Resources are defined as submultisets of Petri net markings. Two resources are called similar if replacing one of them by another in any marking doesn’t change the Petri net’s behavior. We define the relations of resource similarity and resource bisimulation and show that they are finitely based. In this paper the resource bisimulation is studied for different classes of Petri nets: ordinary Pe...

Recently hybrid modelling and simulation of biochemical systems have attracted increasing interest. This is motivated by the need of simulating systems which integrate different sub-cellular models, and the fact that bio networks themselves are inherently stochastic, however stochastic simulation is time expensive. Compared to other methods of biological modelling, Petri nets are characterized ...

This paper is dedicated to an extended class of hybrid Petri nets called controlled Generalized Batches Petri Nets. The novel feature of these nets is that the firing flow of continuous and batch transitions and the transfer speed of batch places are control variables. First we propose a linear programming problem to compute the instantaneous firing flow vector and the instantaneous transfer sp...

Our goal was to realize a truly hybrid simulation system, which allows the simultaneous use of discreet event simulation and continuous 3D-simulation on a unified database. The key component is an active real-time simulation database, which is an object-oriented, self-reflecting graph database, with a powerful metainformation system. We achieve this by using State Oriented Modeling, which combi...

In the area of Petri nets, many diierent developments have taken place within the last 30 years, in academia as well as in practice. For an adequate use in practice, a coherent and application oriented combination of various types and techniques for Petri nets is necessary. In order to attain a formal basis for diierent classes of Petri nets we introduce the concept of abstract Petri nets. The ...