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Object Nets: Definition and Properties.

The central topic of this thesis is the theoretical investigation of the object-net formalism. This formalism extends usual ones by allowing tokens with inner activity. These active tokens are modelled by Petri nets again, so we consider "nets within nets". The recursive nesting is unbounded, since the net-tokens can again carry nets as tokens.

The possibility, to consider Petri nets as tokens has fundamental consequences for the general theory, since the concept of a Petri net is no longer an object at the meta-level - instead it becomes an object of the formalism itself at theory-level. So, the concept of "nets within nets" makes the theory of Petri nets reflexive, i.e. it can treat itself as an object of interest in some way.

The idea of using Petri nets as tokens is due to Rüdiger Valk who defined it in the context of "Task/Flow Systems" where the tasks are modelled as Petri nets being processed in the system which is modelled also as a Petri net. Valk extended this approach by dropping the restriction of task-nets being causal nets. The resulting formalism is known as "elementary object systems". These systems are called "elementary" since the nesting of nets is still restricted towards two levels. This thesis studies the general model with unbounded nesting structure.

The idea of using nets as tokens can be formalised in two different ways. The first one - called value semantics - considers the net-tokens as values marking a place, while the second one - called reference semantics - considers net-tokens as references towards the object net. The nomen clatura is borrowed from prgramming languages where parameters can be passed using "call by value" and "call by reference".

First, the thesis investigates whether object-nets can be seen as a canonical extension of Petri nets, when nesting is not used. It is also analysed whether object-nets have extended power w.r.t. typical decidability questions like reachability or boundedness. The power gained from extending the model also depends on the semantics used.

Secondly, the existence of two different semantics is anlysed w.r.t. the inner relationships of both. The circumstances are studied under which one semantics can be simulated by the other one. Especially those processes are of interest that can be simulated in both ways, since the these processes only differ in the representation but not in the inner strcuture.

The whole analysis is embedded in the context of the foundation of multi-agent systems. The theoretical results contribute to the design of mobile agents, since object-nets can directly express fundamental concepts like concurrency, distribution and locality.

Figure 1: A Petri Net as a Token of another Petri Net

Object Nets: Definition and Properties (in german). Logos Verlag, Berlin. 2004.

Last Change: 13:58 02/02/2012