Karsten Gabriel

Modelling evolution of communication platforms and scenarios based on transformations of high-level nets and processes

Algebraic High-Level (AHL) nets are a well-known modelling technique based on Petri nets with algebraic data types, which allows to model the communication structure and the data flow within one modelling framework. Transformations of AHL-nets-inspired by the theory of graph transformations-allow in addition to modify the communication structure. Moreover, high-level processes of AHL-nets capture the concurrent semantics of AHL-nets in an adequate way. Altogether, we obtain a powerful integrated formal specification technique to model and analyse all kinds of communication based systems, especially different kinds of communication platforms. In this paper, we show how to model the evolution of communication platforms and scenarios based on transformations of algebraic high-level nets and processes. All constructions and results are illustrated by a small case study showing the evolution of Apache Wave platforms and scenarios. The evolution of platforms is modelled by the transformation of AHL-nets and that of scenarios by the transformation of AHL-net processes. Two new results for transformation of AHL-net processes are presented, motivated by the evolution of communication platforms and scenarios.

Composition and Independence of High-Level Net Processes

Mobile ad-hoc networks (manets) are networks of mobile devices that communicate with each other via wireless links without relying on an underlying infrastructure. To model workflows in manets adequately a formal technique is given by algebraic higher-order nets. For this modeling technique we here present a high-level net process semantics and results concerning composition and independence. Based on the notion of processes for low-level Petri nets we analyse in this paper high-level net processes defining the non-sequential behaviour of high-level nets. In contrast to taking low-level processes of the well known flattening construction for high-level nets our concept of high-level net processes preserves the high-level structure. The main results are the composition, equivalence and independence of high-level net processes under suitable conditions. Independence means that they can be composed in any order leading to equivalent high-level net processes which especially have the same input/output behaviour. All concepts and results are explained with a running example of a mobile ad-hoc network in the area of a university campus.

Satisfaction, Restriction and Amalgamation of Constraints in the Framework of M-Adhesive Categories

Application conditions for rules and constraints for graphs are well-known in the theory of graphtransformation and have been extended already to M-adhesive transformation systems. Accordingto the literature we distinguish between two kinds of satisfaction for constraints, called general andinitial satisfaction of constraints, where initial satisfaction is defined for constraints over an initialobject of the base category. Unfortunately, the standard definition of general satisfaction is not com-patible with negation in contrast to initial satisfaction.Based on the well-known restriction of objects along type morphisms, we study in this paper re-striction and amalgamation of application conditions and constraints together with their solutions. Inour main result, we show compatibility of initial satisfaction for positive constraints with restrictionand amalgamation, while general satisfaction fails in general.Our main result is based on the compatibility of composition via pushouts with restriction, whichis ensured by the horizontal van Kampen property in addition to the vertical one that is generallysatisfied in M-adhesive categories.

Modelling of communication platforms using algebraic high-level nets and their processes

Algebraic high-level (AHL) nets are a well-known modelling technique based on Petri nets with algebraic data types, which allows to model the communication structure and the data flow within one modelling framework. In this paper we give an overview how to model the system behaviour of communication platforms and scenarios based on algebraic high-level nets and their processes. For modelling the evolution of communication platforms we show by example how to use transformations of AHL-nets inspired by the theory of graph transformation. As running example we show the modelling and evolution of Apache Wave platforms and Waves.

Process Evolution based on Transformation of Algebraic High-Level Nets with Applications to Communication Platforms

Algebraic High-Level (AHL) nets are a well-known modelling technique based on Petri nets with algebraic data types, which allows to model the communication structure and the data flow within one modelling framework. Transformations of AHL-nets – inspired by the theory of graph transformations – allow in addition to modify the communication structure. Moreover, high-level processes of AHL-nets capture the concurrent semantics of AHL-nets in an adequate way. In this paper we show how to model the evolution of communication platforms and scenarios based on transformations of algebraic high-level nets and processes. All constructions and results are illustrated by a running example showing the evolution of Apache Wave platforms and scenarios. The evolution of platforms is modelled by the transformation of AHL-nets and that of scenarios by the transformation of AHL-net processes. Our main result is a construction for the evolution of AHL-processes based on the evolution of the corresponding AHL-net. This result can be used to transform scenarios in a communication platform according to the evolution of possibly multiple actions of the platform.