Section: Overall Objectives

Necessity of quantitative models

Several disciplines in computer science have of course addressed some of the issues raised by large systems. For example, formal methods (essentially for verification purposes), discrete-event systems (diagnosis, control, planning, and their distributed versions), but also concurrency theory (modelling and analysis of large concurrent systems). Practical needs have oriented these methods towards the introduction of quantitative aspects, such as time, probabilities, costs, and their combinations. This approach drastically changes the nature of questions that are raised. For example, verification questions become the reachability of a state in a limited time, the average sojourn duration in a state, the probability that a run of the system satisfies some property, the existence of control strategies with a given winning probability, etc. In this setting, exact computations are not always appropriate as they may end up with unaffordable complexities, or even with undecidability. Approximation strategies then offer a promising way around, and are certainly also a key to handling large systems. Approaches based on discrete-event systems follow the same trend towards quantitative models. For diagnosis aspects, one is interested in the most likely explanations to observed malfunctions, in the identification of the most informative tests to perform, or in the optimal placement of sensors. For control problems, one is of course interested in optimal control, in minimizing communications, in the robustness of the proposed controllers, in the online optimization of QoS (Quality of Service) indicators, etc.