aspect of systems for practical applications, e.g. in the area of embedded systems. And yet, only few results exist on the design of timed component-based systems. In [13] , we propose a timed extension of modal specifications, together with fundamental operations (conjunction, product, and quotient) that enable reasoning in a compositional way about timed system. The specifications are given as modal event-clock automata, where clock resets are easy to handle. We develop an entire theory that promotes ecient incremental design techniques.