Global Graph Transformations

In this paper, we consider Global Graph Transformations where all occurrences of a set of predefined local rules are applied altogether synchronously so that each part of the original graph gives rise to a part of the result graph, without any reference to the original one. The particularity here is that our framework is deterministic. This is achieved by incorporating a notion of mutual agreement between its local rules. Our proposition is first motivated and illustrated on existing problems coming from different domains. It is then formalized as a categorical construction which is finally compared to more usual algebraic constructions, in particular to the strongly related Amalgamation Theorem. Applications of this work include the generalization of cellular automata and the clarification of some frameworks of complex systems modeling where the usual mutual exclusion of rule applications can be replaced by a concept of mutual agreement.