1
$\begingroup$

Suppose I have the following Petri net:

Petri net

I wonder whether it is possible to model an inverse relationship between $p2$ and $p3$. Basically what I want to achieve is to make either $t1$ or $t2$ fireable but never both. Currently, I just set a token in $p2$ and leave $p3$ empty if I want to make $t1$ fireable (or vice versa for $t2$). I believe there must be a way to omit one place and achieve the same result, i.e., putting one token in $p2$ activates $t1$ but not $t2$ and zero tokens in $p2$ achieves the reverse.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

Without extra transitions, the best you can do is make them alternate:

The original net plus two additional arcs

Extra transitions can be used to choose between filling p2 or p3:

The original net plus two additional transitions and a place

You can do the same without the additional place:

The original net plus two additional transitions

You might even consider dropping one of the added transitions, to model the situation in which they are enabled in order.

Improve this answer
$\endgroup$
6
  • $\begingroup$ Hi, thanks a lot for your help. However, your suggestions do not yield my desired result. Basically, I want to omit $p2$ or $p3$ (because their meaning is redundant) and not make them alternating. The idea is that $p2$ represents semantically the inverse of $p3$. So if I have initially one marking in $p2$, it means that $p3$ should have zero markings and vice versa. Obviously, I can always set and check the tokens in both places manually, but I thought that maybe there is a better way to model it without having to use both places. $\endgroup$
    – user3475602
    Oct 2, 2021 at 12:55
  • $\begingroup$ So you don't want to add things, instead you want to omit a place, and only fire a transition when it has no token. This is impossible; regular Petri nets (Place/Transition nets) cannot have negative conditions like that. You'll need an extended formalism; e.g. Predicate/Transition nets (see Wolfgang Reisig's works) or inhibitor arcs. $\endgroup$
    – reinierpost
    Oct 2, 2021 at 18:38
  • $\begingroup$ Thanks for your explanation. Yes, I want to omit a place, but I don't want to fire it when it has no token. I am aware that this is impossible. To give you an example: $p2$ represents ($\rightarrow$) "Product 1 in stock", $t1$ $\rightarrow$ "Ship Product 1", $p3$ $\rightarrow$ "No products in stock", $t2$ $\rightarrow$ "refill stock". When I want to model the scenario that product 1 is shipped, I have to put a token in $p2$ but at the same time I have to ensure that $p3$ has no tokens. This is a bit redundant. I thought that there is maybe a way to model this inverse relationship. $\endgroup$
    – user3475602
    Oct 2, 2021 at 19:28
  • $\begingroup$ Addendum: The other scenario is that there is no product in stock ($p3$ has a token), meaning that $p2$ should have zero tokens to make $t1$ not fireable. I thought that I can somehow omit either $p2$ or $p3$ or at least make this inverse relationship explicit in the Petri net. $\endgroup$
    – user3475602
    Oct 2, 2021 at 19:31
  • $\begingroup$ You can make sure $p3$ has no token whenever $p2$ has one by adding arcs such that every transition that puts a token into $p3$ takes one from $p2$ and vice versa (my first example). They'll have converse flow relations. This may affect the transition relation: new incoming arcs may enable transitions that were enabled before, while new outgoing arcs may enable them. Similarly, given a $p2$, you can add a 'converse' $p3$, but in general, this will affect the transition relation. $\endgroup$
    – reinierpost
    Oct 3, 2021 at 11:17

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.