Pure bigraphs

Bigraphs are graphs whose nodes may be nested, representing locality, independently of the edges connecting them. T hey may be equipped with reaction rules, forming a bigraphical reactive system(Brs) in which bigraphs can reconfigure themselves. Brss aim to uni fy process calculi, and to model applications —such as pervasive comput ing— where locality and mobility are prominent. The paper is devoted to the theory of purebigraphs, which underlie various more refined forms. It begi ns by developing a more abstract structure, a wide reactive system(Wrs), of which a Brs is an instance; in this context, labelled transitions a re defined in such a way that the induced bisimilarity is a congruence. This work is then specialised to Brss, whose graphical struc tu e 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 latte r part of the paper emphasizes the parts of bigraphical theory that are co mmon to these applications, especially the treatment of dynamics via lab el ed transitions. As a running example, the theory is applied to finite pure CCS, whose resulting transition system and bisimilarity are analysed in etail. The paper also discusses briefly the use of bigraphs to model b th pervasive computing and biological systems.