In this chapter we shall see how our dynamic theory for a nice BRS can be applied to recover the standard dynamic theory of CCS.

Section 10.1 deals mainly with the translation of finite CCS into bigraphs, covering both syntactic structure and the basic features of reaction. It begins with a summary of all work done on CCS in previous chapters, in order to gather the whole application of bigraphs to CCS in one chapter. It then presents the translation into bigraphs, which encodes each structural congruence class of CCS into a single bigraph. It ends with the simple result that reaction as defined in CCS terms correponds exactly to reaction as defined by bigraphical rules.

Based upon this summary, Section 10.2 lays out the contextual transition system derived for finite CCS by the method of Chapter 8, recalling that its bisimilarity is guaranteed to be a congruence. This congruence is finer than the original bisimilarity of CCS. This is because the original is not preserved by substitution; on the other hand, our derived contextual TS contains transitions that observe the effect of substitution on an agent, and this yields a finer bisimilarity that is indeed a congruence. By omitting the substitutional transitions from the contextual TS, we then obtain a bisimilarity that coincides with the original.

This contextual TS is more complex than the original raw one, since its labels are parametric. But we are able to reduce it to a smaller faithful contextual TS whose labels are no longer parametric, and this corresponds almost exactly with the original raw TS for CCS.

In this chapter we show how bigraphs can be built from smaller ones by composition, product and identities. In this we follow process algebra, where the idea is first to determine how distributed systems are assembled structurally, and then on this basis to develop their dynamic theory, deriving the behaviour of an assembly from the behaviours of its components.

This contrasts with our definition of a bigraph as the pair of a place graph and a link graph. This pairing is important for bigraphical theory, as we shall see later; but it may not reflect how a system designer thinks about a system. The algebra of this chapter, allowing bigraphs to be built from elementary bigraphs, is a basis for the synthetic approach of the system-builder.

Our algebraic structure pertains naturally to the abstract bigraphs Bg(Κ). Much of it pertains equally to concrete bigraphs. Properties enjoyed exclusively by concrete bigraphs are postponed until Chapter 5.

Elementary bigraphs and normal forms

Notation and convention The places of G: 〈m, X〉 → 〈n, Y〉 are its sites m, its nodes and its roots n. The points of G are its ports and inner names X. The links of G are its edges and outer names Y; the edges are closed links, and the outer names are open links. A point is said to be open if its link is open, otherwise it is closed. G is said to be open if all its links are open (i.e. it has no edges).

In this chapter we place the bigraph model in the broader informatic context.

The bigraph model attempts to bridge two distinct cultures. On the one hand is the adolescent culture of ubiquitous computing; on the other hand is the more mature theory of concurrent processes. The first two sections of this chapter describe the two cultures in enough detail to show how the bigraph model fits into each of them, and how together they demand the existence of some such model. In the third section I describe how bigraphs evolved as a generic model of processes. Finally I describe ongoing work to create software tools that will bring bigraphs to life as a language for programming and simulation, thus admitting experiments that will help to assess the scientific value of this model.

Background in ubiquitous computing Let us first look at the vision of ubiquitous computing. Mark Weiser [79] is generally credited with forming this vision and inspiring research that will bring it to reality; I quoted him briefly in the Prologue. The vision represents one of the most ambitious aspirations of computer science, and has been adopted as a Grand Challenge by the UK Computing Research Committee (UKCRC). The title of its manifesto [1], ‘Ubiquitous computing: experience, design and science’, reflects the insight that to realise the vision demands collaboration among three distinct research communities: those concerned with the human–computer interface and human behaviour, those concerned with engineering principles and design patterns for large systems, and those concerned with theoretical models and the languages that bring them to life. These three themes cannot be addressed in isolation.

The informatic challenge

Computing is transforming our environment. Indeed, the term ‘computing’ describes this transformation too narrowly, because traditionally it means little more than ‘calculation’. Nowadays, artifacts that both calculate and communicate pervade our lives. It is better to describe this combination as ‘informatics’, connoting not only the passive stuff (numbers, documents, …) with which we compute, but also the activity of informing, or interacting, or communicating.

The stored-program computer, which sowed the seeds of this transformation 60 years ago, is itself a highly organised informatic engine specialised to the task of calculation. Computers work by internal communication among their parts; noone expected that, within half a century, most of their work – bar highly specialised applications – would involve external communication. But within 25 years arose networks of interacting computers; the control of interaction then became a prime concern. Interacting systems, such as the worldwide web or networks of people with phones, are now commonplace; software takes part in them, but most prominent is communication, not calculation.

These artifacts will be everywhere. They will control driverless motorway traffic, via communication among sensors and effectors at the roadside and in vehicles; they will monitor and treat our health via communication between devices installed in the human body and software in hospitals. Thus the term ‘ubiquitous computing’ represents a vision that is being realised. In 1994 Mark Weiser, a pioneer of this vision, wrote

Populations of computing entities will be a significant part of our environment, performing tasks that support us, and we shall be largely unaware of them.