Biology Reference
In-Depth Information
Fig. 2. An example of a Petri net. Circles and squares represent places and transitions, respectively. Dots within the circles,
specify the marking of the network. The current marking is
M
0
=
(2, 1, 1, 1, 0). An arc, unless labeled differently, is assumed
to have a label of 1.
Definition 6.
(Firing a transition): For a given network
N
and its marking
M
, firing an active transition
t
changes the marking of the network to a new marking
M
(denoted by
M
[
t>M
), obtained from the
old one according to the formula
M
=
M
+
t
(
+
denotes vector addition in
N
S
)
.
We also write
M
[
t>
when the successor marking
M
is irrelevant.
In the example in Fig. 1, the transition
R
is active only if the marking
M
satisfies the following
condition:
M
(
A
)
n, M
(
B
)
m, M
(
C
)
k
that is, when there is enough substrates for the reaction to take place. The transition function for
R
is
defined as follows:
R
(
A
)=
−
n,
R
(
B
)=
−
m,
R
(
C
)=
−
k,
R
(
D
)=
y,
and
R
(
E
)=
x.
A more complex example is depicted in Fig. 2. A dotted line marks active transitions, that is
t
1
,
t
2
and
t
3
. Figure 3 shows the net from Fig. 2, after firing of transition
t
2
.
