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.