A Fully Abstract Presheaf Semantics of SCCS with Finite Delay

Thomas Troels Hildebrandt

September 1999


We present a presheaf model for the observation of infinite as well as finite computations. We apply it to give a denotational semantics of SCCS with finite delay, in which the meanings of recursion are given by final coalgebras and meanings of finite delay by initial algebras of the process equations for delay. This can be viewed as a first step in representing fairness in presheaf semantics. 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. The open map bisimulation is shown to coincide with the extended bisimulation of Hennessy and Stirling. Finally we formulate Milners 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

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