A Fully Abstract Presheaf Semantics of SCCS with Finite Delay

Abstract

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.