System reconfiguration: a graph automata approach

A system comprised of a finite set of components, where between any pair of components it is assumed that some relationship may or may not exist, is considered. Such systems are commonly modeled as graphs, with the nodes and the edges of the graph representing the components and the relationship between the components, respectively. Given such a system and its graph theoretical model, a graph-finite-automata-based dynamic system can be constructed by considering the various different graphs on the fixed vertex set to be the states or configurations of the system, and by defining transitions between states in terms of graph-theoretic edge operations. In these automata, the final states represent the permissible steady system states. An intuitive introduction of such automata is followed by a more formal discussion of the automata that includes a practical description of how it could be used to model the dynamics of a communication system. Some basic properties of the graph finite automata, many of which are arrived at by considering its digraph representation, are analyzed