Petri Net - Restrictions

Restrictions

Instead of extending the Petri net formalism, we can also look at restricting it, and look at particular types of Petri nets, obtained by restricting the syntax in a particular way. The following types are commonly used and studied:

1. In a state machine (SM), every transition has one incoming arc, and one outgoing arc. This means, that there can not be concurrency, but there can be conflict (i.e. Where should the token from the place go? To one transition or the other?). Mathematically:
2. In a marked graph (MG), every place has one incoming arc, and one outgoing arc. This means, that there can not be conflict, but there can be concurrency. Mathematically:
3. In a free choice net (FC), - every arc from a place to a transition is either the only arc from that place or the only arc to that transition. I.e. there can be both concurrency and conflict, but not at the same time. Mathematically:
4. Extended free choice (EFC) - a Petri net that can be transformed into an FC.
5. In an asymmetric choice net (AC), concurrency and conflict (in sum, confusion) may occur, but not symmetrically. Mathematically: