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I have problems with this exercise. First: can the token in place $p_1$ to enable the transitions $t_2$ and $t_3$? The place $p_1$ has a single token, I think it fails to enable $t_2$ and $t_3$. Any suggestions?

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  • $\begingroup$ sorry i did not understand problem $\endgroup$ – dato datuashvili Jun 26 '12 at 10:38
  • $\begingroup$ I'm not sure what the question is, but in the usual Petri net formalism, the state you've shown here allows either a $t_2$ transition or a $t_3$ transition to happen next. Once either of them has happened, there is no token left in $p_1$, so the other one is now blocked. $\endgroup$ – Henning Makholm Jun 26 '12 at 11:58
  • $\begingroup$ I meant just that. Then (if I understand correctly) if $t_2$ is enabled, $t_3$ is disabled, and $t_1$ is always disabled? $\endgroup$ – Mark Jun 26 '12 at 17:29
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For the Petri Net in Figure 1, (the status of) transition t_2 is enabled, (the status of) transition t_3 is enabled, and (the status of) every other transition is not enabled. This is why the colour of (the status of) transition t_2 and the colour of (the status of) transition t_3 are green.

If transition t_2 (in Figure 1) fires then the result looks like the net in Figure 2. If transition t_3 (in Figure 1) fires then the result loos like the net in Figure 3. If transition t_4 or t_5 (in Figure 2 or in Figure 3 respectively) fires the result looks like the net in Figure 1.

For the PDF version of this reply, the Petri Net in Figure 4 is an interactive, dynamic diagram. It was created based on the Petri Net in Figure 1 using the definition of a Place/Transition Net with additional annotations such as colours for transition status, execution logic and user event-handling routines (Chionglo, 2014).

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References

Chionglo, J. F. (2014). Net Elements and Annotations for Computer Programming: Computations and Interactions in PDF. Available at http://www.aespen.ca/NetElementsAndAnnotationsForComputerProgramming.pdf.

Murata, T. (1989). “Petri Nets: Properties, Analysis and Applications”, Proceedings of the IEEE, vol. 77, no. 4, April 1989, pp. 541 – 580. Retrieved on May 26, 2015 at https://inst.eecs.berkeley.edu/~ee249/fa07/discussions/PetriNets-Murata.pdf.

“Petri Net Analysis” (2012). Mathematics Stack Exchange. Retrieved on Nov. 9, 2015 at Petri net analysis..

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you have been confused because you may not know difference between place and transactions!

suppose that there is a transaction which has an input with just one token and how multiple outputs (such as 3), then when this transaction becomes enable, this one token turns to multiple token(in this case 3 token)! in other hand when a place has one token and has multiple output to transactions this one token can not turn to multiple tokens. and it just can be passed to just one place!

so in your case the toke in $p_1$ can just goes to either $t_2$ or $t_3$. now the question is where this token will go?

answer is : its totally depends! one and most common candidate to determine this dependency is Priority, that is the priority of $t_2$ and $t_3$ will determine which transaction token will go.

but there are some type of petri nets such as colored petri net , timed petri nt and time petri net which solve this problem.

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