Real-time reactive systems are some of the most complex systems, so the modeling and development of real-time reactive systems becomes a very challenging and difficult task. On the other hand, autonomic computing is the new research area which focuses on developing complex computing system smarter and easier to manage. The Reactive Autonomic System Framework (RASF, previously named AS-TRM) is a formal framework to leverage the modeling, development, integration and maintenance of the Reactive Autonomic Systems (RASs), which systems can simplify and enhance the end-users experience by anticipating their needs in a complex, dynamic, uncertain, and real-time environment. It adds the reactive behavior to the autonomic behavior that focuses on making complex computing systems smarter and easier to manage. To our knowledge, the RASF represents the first attempt to model reactive behavior for autonomic systems. The latest 5-tier formal model of the RASF describes the LSL for ADT, the formal specification for RAO, RAC, RACG, RAS, and their corresponding theories. In the layered architecture of the RASF, each tier communicates only with the tier immediately above it or below it. So, the independence of the tiers makes their modularity, reuse, hierarchical decomposition, and encapsulation possible. Autonomic behaviors are implemented by the local managers, group managers and global managers at the RAC, RACG, as well as RAS tier respectively.