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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 ?enter image description here

Usman YousafZai
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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

Charlie Martin
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I think the number of "reachable states" of your net is infinite.

I took the liberty of creating an interactive PDF version of your diagram so that you can "manually" fire the transitions and see for your self the kind of markings the evolve from firing the enabled transitions.

An Interactive Version of Usman's Petri Net 1

Here is the link: https://www.academia.edu/34702296/An_Interactive_Version_of_Usmans_Petri_Net

John Frederick Chionglo
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  • The link is dead. – Teun Kooijman Sep 26 '17 at 12:31
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    Thanks for checking it out. I uploaded a copy of document to the following url: https://www.academia.edu/34702296/An_Interactive_Version_of_Usmans_Petri_Net. I will also change the original link from http://www.aespen.ca/AEnswers/1440257847.pdf to the new one. Thanks again. – John Frederick Chionglo Sep 28 '17 at 08:26