Graphics Programs Reference
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and the substitution function sub must satisfy the set of predicates PRED.
PN systems are obtained from PN models by specializing the initial marking.
Moving in the opposite direction, it is possible to generalize from a Petri
net model by not considering the initial marking at all. This is equivalent
to considering only the underlying structure of the model as a weighted
bipartite graph. This structure is simply called a net (or a Petri net), and
it is formally defined as follows:
Definition 2.2.2 A net (or a Petri net) is the 5-tuple
N = { P,T,I,O,H } (2.4)
where
P is the set of places;
T is the set of transitions, T P = ;
I,O,H : T Bag(P), are the input, output and inhibition functions, re-
spectively, where Bag(P) is the multiset on P.
Given a PN model M = { P,T,I,O,H,PAR,PRED,MP } we can define
the net derived from model M as
N = { P 0 ,T 0 ,I 0 ,O 0 ,H 0 } (2.5)
where P 0 = P, T 0 = T, I 0 = I, O 0 = O, H 0 = H.
Observe that, in general, properties derived for a PN system are valid only
for the selected instance of the initial marking, whereas assertions proved
for the PN model are valid for all PN systems obtained from the model
by specializing the initial marking. Moreover, any property proved on a
Petri net holds true for all PN models obtained from that net by selecting
a parametric initial marking, and hence for all PN systems obtained from
such models by instantiation of the marking parameters. Properties derived
from a Petri net are usually termed “structural properties”.
From a modelling point of view, the main interest is on PN models: indeed,
PN systems may be too specific (for example, in order to study the behaviour
of a given computer system as a function of the number of tasks circulating
in it, different PN systems must be set up and analysed, all with the same
structure, but with different initial markings), while Petri nets may be too
abstract (the behaviour of two identical nets may differ significantly if no
restriction is imposed on the possible initial markings).
2.3
System Dynamics
So far we have dealt with the static component of a PN model. We now turn
our attention to the dynamic evolution of the PN marking that is governed
by transition firings which destroy and create tokens.
 
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