No abstract

Refinement in a concurrent context, as typified by a process algebra, takes a number of different forms depending on what is considered observable. Observations record, for example, which events a system is prepared to accept or refuse. Concurrent refinement relations include trace refinement, failures–divergences refinement, readiness 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 the input–output behaviour of abstract programs. These refinements are normally verified by using two simulation rules which help make the verification tractable. This paper unifies these two standpoints by generalising the standard relational model to include additional observable aspects. These are chosen in such a way that they represent exactly the notions of observation embedded in the various concurrent refinement relations. As a consequence, simulation rules for the tractable verification of concurrent refinement can be derived. We develop such simulation rules for failures–divergences refinement and readiness refinement in particular, using an alternative relational model in the latter case.

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This paper discusses theoretical background for the use of Z as a language for partial specification, in particular techniques for checking consistency between viewpoint specifications. The main technique used is unification, i.e. finding a (candidate) least common refinement. The corresponding notion of consistency between specifications turns out to be different from the known notions of consistency for single Z specifications. A key role is played by correspondence relations between the data types used in the various viewpoints.

Abstract. Two styles of description arise naturally in formal specification: state-based and behavioural. In state-based notations, a system is characterised by a collection of variables, and their values determine which actions may occur throughout a system history. Behavioural specifications describe the chronologies of actions -interactions between a system and its environment. The exact nature of such interactions is captured in a variety of semantic models with corresponding notions of refinement; refinement in state based systems is based on the semantics of sequential programs and is modelled relationally. Acknowledging that these viewpoints are complementary, substantial research has gone into combining the paradigms. The purpose of this paper is to do three things. First, we survey recent results linking the relational model of refinement to the process algebraic models. Specifically, we detail how variations in the relational framework lead to relational data refinement being in correspondence with traces-divergences, singleton failures and failures-divergences refinement in a process semantics. Second, we generalise these results by providing a general flexible scheme for incorporating the two main "erroneous" concurrent behaviours: deadlock and divergence, into relational refinement. This is shown to subsume previous characterisations. In doing this we derive relational refinement rules for specifications containing both internal operations and outputs that corresponds to failures-divergences refinement. Thirdly, the theory has been formally specified and verified using the interactive theorem prover KIV.

The version in the Kent Academic Repository may differ from the final published version. Users are advised to check http://kar.kent.ac.uk for the status of the paper. Users should always cite the published version of record.

No abstract

The version in the Kent Academic Repository may differ from the final published version. Users are advised to check http://kar.kent.ac.uk for the status of the paper. Users should always cite the published version of record.