Michael Köhler-Bußmeier

Hornets: Nets within Nets Combined with Net Algebra

In this contribution we propose an algebraic extension of object nets. Object nets, also known as nets within nets , allow nets itself as tokens. The algebraic structure introduced here refers to the topology of these net-tokens, i.e. we have operators which compose nets. Object nets that use net operations in arc expression are called Higher Order Recursive Nets , or short: Hornets . The operations on nets allow to modify the structure of net-tokens at run-time. We apply this construct to the workflow management domain. We propose a simple Hornet model of a distributed workflow management system . This system consists of a network of workflow management agents. The agents cooperatively transfer workflows over the network for distributed execution, monitor their processes, and reorganise the workflow repository to improve e.g. the systems performance.

Safeness for Object Nets

In this paper we discuss the concept of safeness for Elementary Object Nets (EOS). Object nets are Petri nets which have Petri nets as tokens - an approach known as the nets-within-nets paradigm. Object nets are called elementary if the net system has a two levelled structure. The well known p/t nets can be considered as a special case of EOS. For p/t nets the concept of safeness means that there is at most one token on each place. Since object nets have nested markings there are different possibilities to generalise this idea for EOS. In this paper we define different variants of EOS safeness, discuss their relationships, show that they all coincide for p/t-like EOS, and address the complexity of well known Petri net problems like reachability and liveness for this new class of object nets.

On the Expressiveness of Communication Channels for Object Nets

In this work we present object net systems, i.e. Petri nets with nets as token objects, which are equipped with channels that allow to transfer net-tokens in the vertical dimension of the nested marking. These channels are a modelling element powerful enough to describe a direct simulation of counter programs which shows that typical net problems like boundedness, coverability, and reachability are undecidable.

Liveness of Safe Object Nets

In this paper we study the complexity of the liveness problem for safe Elementary Object Nets (EOS). Object nets are Petri nets which have Petri nets as tokens. They are called elementary if the net system has a two levelled structure. The concept of safeness bounds the number of tokens which may reside on a place. PSPACE-hardness of the liveness problem for safe EOS directly follows from the related result for safe p/t nets. We then devise a polynomial space algorithm for this problem and indeed for every property that can be expressed in the temporal logic CTL.

From Multi-Agent to Multi-Organization Systems: Utilizing Middleware Approaches

Modern software systems share with social organizations the attributes of being large-scale, distributed and heterogeneous systems of systems. The organizational metaphor for software engineering has particularly been adopted in the field of multi-agent systems but not entirely exploited due to an inherent lack of collective levels of action. We propagate a shift from multi-agent to multi-organization systems that we rest upon an organization theoretically inspired reference architecture. We further suggest to utilize agent-oriented technology as a means for realization. We draw upon the wide variety of organizational modelling and middleware approaches and establish a best fit between different approaches and requirements for different architectural levels.

On the Complexity of the Reachability Problem for Safe, Elementary Hornets

In this paper we study the complexity of HORNETS, an algebraic extension of object nets. We define a restricted class: safe, elementary HORNETS, to guarantee finite state spaces. It will turn out, that the reachability problem for this class requires exponential space, which is a major increase when compared to safe, elementary object nets, which require polynomial space.

Complexity results for elementary hornets

In this paper we study the complexity of Hornets, an algebraic extension of object nets. We define a restricted class: safe, elementary Hornets, to guarantee finite state spaces. We have shown previously that the reachability problem for this class requires at least exponential space, which is a major increase when compared to safe, elementary object nets, which require polynomial space. Here, we show how a safe, elementary Hornets can be simulated by a safe Eos, which establishes an upper bound for the complexity, since we know that that the reachability problem for safe Eos is PSpace-complete.

P- and t-systems in the nets-within-nets-formalism

We are concerned with (strongly deterministic) generalised state machines (GSMs), a restricted formalism of the nets-within-nets-family, and further restrict the involved nets to P- and T-nets. While GSMs with these restrictions are likely to be of little use in modelling applications, understanding them better might help in future attempts to analyse more sophisticated formalisms. We show that, given a strongly deterministic GSM where the system net and all object nets are P-nets, it is PSpace-complete to decide the reachability of a given marking. In past work we have already shown that the same restriction to T-nets remains solvable in polynomial time. We discuss this work in the context given here. At last we give some initial results concerning other combinations of restricting the system and/or the object nets to P- and/or T-nets. Throughout we also discuss the effect of dropping the restriction to strongly deterministic GSMs.

Conservative Elementary Object Systems

This contribution presents decidability results for 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. In this paper we study the relationship of the reachability and the liveness problem. We prove that both problems are undecidable for EOS even for the subclass of conservative EOS while it is well known that both are decidable for classical p/t nets. Despite these undecidability results, boundedness can be decided for conservative EOS using a monotonicity argument similar to that for p/t nets.

Modelling distributed network security in a petri net- and agent-based approach

Distributed network security is an important concern in modern business environments. Access to critical information and areas has to be limited to authorised users. The Herold research project aims to provide a novel way of managing distributed network security through the means of agent-based software. In this paper we present the first models, both conceptual and technical that have been produced in this project. Furthermore we examine the Paose development approach used within the project and how it contributes to Herold.