Process Evolution based on Transformation of Algebraic High-Level Nets with Applications to Communication Platforms

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. 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.Our main result is a construction for the evolution of AHL-processes based on the evolution of the corresponding AHL-net. This result can be used to transform scenarios in a communication platform according to the evolution of possibly multiple actions of the platform

RONs Revisited: General Approach to Model Reconfigurable Object Nets based on Algebraic High-Level Nets

Reconfigurable Object Nets (RONs) have been implemented in our group to support the visual specification of controlled rule-based transformations of marked place/transition (P/T) nets. RONs are high-level nets (system nets) with two types of tokens: object nets (P/T nets) and net transformation rules. System net transitions can be of different types to fire object net transitions, move object nets through the system net, or to apply a net transformation rule to an object net. The disadvantage of the RON approach and tool is the limitation of object nets to P/T nets and the limitation of the underlying semantics of RONs due to the fixed types for system net transitions. Often, a more general approach is preferred where the type of object nets and the behavior of reconfigurations may be defined in a more flexible way. In this paper, we propose to use Algebraic High-Level nets with individual tokens (AHLI nets) as system nets. In this more general approach, tokens may be any type of Petri nets, defined by the corresponding algebraic signature and algebra. To support this general approach, a development environment for AHLI nets is currently implemented which allows the user to edit and simulate AHLI nets. We present the formalization of RONs as special AHLI nets and describe the current state of the AHLI net tool environment

Basic Results for Two Types of High-Level Replacement Systems1 1Research partially supported by the European Community under TMR Network GETGRATS and the ESPRIT Working Group APPLIGRAPH.

AbstractThe general idea of high-level replacement systems is to generalize the concept of graph transformation systems and graph grammars from graphs to all kinds of structures which are of interest in Computer Science and Mathematics. Within the algebraic approach of graph transformation this is possible by replacing graphs, graph morphisms, and pushouts (gluing) of graphs by objects, morphisms, and pushouts in a suitable category. Of special interest are categories for all kinds of labelled and typed graphs, hypergraphs, algebraic specifications and Petri nets. In this paper, we review the basic results for high-level replacement systems in the algebraic double-pushout approach in the symmetric case, where both rule morphisms belong to a distinguished class M . Moreover we present for the first time the asymmetric type of high-level replacement systems, where only the left rule morphism K → L belongs to M

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

Integration of an object formalism within a hybrid dynamic simulation environment

PrODHyS is a general object-oriented environment which provides common and reusable components designed for the development and the management of dynamic simulation of systems engineering. Its major characteristic is its ability to simulate processes described by a hybrid model. In this framework, this paper focuses on the "Object Differential Petri Net" (ODPN) formalism integrated within PrODHyS. The use of this formalism is illustrated through a didactic example relating to the field of Chemical Process System Engineering (PSE)

Two Algebraic Process Semantics for Contextual Nets

We show that the so-called 'Petri nets are monoids' approach initiated by Meseguer and Montanari can be extended from ordinary place/transition Petri nets to contextual nets by considering suitable non-free monoids of places. The algebraic characterizations of net concurrent computations we provide cover both the collective and the individual token philosophy, uniformly along the two interpretations, and coincide with the classical proposals for place/transition Petri nets in the absence of read-arcs

Integrated Structure and Semantics for Reo Connectors and Petri Nets

In this paper, we present an integrated structural and behavioral model of Reo connectors and Petri nets, allowing a direct comparison of the two concurrency models. For this purpose, we introduce a notion of connectors which consist of a number of interconnected, user-defined primitives with fixed behavior. While the structure of connectors resembles hypergraphs, their semantics is given in terms of so-called port automata. We define both models in a categorical setting where composition operations can be elegantly defined and integrated. Specifically, we formalize structural gluings of connectors as pushouts, and joins of port automata as pullbacks. We then define a semantical functor from the connector to the port automata category which preserves this composition. We further show how to encode Reo connectors and Petri nets into this model and indicate applications to dynamic reconfigurations modeled using double pushout graph transformation