Information Technology Reference
In-Depth Information
CHAPTER
2
Petri Net Formalism
2.1 BASIC PETRI NETS
Tomake this topic self-contained and help readers understand subsequent
chapters more easily (especiallyChapters 3-5), in this chapter, we give an
introduction to a Petri net formalism and its extensions. We start with the
definition of Petri nets, and then discuss a special form of Petri nets, that
is, the workflow net that is widely used in the modeling and analysis of
workflow and Web service composition. We also introduce another
extension of Petri nets, that is, colored Petri net (CPN) that is capable
of describing different data types in a compact way. We assume that
readers have a basic understanding of set theory, matrix, and graph theory.
Petri nets [78-80] are a graphical and mathematical modeling and
analysis tool for many systems, especially those with nondeterministic,
distributed, asynchronous, and concurrent behavior. Workflows and
service compositions can be viewed as such type of systems. Many
researchers in the field of workflow and service composition have used
Petri nets as a powerful framework to study various issues.
Definition 2.1. (Petri Nets)
A Petri net is a five-tuple,
PN
¼
(
P
,
T
,
F
,
W
,
M
0
), where,
P
¼
{
p
1
,
p
2
,...,
p
m
} is a finite set of places,
T
¼
{
t
1
,
t
2
,...,
t
n
} is a finite set of transitions with
P
\
T
¼
1
and
P
[
T
6¼
1
,
