What will be the number of reachable states if Petri-Net model states are in loop

Question

If i have a Petri-net Model of 8 Places and 8 Transactions.There is not any dead state in this model because the token is in loop and going through all 8 places in first loop. In second and remaining loops it will go through 6 places because the token will come to Place3 when T5 is executed. Here i want to know what will be the number of reachable states. Is Reachable states will infinite (because of the loop) or what ?

Answer 1

It's a little hard to answer without seeing the exact net, but assuming it's a simple loop with one token, then there are four states -- distinct labeling of the places with tokens -- that repeat infinitely.

Update

Aha! That's a whole 'nother kettle of fish. Olay, so hand-simulate it. I did it by putting one finger on each token and following them. I'm going to name the places p_0 through P_7 by taking P_0 at top left and P_7 at bottom right, so the left column is P_0, P_1, P_2, the middle is P_3, P_4, the right P_5, P_6, P_7. So, we start with the labeled places as {P_0,P_7}.

Start:

• {P_0, P_7}, T_1, T_6 fire.

• {P_1, P_3} and T_1,T_4 fire.

• {P_2, P_4} and T_2, T_5 fire and here's the kicker:

• {P_2, P_3, P_5} now all have tokens. There is no pathway that "eats" tokens, no sinks, so every time P_4 gets a token, T_5 fires, and a new token appears in P_5. T_5 will be enabled infinitely often, the number of tokens grows by at least 1 every time, and so the reachability set is infinite.

This is a nice slide deck on Petri nets. http://www.labri.fr/perso/anca/FDS/Pn-ESTII.pdf