A PARTIAL TRACE SEMANTICS FOR PETRI NETS

We introduce the notion of partial trace. A partial trace is an equiva lence class of some labelled partial orders over a dependence alphabet (SIGMA, SD). Partial traces arise in a natural way by the synchroniza tion of semi-traces. They form a monoid which is shown to be free part ially commutative. We prove an embedding theorem which shows that any partial trace has a canonical representation as a tuple of words. We t hen apply this concept to Petri nets. We define the behavior of a P/T- system in terms of partial traces. We consider local morphisms between Petri nets and we show how this relates to the partial trace behavior . In particular, we obtain the desired result that the partial trace b ehavior of a synchronized system is the synchronization of its local b ehavior.