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3 - Algebra for bigraphs

Published online by Cambridge University Press:  05 August 2012

Robin Milner
Affiliation:
University of Cambridge
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Summary

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).

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Publisher: Cambridge University Press
Print publication year: 2009

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  • Algebra for bigraphs
  • Robin Milner, University of Cambridge
  • Book: The Space and Motion of Communicating Agents
  • Online publication: 05 August 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511626661.004
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  • Algebra for bigraphs
  • Robin Milner, University of Cambridge
  • Book: The Space and Motion of Communicating Agents
  • Online publication: 05 August 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511626661.004
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Algebra for bigraphs
  • Robin Milner, University of Cambridge
  • Book: The Space and Motion of Communicating Agents
  • Online publication: 05 August 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511626661.004
Available formats
×