On the expressive power of CSP refinement

  • Authors:
  • A. W. Roscoe

  • Affiliations:
  • Oxford University Computing Laboratory, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

  • Venue:
  • Formal Aspects of Computing
  • Year:
  • 2005

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Abstract

We show that wide-ranging classes of predicates on the failures-divergences model for CSP can be represented by refinement checks in a general form. These are predicates of a process P expressible as F(P)⊏G(P), where F and G are CSP contexts and ⊏ is refinement. We use ideas similar to full abstraction, but achieve a stronger property than that. Our main result is that topologically-closed predicates are precisely those representable when F and G are both uniformly continuous. We show that sub-classes of predicates such as refinement-closed and distributive ones are represented by special forms of this check.