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Refinement in Object-Z and CSP

  • Christie Bolton
  • Jim Davies
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2335)

Abstract

In this paper we explore the relationship between refinement in Object-Z and refinement in CSP. We prove with a simple counter-example that refinement within Object-Z, established using the standard simulation rules, does not imply failures-divergences refinement in CSP. This contradicts accepted results.

Having established that data refinement in Object-Z and failures refinement in CSP are not equivalent we identify alternative refinement orderings that may be used to compare Object-Z classes and CSP processes. When reasoning about concurrent properties we need the strength of the failures-divergences refinement ordering and hence identify equivalent simulation rules for Object-Z. However, when reasoning about sequential properties it is sufficient to work within the simpler relational semantics of Object-Z. We discuss an alternative denotational semantics for CSP, the singleton failures semantic model, which has the same information content as the relational model of Object-Z.

Keywords

Semantic Model Concrete State State Transition System External Choice Internal Choice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Christie Bolton
    • 1
  • Jim Davies
    • 1
  1. 1.Oxford University Computing LaboratoryOxford

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