This contribution presents the formalism of Elementary Object Systems (Eos). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. Since object nets in general are immediately Turing complete, we introduce the restricted class of elementary object nets which restrict the nesting of nets to the depth of two. One central aim of this contr...

Elementary Object Systems (EOS) is a class of Object Petri Nets that follows the “nets-within-nets” paradigm. It combines several practical as well as theoretical properties for the needs of multi-agent-systems. However, it comes with some constraints that limit their expressiveness for automatic verification purposes due to the highly expressive nature of the underlying class of Petri nets. In...

The voltage-dependent K+ channel Kv1.3 (also known as KCNA3), which plays crucial roles in leukocytes, physically interacts with KCNE4. This interaction inhibits the K+ currents because the channel is retained within intracellular compartments. Thus, KCNE subunits are regulators of K+ channels in the immune system. Although the canonical interactions of KCNE subunits with Kv7 channels are under...

In this article I will prove undecidability results for elementary object net systems (Eos). Object nets are Petri nets which have Petri nets as tokens – an approach which is called the “nets-within-nets” paradigm. Eos are special object net system which have a two leveled structure.

Petri hypernets, a novel framework for modeling mobile agents based on nets-within-nets paradigm is presented. Hypernets employ a local and finitary character of interactions between agents, and provide means for a modular and hierarchical description. They are capable of modelling mobile agents tfrahat can dynamically change their hierarchy, and can communicate with each other and with the out...

Nested Petri nets (NP-nets) is an extension of the Petri nets formalism within the “nets-within-nets” approach, when tokens in a marking are themselves Petri nets which have autonomous behavior and synchronize with the system net. The formalism of NP-nets allows modeling multi-level multi-agent systems with a dynamic structure in a natural way. In this paper we define branching processes and un...

The subresultants play a fundamental role in elimination theory and computer algebra. Recently they have been extended to Ore polynomials. They are de ̄ned by an expression in the coe±cients of Ore polynomials. In this paper, we provide another expression for them. This expression is written in terms of the \solutions" of Ore polynomials (in \generic" case). It is a generalization of our previou...

In this work we present the model of “mobile object net systems” – an algebraic formalisation of the “nets within nets”-paradigm, which is well suited to express the dynamics of open, mobile systems, since it allows tokens to be active. The algebraic theory of “nets within nets” covers an integrated view of the two major topics concurrency and locality, which are central in the area of mobile c...

Current modeling techniques are not well equipped to design dynamic software architectures. In this work we present the basic concepts for a dynamic architecture modeling using nets-within-nets. Netswithin-nets represent a powerful formalism that allows active elements, i.e. nets, to be nested in arbitrary and dynamically changeable hierarchies. Applying the concepts from nets-within-nets, ther...