Modelling Emergency Scenarios using Algebraic High Level Net Transformation Systems with Net Patterns

Emergency operations are a good case study for dynamic systems. Their size and high dynamicity make modelling them a challenging task. Algebraic high level net transformation systems are a well suited technique for modelling such dynamic systems. They consist of an algebraic high level net and a set of graph transformation rules. The net reflects the initial state of the operation and the transformation rules can be used to adapt this state to reflect the dynamicity of the operation. The applicability of graph transformation rules depends on the existence of a match morphism. While designing the algebraic high level net transformation system the designer has to ensure the existence of the right match morphisms for all reachable runtime states. This can be a tedious and error prone task for the designer. This paper uses a case study for modelling emergency operations with algebraic high level net transformation systems to show how the notion of net patterns can help the designer to cope with rule applicability

Functorial Analysis of Algebraic Higher-Order Net Systems with Applications to Mobile Ad-Hoc Networks

Algebraic higher-order (AHO) net systems are Petri nets with place/ transition systems, i.e. place/transition nets with initial markings, and rules as tokens. In several applications, however, there is the need for explicit data modeling. The main idea of this paper is to introduce AHO net systems with high-level net systems and corresponding rules as tokens. We relate them to AHO net systems with low-level net systems as tokens and analyze the firing and transformation properties of the corresponding net class transformation defined as functors between the corresponding categories of AHO net systems. All concepts and results are explained with an example in the application area of mobile ad-hoc networks. From an abstract point of view, mobile ad-hoc networks consist of mobile nodes which communicate with each other independent of a stable infrastructure, while the topology of the network constantly changes depending on the current position of the nodes and their availability. To ensure satisfactory team cooperation in workflows of mobile ad-hoc networks we use the modeling technique of AHO net systems

Modelling Evolution of Communication Platforms and Scenarios based on Transformations of High-Level Nets and Processes : Extended Version

Algebraic High-Level (AHL) nets are a well-known modelling technique based on Petri nets with algebraic data types, which allows to model the communication structure and the data flow within one modelling framework. Transformations of AHL-nets – inspired by the theory of graph transformations – allow in addition to modify the communication structure. Moreover, high-level processes of AHL-nets capture the concurrent semantics of AHL-nets in an adequate way. Altogether we obtain a powerful integrated formal specification technique to model and analyse all kinds of communication based systems, especially different kinds of communication platforms. In this paper we show how to model the evolution of communication platforms and scenarios based on transformations of Algebraic High-Level Nets and Processes. All constructions and results are illustrated by a running example showing the evolution of Apache Wave platforms and scenarios. The evolution of platforms is modelled by the transformation of AHL-nets and that of scenarios by the transformation of AHL-net processes. The first main result shows under which conditions AHL-net processes can be extended if the corresponding AHL-net is transformed. This result can be applied to show the extension of scenarios for a given platform evolution. The second main result shows how AHL-net processes can be transformed based on a special kind of transformation for AHL-nets, corresponding to action evolution of platforms. Finally, we briefly discuss the case of multiple action evolutions

Algebraic High-Level Nets and Processes Applied to Communication Platforms

Petri nets are well-known to model communication structures and algebraic specifications for modeling data types. Algebraic High-Level (AHL) nets are defined as integration of Petri nets with algebraic data types, which allows to model the communication structure and the data flow within one modelling framework. Transformations of AHL-nets – inspired by the theory of graph transformations – allow in addition to modify the communication structure. Moreover, highlevel processes of AHL-nets capture the concurrent semantics of AHL-nets in an adequate way. Altogether we obtain a powerful integrated formal specification technique to model and analyse all kinds of communication based systems. In this paper we give a comprehensive introduction of this framework. This includes main results concerning parallel independence of AHL-transformations and the transformation and amalgamation of AHL-occurrence nets and processes. Moreover, we show how this can be applied to model and analyse modern communication and collaboration platforms like Google Wave and Wikis. Especially we show how the Local Church-Rosser theorem for AHL-net tranformations can be applied to ensure the consistent integration of different platform evolutions. Moreover, the amalgamation theorem for AHL-processes shows under which conditions we can amalgamate waves of different Google Wave platforms in a compositional way

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

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

Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction

Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn

Automating the transformation-based analysis of visual languages

The final publication is available at Springer via http://dx.doi.org/10.1007/s00165-009-0114-yWe present a novel approach for the automatic generation of model-to-model transformations given a description of the operational semantics of the source language in the form of graph transformation rules. The approach is geared to the generation of transformations from Domain-Specific Visual Languages (DSVLs) into semantic domains with an explicit notion of transition, like for example Petri nets. The generated transformation is expressed in the form of operational triple graph grammar rules that transform the static information (initial model) and the dynamics (source rules and their execution control structure). We illustrate these techniques with a DSVL in the domain of production systems, for which we generate a transformation into Petri nets. We also tackle the description of timing aspects in graph transformation rules, and its analysis through their automatic translation into Time Petri netsWork sponsored by the Spanish Ministry of Science and Innovation, project METEORIC (TIN2008-02081/TIN) and by the Canadian Natural Sciences and Engineering Research Council (NSERC)