Reduction and Synthesis of Live and Bounded Free Choice Petri Nets

AbstractThis paper provides reduction rules that make it possible to reduce all and only live and bounded Free Choice Petri nets to a circuit containing one place and one transition. The reduction algorithm is shown to require polynomial time in the size of the system. The reduction rules can be transformed into synthesis rules, which can be used for the stepwise construction of large systems

Property-preserving subnet reductions for designing manufacturing systems with shared resources

AbstractThis paper handles two problems in manufacturing system design: resource sharing and system abstraction. In a manufacturing system, resources such as robots, machines, etc. are shared by several processes. When the resources are switched from one process to another, they may need some modifications such as cleaning oil, adding equipments and so on. Previous designing methods assume that the resources have no intermediate modifications. Hence, they need to be extended to handle such kinds of resource-sharing problems. As for abstraction, modeling operations with single places in manufacturing system design is very popular. From the viewpoint of verification, the objective is to verify whether the reduced model has the same desirable properties as the original one. This paper presents three kinds of property-preserving subnet reduction methods. For each reduction method, conditions are presented for ensuring that the properties liveness, boundedness and reversibility are preserved. Applications of these reduction methods to handling the above resource sharing and system abstraction problems are illustrated with an example from the manufacturing system

Synthesis and Analysis of Product-form Petri Nets

For a large Markovian model, a "product form" is an explicit description of the steady-state behaviour which is otherwise generally untractable. Being first introduced in queueing networks, it has been adapted to Markovian Petri nets. Here we address three relevant issues for product-form Petri nets which were left fully or partially open: (1) we provide a sound and complete set of rules for the synthesis; (2) we characterise the exact complexity of classical problems like reachability; (3) we introduce a new subclass for which the normalising constant (a crucial value for product-form expression) can be efficiently computed.Comment: This is a version including proofs of the conference paper: Haddad, Mairesse and Nguyen. Synthesis and Analysis of Product-form Petri Nets. Accepted at the conference Petri Nets 201

The complexity of Petri net transformations

Bibliography: pages 124-127.This study investigates the complexity of various reduction and synthesis Petri net transformations. Transformations that preserve liveness and boundedness are considered. Liveness and boundedness are possibly the two most important properties in the analysis of Petri nets. Unfortunately, although decidable, determining such properties is intractable in the general Petri net. The thesis shows that the complexity of these properties imposes limitations on the power of any reduction transformations to solve the problems of liveness and boundedness. Reduction transformations and synthesis transformations from the literature are analysed from an algorithmic point of view and their complexity established. Many problems regarding the applicability of the transformations are shown to be intractable. For reduction transformations this confirms the limitations of such transformations on the general Petri net. The thesis suggests that synthesis transformations may enjoy better success than reduction transformations, and because of problems establishing suitable goals, synthesis transformations are best suited to interactive environments. The complexity of complete reducibility, by reduction transformation, of certain classes of Petri nets, as proposed in the literature, is also investigated in this thesis. It is concluded that these transformations are tractable and that reduction transformation theory can provide insight into the analysis of liveness and boundedness problems, particularly in subclasses of Petri nets

A model driven approach to analysis and synthesis of sequence diagrams

Software design is a vital phase in a software development life cycle as it creates a blueprint for the implementation of the software. It is crucial that software designs are error-free since any unresolved design-errors could lead to costly implementation errors. To minimize these errors, the software community adopted the concept of modelling from various other engineering disciplines. Modelling provides a platform to create and share abstract or conceptual representations of the software system – leading to various modelling languages, among them Unified Modelling Language (UML) and Petri Nets. While Petri Nets strong mathematical capability allows various formal analyses to be performed on the models, UMLs user-friendly nature presented a more appealing platform for system designers. Using Multi Paradigm Modelling, this thesis presents an approach where system designers may have the best of both worlds; SD2PN, a model transformation that maps UML Sequence Diagrams into Petri Nets allows system designers to perform modelling in UML while still using Petri Nets to perform the analysis. Multi Paradigm Modelling also provided a platform for a well-established theory in Petri Nets – synthesis to be adopted into Sequence Diagram as a method of putting-together different Sequence Diagrams based on a set of techniques and algorithms

Automated composition of sequence diagrams

Software design is a significant stage in software development life cycle as it creates a blueprint for the implementation of the software. Design-errors lead to costly and insufficient implementation. Hence, it is crucial to provide solutions to discover the design error in early stage of the system development and solve them. Inspired by various engineering disciplines, the software community proposed the concept of modelling in order to reduce these costly errors. Modelling provides a platform to create an abstract representation of the software systems concluding to the birth of various modelling languages such as Unified Modelling Language (UML), Automata, and Petri Net. Due to the modelling raises the level of abstraction throughout the analysis and design process, it enables the system discovers to efficiently identify errors. Since modern systems become more complex, models are often produced part-by-part to help reduce the complexity of the design. This often results in partial specifications captured in models focusing on a subset of the system. To produce an overall model of the system, such partial models must be composed together. Model composition is the process of combining partial models to create a single coherent model. Due to manual model composition is error prone, time-consuming and tedious, it must be replaced by automated model compositions. This thesis presents a novel approach for an automatic composition technique for creating behaviour models, such as a sequence diagram, from partial specifications captured in multiple sequence diagrams with the help of constraint solvers

Modellierung, Integration und Analyse von Ressourcen in Geschäftsprozessen

Geschäftsprozess- und Ressourcenmodelle können bislang nur eingeschränkt zur Untersuchung des Ressourceneinsatzes genutzt werden, da relevante Eigenschaften nicht adäquat abgebildet werden. Aus diesem Grund wird in dieser Arbeit die Resource Modeling Language (RML) konzipiert und durch Ressourcen-Netze in die Geschäftsprozessmodellierung integriert. Zur Modellierung und Analyse wird das Werkzeug RAvEN konzipiert. Die Analyse des Ressourceneinsatzes erfolgt durch Simulationsexperimente

Modellierung, Integration und Analyse von Ressourcen in Geschäftsprozessen

Geschäftsprozess- und Ressourcenmodelle können bislang nur eingeschränkt zur Untersuchung des Ressourceneinsatzes genutzt werden, da relevante Eigenschaften nicht adäquat abgebildet werden. Aus diesem Grund wird in dieser Arbeit die Resource Modeling Language (RML) konzipiert und durch Ressourcen-Netze in die Geschäftsprozessmodellierung integriert. Zur Modellierung und Analyse wird das Werkzeug RAvEN konzipiert. Die Analyse des Ressourceneinsatzes erfolgt durch Simulationsexperimente