scholarly journals The Formalization of Decision-Free Petri Net

2014 ◽  
Vol 22 (1) ◽  
pp. 29-35
Author(s):  
Pratima K. Shah ◽  
Pauline N. Kawamoto ◽  
Mariusz Giero
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Directed Path ◽  
Natural Numbers ◽  
Definition Of ◽  
Directed Circuit ◽  
Zero Number

Summary In this article we formalize the definition of Decision-Free Petri Net (DFPN) presented in [19]. Then we formalize the concept of directed path and directed circuit nets in Petri nets to prove properties of DFPN. We also present the definition of firing transitions and transition sequences with natural numbers marking that always check whether transition is enabled or not and after firing it only removes the available tokens (i.e., it does not remove from zero number of tokens). At the end of this article, we show that the total number of tokens in a circuit of decision-free Petri net always remains the same after firing any sequences of the transition.

scholarly journals A Petri Net Definition of a System Description Language

1981 ◽  
Vol 8 (96) ◽  
Author(s):  
Kurt Jensen ◽  
Morten Kyng ◽  
Ole Lehrmann Madsen
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Formal Model ◽  
Concurrent Systems ◽  
Formal Definition ◽  
Concurrent System ◽  
Description Language ◽  
System Description ◽  
Definition Of ◽  
Further Development

<p>This paper introduces a language, Epsilon, for the description of systems with concurrency, and presents a formal definition of Epsilon's semantics. The language is based on Delta ‹ the first major attempt to create a language solely aimed at system description without the restrictions placed on languages executable on digital computers. The design of Delta was itself heavily influenced by the experience from the development and use of Simula.</p><p>It is not obvious what kind of semantics a system description language should have. The situation is more complex than with normal algorithmic languages and none of the existing semantic approaches appear to be satisfactory.</p><p>To clarify the situation, we first describe the language Epsilon, which contains only a few basic primitives. Then we define the semantics of Epsilon by means of a formal model based on Petri nets. The model called ''Concurrent systems'' is an extension of Petri nets with a data part and with expressions attached to transitions and to places. The model is a further development of formalisms proposed by R.M. Keller and A. Mazurkiewicz. The expressions attached to places is a novel feature and is used to define continuous transformations on the data part. The semantics of a given system description is defined in terms of firing sequences of the corresponding concurrent system.</p><p>To be presented at the Evian Conference on Semantics of Concurrent Computations, July 1979.</p>

scholarly journals Modeling Workflow Systems Constrained by Inputs and Outputs − An Approach Based on Petri Nets

2015 ◽  
Vol 15 (4) ◽  
pp. 27-41
Author(s):  
Changyou Zheng ◽  
Yi Yao ◽  
Song Huang ◽  
Zhengping Ren
Keyword(s):  
Performance Analysis ◽  
Petri Nets ◽  
Petri Net ◽  
Daily Life ◽  
Modeling Method ◽  
Testing Methods ◽  
Workflow Systems ◽  
Input And Output ◽  
Definition Of ◽  
Inputs And Outputs

Abstract Workflow systems are widely used in our daily life so that the validity, dependability and security with which they need to be assured are important. However, existing researches mainly focus on correctness validation, performance analysis and assignment scheduling, but the testing methods have been seldom suited. In this paper a formalized definition of workflows constrained by an input and output is presented, and based on that, a Petri Net-based model (I/O_WF_Net) is proposed. In I/O_WF_Net, the activities of the workflow can be modeled as transitions of a Petri Net, and the inputs and outputs of an activity can be modeled as places. After the modeling method for I/O constrained workflow net into the I/O_WF_Net model is described, the corresponding transforming algorithm and its simplifying method are given.

scholarly journals Formulation of Cell Petri Nets

2013 ◽  
Vol 21 (4) ◽  
pp. 241-247
Author(s):  
Mitsuru Jitsukawa ◽  
Pauline N. Kawamoto ◽  
Yasunari Shidama
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Colored Petri Nets ◽  
Colored Petri Net ◽  
Neighborhood Relationship ◽  
Definition Of

