School of Computing

Unifying concurrent and relational refinement

Eerke Boiten and John Derrick

In John Derrick, Eerke Boiten, Jim Woodcock, and Joakim von Wright, editors, REFINE 02: The BCS FACS Refinement Workshop, volume 70(3) of Electronic Notes in Theoretical Computer Science, pages 182-196. Elsevier Science Publishers, July 2002.


Refinement in a concurrent context, as typified by a process algebra, takes a number of different forms depending on what is considered observable, where observations record, for example, which events a system is prepared to accept or refuse. Examples of concurrent refinement relations include trace refinement, failures-divergences refinement and bisimulation.

Refinement in a state-based language such as Z, on the other hand, is defined using a relational model in terms of input/output behaviour of abstract programs. These refinements are verified by using two simulation rules which help make the verification tractable.

The purpose of this paper is to unify these two standpoints, and we do so by generalising the standard relational model to include additional observable aspects. The central result of the paper is then to develop simulation rules to verify relations such as failures-divergences refinement in a relational setting, and show how these might be applied in a specification language such as Z.

Paper in ENTCS

Bibtex Record

author = {Eerke Boiten and John Derrick},
title = {Unifying concurrent and relational refinement},
month = {July},
year = {2002},
pages = {182-196},
keywords = {determinacy analysis, Craig interpolants},
note = {},
doi = {},
url = {},
    publication_type = {inproceedings},
    submission_id = {27976_1038826463},
    booktitle = {REFINE 02: The BCS FACS Refinement Workshop},
    editor = {John Derrick and Eerke Boiten and Jim Woodcock and Joakim von Wright},
    volume = {70(3)},
    series = {Electronic Notes in Theoretical Computer Science},
    publisher = {Elsevier Science Publishers},

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