Noun
One of several mathematical representations of discrete distributed systems, a 5-tuple
(
S
,
T
,
F
,
M
0
,
W
)
{\displaystyle (S,T,F,M_{0},W)\!}
, where
S
{\displaystyle S}
is a set of places.
T
{\displaystyle T}
is a set of transitions.
S
{\displaystyle S}
and
T
{\displaystyle T}
are disjoint, i.e. no object can be both a place and a transition
F
{\displaystyle F}
is a set of arcs known as a flow relation. The set
F
{\displaystyle F}
is subject to the constraint that no arc may connect two places or two transitions, or more formally:
F
⊆
(
S
×
T
)
∪
(
T
×
S
)
{\displaystyle F\subseteq (S\times T)\cup (T\times S)}
.
M
0
:
S
→
N
{\displaystyle M_{0}:S\to \mathbb {N} }
is an initial marking, where for each place
s
∈
S
{\displaystyle s\in S}
, there are
n
s
∈
N
{\displaystyle n_{s}\in \mathbb {N} }
tokens.
W
:
F
→
N
+
{\displaystyle W:F\to \mathbb {N^{+}} }
is a set of arc weights, which assigns to each arc
f
∈
F
{\displaystyle f\in F}
some
n
∈
N
+
{\displaystyle n\in \mathbb {N^{+}} }
denoting how many tokens are consumed from a place by a transition, or alternatively, how many tokens are produced by a transition and put into each place.