Towards categorical models for fairness: fully abstract presheaf semantics of SCCS with finite delay

  • Authors:

  • Thomas T. Hildebrandt

  • Affiliations:

  • Theory Department, IT University of Copenhagen, Copenhagen, Denmark

  • Venue:
  • Theoretical Computer Science - Category theory and computer science
  • Year:
  • 2003

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Abstract

We present a presheaf model for the observation of infinite as well as finite computations. We give a concrete representation of the presheaf model as a category of generalised synchronisation trees and show that it is coreflective in a category of generalised transition systems, which are a special case of the general transition systems of Hennessy and Stirling. This can be viewed as a first step towards representing fairness in categorical models for concurrency. The open map bisimulation is shown to coincide with extended bisimulation of Hennessy and Stirling, which is essentially fair CTL*-bisimulation. We give a denotational semantics of Milner's SCCS with finite delay in the presheaf model, which differs from previous semantics by giving the meanings of recursion by final coalgebras and meanings of finite delay by initial algebras of the process equations for delay. Finally, we formulate Milner's operational semantics of SCCS with finite delay in terms of generalised transition systems and prove that the presheaf semantics is fully abstract with respect to extended bisimulation.