Petri nets, event structures and domains, part I

Abstract

The general aim of this paper is to find a theory of concurrency combining the approaches of Petri and Scott (and others). In part I we introduce our formalisms. To connect the abstract ideas of events and domains of information, we show how casual nets induce certain kinds of domains where the information points are certain sets of events. This allows translations between the languages of net theory and domain theory. Following the idea that events of causal nets are occurrences, we generalise causal nets to occurrence nets, by adding forwards conflict. Just as infinite flow charts unfold finite ones, so transition nets can be unfolded into occurrence nets. Next we extend the above connections between nets and domains to these new nets. Event structures which are intermediate between nets and domains play an important part in all our work. Finally, as an example of how concepts translate from one formalism to the other, we show how Petri's notion of confusion ties up with Kahn and Plotkin's concrete domains. In part II we shall continue the job of connecting up notions within net theory and the theory of domains. In particular, we shall examine the idea of states of computations.