### Categorical Net Transformations for Petri Net Technology

### Milan Urbasek

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ISBN 978-3-8325-0327-7

215 Seiten, Erscheinungsjahr: 2003

Preis: 40.50 €

The aim of this thesis is elaboration of net transformations used in
the Petri net technology called "Petri Net Baukasten".
The application oriented Petri net technology "Petri Net Baukasten"
provides a collection of different Petri net techniques and principles
for their combination. In general, the techniques are independent of each other.
Their actual use is usually given by needs of real applications and
projects they operate on. Petri net technology helps to reduce the gap
between academia and practice on the field of Petri nets.
The role of net transformations is crucial for establishing the
formal framework of Petri net technology.

For a systematic study of Petri net transformations we distinguish two
levels of transformations, namely net model transformations and net
class transformations. The net model transformations provide a foundation
for refinement of Petri net based models. Generally, they employ
the rule based approach known from graph transformations, which is applied on Petri nets.
They operate on a given Petri net changing its structure and/or other aspects
yielding new Petri net. A series of net model transformations is a base
for stepwise development of models based on Petri nets.

In order to support formal verification of Petri net based models the
preservation of certain system properties during the stepwise development
is of interest. One of main contributions of this thesis is the development of
liveness preserving net model transformations. Several such
transformations have been investigated, and formal conditions for each
are supplied. Net model transformations preserving safety properties and liveness,
and the possibility of building new property preserving net model
transformations from other ones are presented as well.

Net class transformations allow a model developer to change the underlying
Petri net class during the modeling step. The formalization of this concept
is another important question in Petri net technology. The explosion of
net class transformations when a new aspect of a Petri net is introduced
has shown the need for a generic concept. In this thesis the generic
concept based on comma categories is investigated. It is another important
contribution of this thesis. This concept has been applied on classes of marked
and open preserving place/transition nets, and algebraic high-level
nets. The compatibility of both types of net transformations is
shown as well.

The presented work includes several simple case studies
which proclaim the suitability of net transformations for applications.