Relational concurrent refinement: timed refinement

  • Authors:
  • John Derrick;Eerke Boiten

  • Affiliations:
  • Department of Computer Science, University of Sheffield, Sheffield, UK;School of Computing, University of Kent, Canterbury, Kent, UK

  • Venue:
  • FMOODS'11/FORTE'11 Proceedings of the joint 13th IFIP WG 6.1 and 30th IFIP WG 6.1 international conference on Formal techniques for distributed systems
  • Year:
  • 2011

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Abstract

Data refinement in a state-based language such as Z is defined using a relational model in terms of the behaviour of abstract programs. Downward and upward simulation conditions form a sound and jointly complete methodology to verify relational data refinements, which can be checked on an event-by-event basis rather than per trace. In models of concurrency, refinement is often defined in terms of sets of observations, which can include the events a system is prepared to accept or refuse, or depend on explicit properties of states and transitions. By embedding such concurrent semantics into a relational one, eventwise verification methods for such refinement relations can be derived. In this paper we continue our program of deriving simulation conditions for process algebraic refinement by considering how notions of time should be embedded into a relational model, and thereby deriving relational notions of timed refinement.