Dynamic Logic for Ensembles

Abstract

An ensemble consists of collaborating entities that are able to adapt at runtime. In this work we consider a particular class of ensembles: an ensemble is formed by a dynamically changing set of entities which interact through message exchange. The members of an ensemble are instances of certain process types. They can be dynamically created to join an ensemble on demand. We propose a dynamic logic to describe the evolution of ensembles from a global perspective. Using the power of dynamic logic with diamond and box modalities over regular expressions of actions (involving message exchange and process creation) we can specify desired and forbidden interaction scenarios. Thus our approach is suitable to write formal requirements specifications for ensemble behaviours. An ensemble realisation takes a local view by giving a constructive specification for each single process type in terms of a process algebraic expression. Correctness of an ensemble realisation is defined semantically: its generated ensemble transition system must be a model of the requirements specification. We consider bisimulation of ensemble transition systems and show that our approach enjoys the Hennessy-Milner property. Moreover, we show that local bisimulation equivalence of process type expressions implies global bisimulation equivalence of the generated ensembles.