Emergent Properties in Reactive Systems

Reactive systems are often described by interconnecting sub-components along architectural connectors defining communication policies. Generally, such global systems may exhibit properties, often called "emergent properties", that cannot be anticipated just from a complete knowledge of components. These emergent properties are twofold: (1) the global system can question properties attached to components; (2) some global properties cannot be inferred only from a complete knowledge of components, but for being inferred, need the knowledge of cooperation mechanisms between components. In practice, properties of the second form combine knowledge inherited from components. Thus, they are often defined in a richer language than the ones associated to each component and the presence of such emergent properties is quite natural. In this paper, we restrict ourselves to reactive systems described by means of transition systems as components and of the usual synchronous product as architectural connector and whose behavior is expressed by logical properties over a modal first-order logic. In this framework, we propose to study complexity of reactive systems through this notion of emergent properties and we will give some conditions to guarantee when a system has not emergent properties of the first form.