Complete Process Semantics for Inhibitor Nets

In this paper we complete the semantical framework proposed in [13] for process and causality semantics of Petri nets by an additional aim and develop process and causality semantics of place/transition Petri nets with weighted inhibitor arcs (pti-nets) satisfying the semantical framework including this aim. The aim was firstly mentioned in [8] and states that causality semantics deduced from process nets should be complete w.r.t. step semantics in the sense that each causality structure which is consistent with the step semantics corresponds to some process net. We formulate this aim in terms of enabled causality structures. While it is well known that process semantics of place/transition Petri nets (p/t-nets) satisfy the additional aim, we show that the most general process semantics of pti-nets proposed so far [13] does not and develop our process semantics as an appropriate generalization.