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5 - Bigraphical structure

Published online by Cambridge University Press:  05 August 2012

Robin Milner
Affiliation:
University of Cambridge
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Summary

This chapter refines the structural analysis of concrete bigraphs. In Section 5.1 we establish some properties for concrete bigraphs, including RPOs. In Section 5.2 we enumerate all IPOs for a given span. Finally, in Section 5.3 we show that RPOs do not exist in general for abstract bigraphs.

RPOs for bigraphs

We begin with a characterisation of epimorphisms (epis) and monomorphisms (monos) in bigraphs. These notions are defined in a precategory just as in a category, as follows:

Definition 5.1 (epi, mono) An arrow f in a precategory is epi if g ° f = h ° f implies g = h. It is mono if f ° g = f ° h implies g = h. 〉

Proposition 5.2 (epis and monos in concrete bigraphs)A concrete place graph is epi iff no root is idle; it is mono iff no two sites are siblings. A concrete link graph is epi iff no outer name is idle; it is mono iff no two inner names are siblings.

A concrete bigraph G is an epi (resp. mono) iff its place graph GPand its link graph GLare so.

EXERCISE 5.1 Prove the above proposition, at least for the case of epi link graphs. Hint: Make the following intuition precise: if G and H differ then, when composed with F, the difference can be hidden if and only if F has an idle name. 〉

The proposition fails for abstract bigraphs, suggesting that concrete bigraphs have more tractable structure. We shall now provide further evidence for this by constructing RPOs for them.

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Publisher: Cambridge University Press
Print publication year: 2009

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  • Bigraphical structure
  • 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/CBO9780511626661.006
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  • Bigraphical structure
  • 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/CBO9780511626661.006
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.

  • Bigraphical structure
  • 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/CBO9780511626661.006
Available formats
×