Abstract Based on the Petri net definitions and theorems already formalized in the Mizar article [13], in this article we were able to formalize the definition of cell Petri nets. It is based on [12]. Colored Petri net has already been defined in [11]. In addition, the conditions of the firing rule and the colored set to this definition, that defines the cell Petri nets are further extended to CPNT.i further. The synthesis of two Petri nets was introduced in [11] and in this work the definition is extended to produce the synthesis of a family of colored Petri nets. Specifically, the extension to a CPNT family is performed by specifying how to link the outbound transitions of each colored Petri net to the place elements of other nets to form a neighborhood relationship. Finally, the activation of colored Petri nets was formalized.

Constrained Petri Nets. Part II: Generalizations and extensions

1983 ◽  
Vol 6 (3-4) ◽  
pp. 333-374
Author(s):  
H.J.M. Goeman ◽  
L.P.J. Groenewegen ◽  
H.C.M. Kleijn ◽  
G. Rozenberg
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Theoretical Framework ◽  
General Constraints ◽  
Context Free ◽  
Boolean Expressions

This paper continues the investigation froll1 [Goeman et al.] concerning the use of sets of places of a Petri net as additional (to input places) constraints for granting concession. Now interpretations of more general constraints are considered and expressed as Boolean expressions. This gives rise to various classes of constrained Petri nets. These are compared in the language theoretical framework introduced in [Goeman et al.]. An upperbound for the language defining power is found in the class of context-free programmed languages.

An Axiomatic Characterization of a Class of Petri Nets

1991 ◽  
Vol 14 (4) ◽  
pp. 477-491
Author(s):  
Waldemar Korczynski
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Axiomatic Characterization ◽  
Algebraic Characterization

In this paper an algebraic characterization of a class of Petri nets is given. The nets are characterized by a kind of algebras, which can be considered as a generalization of the concept of the case graph of a (marked) Petri net.

The Quantitative Assessment of Domino Effects Based on Stochastic Petri Nets

2008 ◽  
Vol 44-46 ◽  
pp. 537-544
Author(s):  
Shi Yi Bao ◽  
Jian Xin Zhu ◽  
Li J. Wang ◽  
Ning Jiang ◽  
Zeng Liang Gao
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Petri Net ◽  
Quantitative Assessment ◽  
Stochastic Petri Nets ◽  
Industrial Park ◽  
Domino Effect ◽  
State Space Explosion ◽  
Stochastic Petri Net ◽  
Chemical Industrial Park

The quantitative analysis of “domino” effects is one of the main aspects of hazard assessment in chemical industrial park. This paper demonstrates the application of heterogeneous stochastic Petri net modeling techniques to the quantitative assessment of the probabilities of domino effects of major accidents in chemical industrial park. First, five events are included in the domino effect models of major accidents: pool fire, explosion, boiling liquid expanding vapour explosion (BLEVE) giving rise to a fragment, jet fire and delayed explosion of a vapour cloud. Then, the domino effect models are converted into Generalized Stochastic Petri net (GSPN) in which the probability of the domino effect is calculated automatically. The Stochastic Petri nets’ models, which are state-space based ones, increase the modeling flexibility but create the state-space explosion problems. Finally, in order to alleviate the state-space explosion problems of GSPN models, this paper employs Stochastic Wellformed Net (SWN), a particular class of High-Level (colored) SPN. To conduct a case study on a chemical industrial park, the probability of domino effects of major accidents is calculated by using the GSPN model and SWN model in this paper.

