Functorial Analysis of Algebraic Higher-Order Net Systems with Applications to Mobile Ad-Hoc Networks

Abstract

Algebraic higher-order (AHO) net systems are Petri nets with place/
transition systems, i.e. place/transition nets with initial markings, and rules as tokens.
In several applications, however, there is the need for explicit data modeling.
The main idea of this paper is to introduce AHO net systems with high-level net
systems and corresponding rules as tokens. We relate them to AHO net systems
with low-level net systems as tokens and analyze the firing and transformation properties
of the corresponding net class transformation defined as functors between the
corresponding categories of AHO net systems.
All concepts and results are explained with an example in the application area of
mobile ad-hoc networks. From an abstract point of view, mobile ad-hoc networks
consist of mobile nodes which communicate with each other independent of a stable
infrastructure, while the topology of the network constantly changes depending on
the current position of the nodes and their availability. To ensure satisfactory team
cooperation in workflows of mobile ad-hoc networks we use the modeling technique
of AHO net systems.