On the Scott-continuity of tagged signal processes

Process networks are frequently used to model signal processing and multimedia applications. It is important to ensure that a process network has a uniquely defined behavior in order to correctly model such deterministic systems. Furthermore, a constructive procedure to determine this unique behavior is necessary for its simulation and execution. By the Kahn principle, the unique behavior of a process network is known to be the least fixed point of the network functional when every process computes a Scott-continuous function. The Kahn principle is used in a recent timed extension of the least fixed point semantics of Kahn process networks, using the tagged signal model. In this extension, processes compute a function from input signals to output signals, where a signal is defined as a partial function from a down set of tags to a set of values. However, it is often tedious to formally prove that a tagged signal process is Scott-continuous. This paper presents theorems on Scott-continuity that simplify such proofs. Thus, a general theorem on the necessary and sufficient conditions for the Scott-continuity of tagged signal processes is proven. Scott-continuity is then proven for broad classes of processes, namely the classes of exactly causal processes and of domain-warping processes, which include stateless processes, delays as well as a subset of discrete-event processes.