THE APPLICATION OF PETRI NETS TO WORKFLOW MANAGEMENT

1998 ◽  
Vol 08 (01) ◽  
pp. 21-66 ◽  
Author(s):  
W. M. P. VAN DER AALST
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Business Processes ◽  
State Of The Art ◽  
Workflow Management ◽  
Explicit Representation ◽  
The Other ◽  
Application Domain ◽  
Analysis Techniques ◽  
The One

Workflow management promises a new solution to an age-old problem: controlling, monitoring, optimizing and supporting business processes. What is new about workflow management is the explicit representation of the business process logic which allows for computerized support. This paper discusses the use of Petri nets in the context of workflow management. Petri nets are an established tool for modeling and analyzing processes. On the one hand, Petri nets can be used as a design language for the specification of complex workflows. On the other hand, Petri net theory provides for powerful analysis techniques which can be used to verify the correctness of workflow procedures. This paper introduces workflow management as an application domain for Petri nets, presents state-of-the-art results with respect to the verification of workflows, and highlights some Petri-net-based workflow tools.

Hierarchical Configurable Petri Net Modeling in VHDL

2012 ◽  
Vol 58 (4) ◽  
pp. 397-402 ◽  
Author(s):  
Michał Doligalski ◽  
Marian Adamski
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Control Process ◽  
Discrete Control ◽  
Dual Model ◽  
Description Language ◽  
Direct Support ◽  
Hardware Description ◽  
Logical Synthesis ◽  
State Machine Diagram

Abstract The paper presents method for hierarchical configurable Petri nets description in VHDL language. Dual model is an alternative way for behavioral description of the discrete control process. Dual model consists of two correlated models: UML state machine diagram and hierarchical configurable Petri net (HCfgPN). HCfgPN are Petri nets variant with direct support of exceptions handling mechanism. Logical synthesis of dual model is realized by the description of HCfgPN model by means of hardware description language. The paper presents placesoriented method for HCfgPN description in VHDL language

Some Possibilities of Modeling Colored Petri Nets

2021 ◽  
pp. 77-91
Author(s):  
Goharik Petrosyan ◽  
Armen Gaboutchian ◽  
Vladimir Knyaz
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Optimal Allocation ◽  
Production Systems ◽  
Oriented Graph ◽  
Discrete Systems ◽  
Colored Petri Nets ◽  
Venn Diagram ◽  
Colored Petri Net ◽  
Language Class

Petri nets are a mathematical apparatus for modelling dynamic discrete systems. Their feature is the ability to display parallelism, asynchrony and hierarchy. First was described by Karl Petri in 1962 [1,2,8]. The Petri net is a bipartite oriented graph consisting of two types of vertices - positions and transitions connected by arcs between each other; vertices of the same type cannot be directly connected. Positions can be placed by tags (markers) that can move around the network. [2] Petri Nets (PN) used for modelling real systems is sometimes referred to as Condition/Events nets. Places identify the conditions of the parts of the system (working, idling, queuing, and failing), and transitions describe the passage from one state to another (end of a task, failure, repair...). An event occurs (a transition fire) when all the conditions are satisfied (input places are marked) and give concession to the event. The occurrence of the event entirely or partially modifies the status of the conditions (marking). The number of tokens in a place can be used to identify the number of resources lying in the condition denoted by that place [1,2,8]. Coloured Petri nets (CPN) is a graphical oriented language for design, specification, simulation and verification of systems [3-6,9,15]. It is in particular well-suited for systems that consist of several processes which communicate and synchronize. Typical examples of application areas are communication protocols, distributed systems, automated production systems, workflow analysis and VLSI chips. In the Classical Petri Net, tokens do not differ; we can say that they are colourless. Unlike standard Petri nets in Colored Petri Net of a position can contain tokens of arbitrary complexity, such as lists, etc., that enables modelling to be more reliable. The article is devoted to the study of the possibilities of modelling Colored Petri nets. The article discusses the interrelation of languages of the Colored Petri nets and traditional formal languages. The Venn diagram, which the author has modified, shows the relationship between the languages of the Colored Petri nets and some traditional languages. The language class of the Colored Petri nets includes a whole class of Context-free languages and some other classes. The paper shows modelling the task synchronization Patil using Colored Petri net, which can't be modeled using well- known operations P and V or by classical Petri network, since the operations P and V and classical Petri networks have limited mathematical properties which do not allow to model the mechanisms in which the process should be synchronized with the optimal allocation of resources.

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