Graphics Programs Reference
In-Depth Information
2
PETRI NETS AND THEIR
PROPERTIES
In this chapter we introduce all the definitions, concepts and analysis meth-
ods for untimed Petri nets that are used in the later chapters of the topic.
The choice of the topics included in this chapter is mainly guided by the
desire to present in a formal setting all the definitions and properties to
be used later, without trying to be complete with respect to the Petri nets
literature.
In particular, we first emphasize the difference between a Petri net (a set
of places, transitions and weighted arcs), a PN system (a Petri net with a
fixed initial marking), and a PN model (a Petri net with a parametric initial
marking). Following this distinction, we discuss the analysis methods that
can be applied to each class.
The definitions and properties are introduced by means of a formal notation,
with the help of an example derived from a variation of the well-known model
of the readers & writers algorithm.
2.1
Petri Net Models
A PN model is graphically represented by a directed bipartite graph in which
the two types of nodes (places and transitions) are drawn as circles, and
either bars or boxes, respectively.
The arcs of the graph are classified (with respect to transitions) as:
•
input arcs: arrow-headed arcs from places to transitions
•
output arcs: arrow-headed arcs from transitions to places
•
inhibitor arcs: circle-headed arcs from places to transitions
Multiple (input, output, or inhibitor) arcs between places and transitions
are permitted and annotated with a number specifying their multiplicities.
29
Search WWH ::
Custom Search