Formalization of Petri Nets with Individual Tokens as Basis for DPO Net Transformations

Abstract

Reconfigurable place/transition systems are Petri nets with initial markings
and a set of rules which allow the modification of the net structure during runtime.
They have been successfully used in different areas like mobile ad-hoc networks.
In most of these applications the modification of net markings during runtime
is an important issue. This requires the analysis of the interaction between firing and
rule-based modification. For place/transition systems this analysis has been started
explicitly without using the general theory of M-adhesive transformation systems,
because firing cannot be expressed by rule-based transformations for P/T systems in
this framework. This problem is solved in this paper using the new approach of P/T
nets with individual tokens. In our main results we show that on one hand this new
approach allows to express firing by transformation via suitable transition rules. On
the other hand transformations of P/T nets with individual tokens can be shown to
be an instance ofM-adhesive transformation systems, such that several well-known
results, like the local Church-Rosser theorem, can be applied. This avoids a separate
conflict analysis of token firing and transformations. Moreover, we compare
the behavior of P/T nets with individual tokens with that of classical P/T nets. Our
new approach is also motivated and demonstrated by a network scenario modeling
a distributed communication system.