Spatial Organization of the Chemical Paradigm and the Specification of Autonomic Systems

The chemical paradigm is an unconventional programming paradigm well fitted to the high-level specification of parallel systems. Based on the fixed point iterations of local rules, its use has been advocated for the programming of autonomic and amorphous systems . However, this model lacks an explicit handling of spatial relationships. In this contribution, we first show how the chemical paradigm can be extended beyond multisets to arbitrary topological collections . Topological collections handle in a uniform way sophisticated data structures required in algorithmics as well as distributed data structures needed for the programming of autonomic or amorphous systems. Then we adapt a well-known result on multiset ordering to the more general case of topological collections. Well-founded ordering on topological collection can be used to prove the termination of the fixed point iteration of local rules