Step traces

In the classical Mazurkiewicz trace approach the behaviour of a concurrent system is described in terms of sequential observations that differ only with respect to their ordering of independent actions. This paper investigates an extension of the trace model to the case that actions can be observed as occurring simultaneously. Thus observations are sequences of steps, i.e., sets of actions. This leads to a step trace model based on three relations between events: simultaneity, serialisability, and interleaving. Whereas the underlying causal structures of traces are based on dependencies between actions leading to a partial order interpretation, more general causal structures are needed to describe the invariant relationships between the action occurrences in a step trace. We present a complete picture including dependence structures extending dependence graphs, and a characterisation of step traces in terms of invariant order structures.