Semantics of networks containing indeterminate operators

Abstract

We discuss a denotational semantics for networks containing indeterminate operators. Our approach is based on modelling a network by the set of all its possible behaviors. Our notion of behavior is a sequence of computational actions. The primitive computational action is an event: the appearance or consumption of a token on a data path. A sequence of such events is called a history and a set of such histories is called an archive. We give composition rules that allow us to derive an archive for a network from the archive of its constituents. Causal and operational constraints on network behavior are encoded into the definitions of archives. We give a construction that allows us to obtain the denotation of networks containing loops by a process of successive approximations. This construction is not carried out in the traditional domain-theoretic setting, but rather resembles the category theoretic notion of limit. By using this construction, we avoid having to impose any closure conditions on the set of behaviors, as are typically necessary in powerdomain constructions. The resulting theory is general and compositional, but is also close to operational ideas making it a useful and flexible tool for modelling systems.