A Petri Nets Semantics for Data Flow Networks

This work presents a truly concurrent operational semantics for nondeterministic data flow networks. We introduce a model, the df-process, which is a notion similar to that of non-sequential process for a Petri net: a df-process is defined as a mapping from an occurrence net K to a data flow net N, such that the places and the transitions of K are mapped onto the channels and the nodes of N. A df-process contains, by means of some labelling of the places, information on the value and the order in which data flow through the channels during a computation. Df-processes for a data flow network are characterized in an abstract way by a set of properties and in general a df-process corresponds to a set of computations of the network. We give a way to build the df-process corresponding to a computation incrementally at each event occurrence: a main result of the paper is that the incremental construction yields exactly the same set of df-processes as abstractly defined. We also show that df-processes are compositional. The model is intended to be used by distributed systems designers: it contains enough information to be a guideline for the designer and to be a base to develop dynamic checking tools. We outline how df-processes can be used in the design phase of a system.