A Graphical Petri Nets Simulator - Rochester Institute of Technology

output function O defines, for each transition tj, the set of output places for it.
Formally, a Petri Net C is defined as the four-tuple C = (P,TJ,0).
Fig. 2 is the structure ofthe Petri Net represented in Fig. 1
C = (P,T,I,0)
P = (Pl> P2, P3, P4, P5, P6, P7J
T = {ti,t2,t3,t4, t5,t6}
/(ti) = {P2} O(ti) = {pi}
Z(t2) = {pi}
/(t3) = {p3,P5}
/(t4) = {p4}
0(t2) = {p2,P3}
0(t3) = {p3}
O(U) = (P5l
Z(t5) = {p3,P7} 0(t5) = {p6}
/(t6) = {P6l
0(t6) = {P7l
Fig. 2
The information content ofboth the graph and structure is identical[5].
In addition to the static properties represented by the graph,
a Petri
Net has dynamic properties that result from its execution. Tokens (black dots)
are used to model the concurrent behavior of a system. Petri Nets with tokens
are called Marked Nets. A token residing on a place means the corresponding
condition is true. Otherwise, the corresponding condition is not true. A
transition is enabled if all its input places has a token and all its outputs are
empty. The enabled transition could be fired by removing the enabling token
from its input places and depositing each ofits output places with a new token.
Petri Nets that are constructed such that no more than one token can ever be
in any place at the same time are safe nets. The definition could be extended to
where Petri Nets can have no more than k tokens in any given place at the
same time. A Petri Net in which the number of tokens in any place is bounded
by k is called a k-bounded net. Of course, in this situation, a transition could
be enabled without all its outputs being empty. If tokens are used to represent
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