On Hierarchical Graphs: Reconciling Bigraphs, Gs-monoidal Theories and Gs-graphs

Abstract

Compositional graph models for global computing systems must account for two relevant dimensions, namely structural containment and communication linking. In Milner's bigraphs the two dimensions are made explicit and represented as two loosely coupled structures: the place graph and the link graph. Here, bigraphs are compared with an earlier model, gs-graphs, originally conceived for modelling the syntactical structure of agents with α-convertible declarations. We show that gs-graphs are quite convenient also for the new purpose, since the two above mentioned dimensions can be recovered by considering only a specific class of hyper-signatures. With respect to bigraphs, gs-graphs can be proved essentially equivalent, with minor differences at the interface level. We argue that gs-graphs offer a simpler and more standard algebraic structure, based on monoidal categories, for representing both states and transitions. Moreover, they can be equipped with a simple type system to check the well-formedness of legal gs-graphs that are shown to characterise binding bigraphs. Another advantage concerns a textual form in terms of sets of assignments, which can make implementation easier in rewriting frameworks like Maude.