Formal Modeling of Communication Platforms using Reconfigurable Algebraic High-Level Nets

Communication nowadays is based on communication platforms like Skype, Facebook, or SecondLife. The formal modeling and analysis of communication platforms poses considerable challenges, namely highly dynamic structures and complex behavior. Since most of the well-known formal modeling approaches are adequate only for specific aspects of communication platforms, in this paper we introduce the approach of reconfigurable algebraic high-level nets with individual tokens and show in our case study Skype that this approach is adequate for modeling the main aspects and features of communication platforms

Reconfigurable Decorated PT Nets with Inhibitor Arcs and Transition Priorities

In this paper we deal with additional control structures for decorated PT Nets. The main contribution are inhibitor arcs and priorities. The first ensure that a marking can inhibit the firing of a transition. Inhibitor arcs force that the transition may only fire when the place is empty. an order of transitions restrict the firing, so that an transition may fire only if it has the highest priority of all enabled transitions. This concept is shown to be compatible with reconfigurable Petri nets

Subtyping for Hierarchical, Reconfigurable Petri Nets

Hierarchical Petri nets allow a more abstract view and reconfigurable Petri nets model dynamic structural adaptation. In this contribution we present the combination of reconfigurable Petri nets and hierarchical Petri nets yielding hierarchical structure for reconfigurable Petri nets. Hierarchies are established by substituting transitions by subnets. These subnets are themselves reconfigurable, so they are supplied with their own set of rules. Moreover, global rules that can be applied in all of the net, are provided

Towards Model Checking Reconfigurable Petri Nets using Maude

This paper introduces an approach to model checking of reconfigurable Petri nets. The main task is to flatten the two levels of dynamic behavior that reconfigurable nets provide, the firing of transitions on the one hand and the transformation of the nets on the other hand. We show how to translate a reconfigurable net into  Maude modules. Maude's LTL model-checker is then used to verify properties of these modules

Formalization of Petri Nets with Individual Tokens as Basis for DPO Net Transformations

Reconfigurable place/transition systems are Petri nets with initial markings and a set of rules which allow the modification of the net structure during runtime. They have been successfully used in different areas like mobile ad-hoc networks. In most of these applications the modification of net markings during runtime is an important issue. This requires the analysis of the interaction between firing and rule-based modification. For place/transition systems this analysis has been started explicitly without using the general theory of M-adhesive transformation systems, because firing cannot be expressed by rule-based transformations for P/T systems in this framework. This problem is solved in this paper using the new approach of P/T nets with individual tokens. In our main results we show that on one hand this new approach allows to express firing by transformation via suitable transition rules. On the other hand transformations of P/T nets with individual tokens can be shown to be an instance ofM-adhesive transformation systems, such that several well-known results, like the local Church-Rosser theorem, can be applied. This avoids a separate conflict analysis of token firing and transformations. Moreover, we compare the behavior of P/T nets with individual tokens with that of classical P/T nets. Our new approach is also motivated and demonstrated by a network scenario modeling a distributed communication system

Non-Deterministic Matching Algorithm for Net Transformations

Modeling and simulating dynamic systems require to represent their processes and the system changes within one model. To that effect, reconfigurable Petri nets consist of a  place/transition net and a set of rules that can  modify the Petri net. The application of a rule is based on finding a suitable match of the rule in the given net. This match is an isomorphic  subnet that  has to be located meeting  requirements of the rule application as well as the simulation. In this paper a non-deterministic algorithm is presented for the matching in reconfigurable Petri nets. It is an extension of the VF2 algorithm for graph (sub-)isomorphisms. We show that this extension is correct and complete.   Non-determinism  ensures that during simulation different matches can be found for  each transformation step and is hence crucial for the simulation. But non-determinism has not been present in the VF2 algorithm. For the matching algorithm non-determinism is proven

On Modelling Communication in Ubiquitous Computing Systems using Algebraic Higher Order Nets

Ubiquitous computing systems (UCSs) are designed to participate almostimperceptibly in everyday life. To ensure a solid operation, a UCS heavily depends on a reliable and efficient communication between its distributed computing components. Moreover components can join and leave the system at any time.In order to guarantee high quality systems, the use of models is inevitable especiallyat an early stage of the development process where models are the only possibilityto address a system which does not yet exist in reality. Petri nets and graph transformationsystems are established, theoretically well-founded concepts for modellingand analysing complex systems.This paper presents a formal approach for modelling core aspects of the communicationin UCSs by using Algebraic Higher Order Nets with Individual Tokens andgraph transformation. The approach is suitable to cover the different aspects ofcommunication and enables the analysis of specific properties. The approach and itssuitability are illustrated based on a running example. The feasibility of embeddingthe approach in a broader context of modelling is demonstrated in applying it to areal world system: the Living Place Hamburg

Algebraic Approach to Timed Petri Nets

One aspect often needed when modelling systems of any kind is time-based analysis, especially for real-time or in general time-critical systems. Algebraic place/transition (P/T) nets do not inherently provide a way to model the passing of time or to restrict the firing behaviour with regards to passing time. In this paper, we present an extension of algebraic P/T nets by adding time durations to transitions and timestamps to tokens. We define categories for different timed net classes and functorial relations between them. Our first result is the definition of morphisms preserving firing behaviour for all timed net classes. As second result, we define structuring techniques for timed P/T nets in a way that our category fulfills the properties of M-adhesive systems, a general categorical framework for structuring and transforming high-level algebraic structures. We demonstrate our approach by applying it to model a real-time communication network