A Formalism for Stochastic Adaptive Systems

Complex systems such as systems of systems result from the combination of several components that are organized in a hierarchical manner. One of the main characteristics of those systems is their ability to adapt to new situations by modifying their architecture. Those systems have recently been the subject of a series of works in the software engineering community. Most of those works do not consider quantitative features. The objective of this paper is to propose a modeling language for adaptive systems whose behaviors depend on stochastic features. Our language relies on an extension of stochastic transition systems equipped with (1) an adaptive operator that allows to reason about the probability that a system has to adapt its architecture over time, and (2) dynamic interactions between processes. As a second contribution, we propose a contract-based extension of probabilistic linear temporal logic suited to reason about assumptions and guarantees of such systems. Our work has been implemented in the Plasma-Lab tool developed at Inria. This tool allows us to define stochastic adaptive systems with an extension of the Prism language, and properties with patterns. In addition, Plasma-Lab offers a simulation-based model checking procedure to reason about finite executions of the system. First experiments on a large case study coming from an industrial driven European project give encouraging results.