Pure bigraphs

Bigraphs are graphs whose nodes may be nested, representing locality, independently of the edges connecting them. They may be equipped with reaction rules, forming a bigraphical reactive system (Brs) in which bigraphs can reconfigure themselves. Brss aim to unify process calculi, and to model applications —such as pervasive computing— where locality and mobility are prominent. The paper is devoted to the theory of pure bigraphs, which underlie various more refined forms. It begins by developing a more abstract structure, a wide reactive system (Wrs), of which a Brs is an instance; in this context, labelled transitions are defined in such a way that the induced bisimilarity is a congruence. This work is then specialised to Brss, whose graphical structure allows many refinements of the dynamic theory. Elsewhere it is shown that behavioural analysis for Petri nets, π-calculus and mobile ambients can all be recovered in the uniform framework of bigraphs. The latter part of the paper emphasizes the parts of bigraphical theory that are common to these applications, especially the treatment of dynamics via labelled transitions. As a running example, the theory is applied to finite pure CCS, whose resulting transition system and bisimilarity are analysed in detail. The paper also discusses briefly the use of bigraphs to model both pervasive computing and biological systems.