A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and communicate. In this memorandum we develop their static and dynamic theory. In part I, we illustrate...

A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and communicate. In this memorandum we develop their static and dynamic theory. In Part I we illustrate...

We introduce explicit fusions of names. An explicit fusion is a process that exists concurrently with the rest of the system and enables two names to be used interchangeably. Explicit fusions provide a small-step account of reaction in process calculi such as the pi calculus and the fusion calculus. In this respect they are similar to the explicit substitutions of Abadi, Cardelli and Curien, which do the same for the lambda calculus. In this paper, we give a technical foundation for explicit fusions. We present the pi-F calculus, a simple process calculus with explicit fusions, and define a strong bisimulation congruence. We study the embeddings of the fusion calculus and the pi calculus. The former is fully abstract with respect to bisimulation.

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. Following an earlier paper describing link graphs, a constituent of bigraphs, this paper is a devoted to pure bigraphs, which in turn underlie various more refined forms. 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 paper first develops the dynamic theory of an 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 theory. The latter part of the paper emphasizes bigraphical theory that is relevant to 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 mentions briefly the use of bigraphs to model pervasive computing and

This paper axiomatises the structure of bigraphs, and proves that the resulting theory is complete. Bigraphs are graphs with double structure, representing locality and connectivity. They have been shown to represent dynamic theories for the #-calculus, mobile ambients and Petri nets, in a way that is faithful to each of those models of discrete behaviour. While the main purpose of bigraphs is to understand mobile systems, a prerequisite for this understanding is a well-behaved theory of the structure of states in such systems. The algebra of bigraph structure is surprisingly simple, as the paper demonstrates; this is because bigraphs treat locality and connectivity orthogonally

A notion of bigraph is proposed as the basis for a model of mobile interaction. A bigraph consists of two independent structures: a topograph representing locality and a monograph representing connectivity. Bigraphs are equipped with reaction rules to form bigraphical reactive systems (BRSs), which include versions of the -calculus and the ambient calculus. Bigraphs are shown to be a special case of a more abstract notion, wide reactive systems (WRSs), not assuming any particular graphical or other structure but equipped with a notion of width, which expresses that agents, contexts and reactions may all be widely distributed entities. A behavioural theory is established for WRSs using the categorical notion of relative pushout; it allows labelled transition systems to be derived uniformly, in such a way that familiar behavioural preorders and equivalences, in particular bisimilarity, are congruential under certain conditions. Then the theory of bigraphs is developed, and they are shown to meet these conditions. It is shown that, using certain functors, other WRSs which meet the conditions may also be derived; these may, for example, be forms of BRS with additional structure. Simple examples of bigraphical systems are discussed; the theory is developed in a number of ways in preparation for deeper application studies.

A framework is defined within which reactive systems can be studied formally. The framework is based upon s-categories, a new variety of categories, within which reactive systems can be set up in such a way that labelled transition systems can be uniformly extracted. These lead in turn to behavioural preorders and equivalences, such as the failures preorder (treated elsewhere) and bisimilarity, which are guaranteed to be congruential. The theory rests upon the notion of relative pushout previously introduced by the authors. The framework

Bigraphs have been introduced with the aim to provide a topographical meta-model for mobile, distributed agents that can manipulate their own linkages and nested locations, generalising both characteristics of the π-calculus and the Mobile Ambients calculus. We give the first bigraphical presentation of a non-linear, higher-order process calculus with nested locations, non-linear active process mobility, and local names, the calculus of Higher-Order Mobile Embedded Resources (Homer). The presentation is based on Milner’s recent presentation of the λ-calculus in local bigraphs. The combination of non-linear active process mobility and local names requires a new definition of parametric reaction rules and a representation of the location of names. We suggest localised bigraphs as a generalisation of local bigraphs in which links can be further localised. Key words: bigraphs, local names, non-linear process mobility

Abstract. This paper is an informal summary of different encoding techniques from process calculi and distributed formalisms to graphic frameworks. The survey includes the use of solo diagrams, term graphs, synchronized hyperedge replacement systems, bigraphs, tile models and interactive systems, all presented at the Dagstuhl Seminar 04241. The common theme of all techniques recalled here is having a graphic presentation that, at the same time, gives both an intuitive visual rendering (of processes, states, etc.) and a rigorous mathematical framework. 1

Overview This paper is written as background for a proposed Grand