An Example of a Simply Connected Surface Bounding a Region by Alexander J. W.

By Alexander J. W.

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B3 retains any such link. Equally, there may be no such link – the context in which the rule is ˘ applied may close it off. Thus B3 can be applied to the system represented by E, or E, allowing an agent in the right-hand building to enter a room. Taking this a step further, observe that in E an agent and a computer are linked only when they occupy the same room. Moreover, starting from E, our rules B1– B3 will preserve this property, since only B3 creates such links, and only within a room. We therefore call the property an invariant for E in the system with this rule-set.

2 (a built environment) The next diagram shows a bare bigraph E over the signature K = {A : 2, B : 1, C : 2, R : 0}, which classifies nodes as agents, buildings, computers and rooms. The node-shapes are not significant, except to indicate the purpose of each port. The figure represents a state which may change because of the movement of agents, and perhaps other movements. Think of the five agents as conducting a conference call (the long link). An agent in a room may also be logged in (the short links) to a computer in the room, and the computers in a building are linked to form a local area network.

E. g = D ◦ h, with h = Di ◦ fi and Ci = D ◦ Di (i = 0, 1)? C0 D D0 C1 D1 f0 f1 In abstract graphs this question has no definite answer. But in the dynamic theory of bigraphs we shall need answers to such questions. They arise in two distinct ways. 1 The words ‘abstract’ and ‘general’ can be confused. They are often used as synonyms, but in this work ‘abstract/concrete’ distinguishes only between graphs in which the nodes and edges are unidentified and those in which they are identified. On the other hand ‘general/specific’ represents a spectrum from lesser to greater definition; for example, it proceeds from ‘precategory’ through ‘s-category’, then through the class of all bigraphical s-categories, then to any specific bigraphical s-category such as Bgccs or `Bgccs .

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