# Is a Petri net without places well-defined?

I'm a bit confused about the definition of a Petri-Net. From Wikipedia (EN) I have this defintion:

A Petri-Net is a 5-Tupel (P, T, F, W, s)

P and T are disjoint finite sets of places and transitions, respectively.

So the defintion says: $P \cap T = \emptyset$ & $P \cup T \neq \emptyset$

Let's say T is $\emptyset$ and P = { p } so both prerequisites are given. I think that is okay. We have a system which stays allways in one state and can not change to another so we do not need any other state or transition.

Now think about the other case: T = { t } and P is $\emptyset$. Now we have a system which does not have a state. The transition can't do anything because we do not have any states and it does not have any meaningful meaning in this case.

So does any Petri-Net which has minimum one transition need two places? Or have I missed out something?

• In a net with 1 transition and 0 places, the transition can fire indefinitely. – reinierpost Apr 25 at 12:59

A net without place does have "state", or a marking in proper terminilogy; as that is a mapping from the set of places into $\Bbb N$, technically this does exist even when the set of places is empty (as a kind of empty relation).