Kahn-extended Event Graphs

Process Networks have long been used as formal Models of Computation in the design of dedicated hardware and software embedded systems and Systems-on-Chip. Choice-less models such as Marked/Event Graphs and their Synchronous Data Flow extensions have been considered to support periodic scheduling analysis. Those models do not hide dependency informations like regular sequential languages: they capture the communication topology through point-to-point channels. Those models are concurrent, formally defined, have a clear semantic but are limited due to static point-to-point channels. Then, further extensions such as Cyclo-Static Data Flow or Boolean-controlled Dataflow (BDF) graphs introduced routing switches, allowing internal choices while preserving conflict-freeness, in the tradition of Kahn Process Networks. We introduce a new model, which we term Kahn-extended Event Graphs (KEG). It can be seen as a specialization of both Cyclo-Static and BDF processes. It consists merely in the addition of Merge/Select routing nodes to former Marked/Event Graphs; but, most importantly, these new nodes are governed by explicit (ultimately periodic) binary-word switching patterns for routing directions. We introduce identities on Merge/Select expressions, and show how they build a full axiomatization for the flow-equivalence between the computation nodes. The transformations carry a strong intuitive meaning, as they correspond to sharing/unsharing the interconnect links. Such interconnect defines each time a precise Network-on-Chip topology, and the switching patterns drive the traffic. One can also compute the buffering space actually required at the various fifo locations. The example of a Sobel edge filter is discussed to illustrate the importance of this model