Non-interference notions based on reveals and excludes relations for petri nets

We introduce two families of relations on the transitions of a Petri net. The first one is an adaptation of the “reveals” relation previously defined on occurrence nets for fault diagnosis applications. Here, this relation is considered for modeling positive information flow, which arises when the occurrence of a transition gives the information that another transition already occurred or will occur. The second one, called “excludes”, is presented for modeling negative information flow, which arises when the occurrence of a transition gives information on the nonoccurrence of another transition, in the past or in the future.We consider the notion of non-interference proposed in the literature for formalizing security in distributed systems. On the basis of reveals and excludes relations we propose a collection of new notions of non-interference for ordinary Petri nets and compare them with notions already proposed in the literature.