School of Computing

Behavioural Subtyping in Process Algebra

Charles Peter Briscoe-Smith

PhD thesis, University of Kent at Canterbury, Canterbury, UK, November 2000.


Subtyping relations embody a notion of substitutability, and are an important tool in formal methods. The downward simulation relation is well-known and widely used as a subtyping and refinement relation for state-based approaches, but there is no single relation which is widely accepted to be the subtyping relation for the behavioural setting; however, there are several candidate relations.

Developments such as the multi-viewpoint specification method of RM-ODP encourage the use of several different formal methods in a single project. Thus, it becomes important to obtain implementations of a single notion of subtyping in several different paradigms. In this thesis, we attempt to find a process algebraic relation which corresponds to the state-based subtyping relation, downward simulation.

While trying to achieve this, we define a translation between a state-based notation and a process algebra, and we uncover some of the similarities and differences between these two specification paradigms. In particular, we investigate the meaning of undefined behaviour in each setting. When a state-based specification does not define an operation, the intent is that the system's behaviour is unspecified (not well-defined) if that operation is invoked. In a process algebra with refusals semantics, however, a process is implicitly specified to refuse any action it is not specified to accept, and such a refusal constitutes well-defined behaviour. As part of our translation, we devise a method of representing the unspecified behaviour of the state-based world in a process definition.

Finally, we use our translation to prove that the presence of subtyping between a pair of state-based specifications implies reduction between their LOTOS translations, but that the presence of reduction does not imply subtyping. We conclude that reduction itself does not correspond to state-based subtyping, but that any relation which does must be based on a stronger semantics than reduction, such as bisimulation semantics.

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Bibtex Record

author = {Charles Peter Briscoe-Smith},
title = {Behavioural Subtyping in Process Algebra},
month = {November},
year = {2000},
pages = {182-196},
keywords = {determinacy analysis, Craig interpolants},
note = {},
doi = {},
url = {},
    publication_type = {phdthesis},
    submission_id = {13144_983789781},
    school = {University of Kent at Canterbury},
    address = {Canterbury, UK},

School of Computing, University of Kent, Canterbury, Kent, CT2 7NF

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