Software complexity crisis becomes an impediment to further development of software. Specifically, in order to manage increasingly complex and massive software systems, researchers involve in building systems with autonomy. The real-time reactive systems with autonomic behaviors could be more selfmanaged and more adaptive to the environment. However, formations of some of such systems are not formalized, which may lead systems to be error-prone. In this research, we proposed a formal way to describe formations of reactive autonomic systems framework. Firstly, we introduce how to from reactive autonomic system, components group, and component, then we focused on categorizing the formations. To do so, the basis of reactive autonomic systems can be built with correct by construction.

Keywords : Reactive Autonomic System; Category Theory; Formation.