16,762 research outputs found
On the Algebraic Structure of Petri Nets
No full textThis paper retraces, collects, and summarises the contributions of the author --- both individually and in collaboration with others --- on the theme of algebraic, compositional approaches to the semantics of Petri nets
The Algebraic Structure of Petri Nets
No full textThis survey retraces, collects, and summarises the contributions of the author --- both individually and in collaboration with others --- on the theme of algebraic, compositional approaches to the semantics of Petri nets
Modeling the fraud-like investment founds by Petri nets
No full textIn this paper we model the fraud-like investment founds using place-transition Petri nets. We will also classify the business using regression line in order to find the possible fraud-like investment founds. In these regression lines we compute analytical the mark of a place in function of some other elements of the Petri net, and next we express this value in function of the same elements using regression. From the identity of the coefficients we find a ratio between two weights of arcs. We make also a program where the marks and transitions are implemented as classes for Petri nets, and, using the heritage mechanism we extend the Petri net to Petri net with priorities.Petri nets, fraud-like investment founds, objects programming.
Deterministic Petri net languages as business process specification language.
No full textToday, a wide variety of techniques have been proposed to model the process aspects of business processes. The problem, however, is that many of these are focused on providing a clear graphical representation of the models and give almost no support for complex verification procedures. Alternatively, the use of Petri Nets as a business process modeling language has been repeatedly proposed. In complex business processes the use of Petri Nets has been criticized and the technique is believed to be unable to capture such processes in all aspects. Therefore, in this paper, we introduce the application of Petri Net language theory for business process specification. Petri Net languages are an extension to the Petri Net theory, and they provide a set of techniques to describe complex business processes more efficiently. More specifically, we advocate the application of deterministic Petri Net languages to model the control flow aspects of business processes. The balance between modeling power and analysis possibilities makes deterministic Petri Nets a highly efficient technique, used in a wide range of domains. The proof of their usability, as business process specification language, is given by providing suitable solutions to model the basic and more complex business process patterns [4]. Additionally, some points of particular interest are concisely discussed.Business; Business process modeling; Control; Model; Models; Patterns; Petri Net theory; Power; Process modeling; Processes; Representation; Theory; Verification;
Representation Theorems for Petri Nets
No full textThis paper retraces, collects, summarises, and mildly extends the contributions of the authors --- both together and individually --- on the theme of representing the space of computations of Petri nets in its mathematical essence
Characterizing Behavioural Congruences for Petri Nets
No full textWe exploit a notion of interface for Petri nets in order to design a set of net combinators. For such a calculus of nets, we focus on the behavioural congruences arising from four simple notions of behaviour, viz., traces, maximal traces, step, and maximal step traces, and from the corresponding four notions of bisimulation, viz., weak and weak step bisimulation and their maximal versions. We characterize such congruences via universal contexts and via games, providing in such a way an understanding of their discerning powers
Petri nets for systems and synthetic biology
No full textWe give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
Process versus Unfolding Semantics for Place/Transition Petri Nets
No full textIn the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical "token game," one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. In our formal development a relevant role is played by DecOcc, a category of occurrence nets appropriately decorated to take into account the history of tokens. The structure of decorated occurrence nets at the same time provides natural unfoldings for Place/Transition (PT) nets and suggests a new notion of processes, the decorated processes, which induce on Petri nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification
The Impact of Petri Nets on System-of-Systems Engineering
No full textThe successful engineering of a large-scale system-of-systems project towards deterministic behaviour depends on integrating autonomous components using international communications standards in accordance with dynamic requirements. To-date, their engineering has been unsuccessful: no combination of top-down and bottom-up engineering perspectives is adopted, and information exchange protocol and interfaces between components are not being precisely specified. Various approaches such as modelling, and architecture frameworks make positive contributions to system-of-systems specification but their successful implementation is still a problem.
One of the most popular modelling notations available for specifying systems, UML, is intuitive and graphical but also ambiguous and imprecise. Supplying a range of diagrams to represent a system under development, UML lacks simulation and exhaustive verification capability. This shortfall in UML has received little attention in the context of system-of-systems and there are two major research issues:
1. Where the dynamic, behavioural diagrams of UML can and cannot be used to model and analyse system-of-systems
2. Determining how Petri nets can be used to improve the specification and analysis of the dynamic model of a system-of-systems specified using UML
This thesis presents the strengths and weaknesses of Petri nets in relation to the specification of system-of-systems and shows how Petri net models can be used instead of conventional UML Activity Diagrams. The model of the system-of-systems can then be analysed and verified using Petri net theory. The Petri net formalism of behaviour is demonstrated using two case studies from the military domain. The first case study uses Petri nets to specify and analyse a close air support mission. This case study concludes by indicating the strengths, weaknesses, and shortfalls of the proposed formalism in system-of-systems specification. The second case study considers specification of a military exchange network parameters problem and the results are compared with the strengths and weaknesses identified in the first case study.
Finally, the results of the research are formulated in the form of a Petri net enhancement to UML (mapping existing activity diagram elements to Petri net elements) to meet the needs of system-of-systems specification, verification and validation
Properties of Distributed Time Arc Petri Nets
No full textIn recent work we started a research on a distributed-timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required for enabling. This formalism enables to model e.g. hardware architectures like GALS. We give a formal definition of process semantics for our model and investigate several properties of local versus global timing: expressiveness, reachability and coverability
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