A Disconnected 1-Safe Petri Net Whose Reachability Tree Is Homomorphic to a Complete Boolean Lattice

2011 ◽  
Author(s):  
Sangita Kansal ◽  
Gajendra Pratap Singh ◽  
Mukti Acharya
Keyword(s):  
Petri Net ◽  
Boolean Lattice ◽  
Reachability Tree

ALGORITHM FOR CONSTRUCTING A REACHABILITY TREE FOR STOCHASTIC PETRI NETS

2021 ◽  
pp. 34-40
Author(s):  
Д.С. Звягин
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Final Stage ◽  
Distribution Systems ◽  
Stochastic Petri Nets ◽  
Matrix Equations ◽  
Correct Process ◽  
Reachability Sets ◽  
Process Failures ◽  
Reachability Tree

Описываются основные определения дерева достижимости сетей Петри. Также рассматриваются различные примеры стохастических сетей Петри, в которых после выставления начальных маркировок в первых позициях определяются значения во всех остальных позициях. Показаны примеры определения маркировок при помощи высчитывания вектора диагональной свертки. Для каждого примера стохастической сети Петри проводится анализ данной сети. Данный анализ необходим для различных распределительных систем и процессов, особенно на заключительном этапе. Основными методами анализа являются дерево достижимости и матричные уравнения. Рассматривается один из таких методов анализа сетей Петри. С использованием дерева достижимости можно проанализировать, выявить и исправить сбои в процессах, которые могут произойти при наличии тупиковых состояний и при неправильной последовательности срабатывания переходов. Исходя из рассмотренных примеров предлагается обобщенный алгоритм построения дерева достижимости для стохастических сетей Петри. Предложенный алгоритм построения дерева достижимости стохастических сетей Петри можно применять для всех сетей как с конечным, так и с бесконечным множеством достижимости. Данный алгоритм будет являться полезным инструментом при анализе стохастических сетей Петри The article describes the basic definitions of the reachability tree of Petri nets. It also considers various examples of stochastic Petri nets, in which, after setting the initial markings in the first positions, the values in all other positions are determined. The work shows examples of determining markings by calculating the vector of the diagonal convolution. Each example of a stochastic Petri net is analyzed. This analysis is necessary for various distribution systems and processes, especially in the final stage. The main analysis methods are reachability tree and matrix equations. I consider one of such methods for analyzing Petri nets. Using the reachability tree, you can analyze, identify, and correct process failures that can occur when there are deadlocks and when transitions are fired incorrectly. Based on the examples considered, I propose a generalized algorithm for constructing a reachability tree for stochastic Petri nets. The proposed algorithm for constructing the reachability tree of stochastic Petri nets can be applied to all nets with both finite and infinite reachability sets. This algorithm will be a useful tool for analyzing stochastic Petri nets

Process Modeling of Virtual Enterprises Partner Selection Based on Petri Net

2012 ◽  
Vol 472-475 ◽  
pp. 3017-3020
Author(s):  
Bin Huang ◽  
Ning Ning Ma ◽  
Liang Chen
Keyword(s):  
Petri Net ◽  
Process Modeling ◽  
Process Model ◽  
Selection Process ◽  
Virtual Enterprise ◽  
Partner Selection ◽  
Virtual Enterprises ◽  
Dynamic Behaviors ◽  
Model Based ◽  
Reachability Tree

Partner selection process is a major issue in the formation of a virtual enterprise. This paper analyzes the partner selection process of a virtual enterprise and provides its model based on Petri net. The model describes the dynamic behaviors such as concurrent, asynchronism among the factors in partner selection process. In addition, paper analyzes the liveness of the process model by means of the reachability tree.

scholarly journals An Automatic Algorithm to Generate a Reachability Tree for Large-Scale Fuzzy Petri Net by And/Or Graph

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 454 ◽  
Author(s):  
Kai-Qing Zhou ◽  
Li-Ping Mo ◽  
Lei Ding ◽  
Wei-Hua Gui
Keyword(s):  
Petri Net ◽  
Large Scale ◽  
Production Rules ◽  
Knowledge Based ◽  
Three Phase ◽  
Fuzzy Petri Net ◽  
Fuzzy Production Rules ◽  
Relationship Of ◽  
Reachability Tree ◽  
Automatic Algorithm

Fuzzy Petri net (FPN) is widely used to repre sent, model and analyse knowledge-based systems (KBSs). Meanwhile, a reachability tree is an important tool to fully represent the flow relationship of FPN and is widely applied to implement inference in industrial areas. However, the traditional reachability ignores recording the dependence relationships (‘and/or’ relationship) among the places in the neighbouring layers. This paper develops a modified reachability tree based on an and/or graph and presents a three-phase generation algorithm to model the reachability tree for the corresponding FPN automatically via fuzzy production rules (FPRs). Four cases are used to verify the correctness and feasibility of the proposed algorithm from different viewpoints, such as general FPRs, FPRs with a condition-sharing situation, FPRs with a conclusion-sharing situation, and FPRs with multi-conclusions. Simulation results reveal that the proposed approach has the ability to automatically generate the reachability tree for the corresponding FPN correctly.

scholarly journals Existence of Forbidden Digraphs for Crisp Boolean Petri Nets

2019 ◽  
Vol 5 (1) ◽  
pp. 83-95
Author(s):  
Gajendra Pratap Singh ◽  
Sujit Kumar Singh ◽  
Madhuri Jha
Keyword(s):  
Mathematical Modeling ◽  
Petri Nets ◽  
Petri Net ◽  
Execution Time ◽  
Graph Model ◽  
Minimum Number ◽  
Reachability Tree

Boolean Petri net (BPN) and Crisp Boolean Petri net (CBPN) is a well-studied graph model since 2010 which has several applications in mathematical modeling of complex or tricky networks. Modeling any network with Petri net which can generate binary numbers as marking vectors in its reachability tree is still has much uses. In CBPN with a minimum number of transition and minimum number of steps of reachability tree, minimal execution time to run the machine has not been noted till date, thus it’s necessary to sort out this problem. Possibly it may occur due to some forbidden structure which hinders any 1-safe Petri net to be a CBPN. In this paper, we present some forbidden digraphs whose presence interrupts the generation of binary n-vectors exactly once. Any 1-safe Petri net is not a CBPN if it contains any of the subnet induced to the four forbidden structures discussed in this paper.

scholarly journals Divide Large Scale Fuzzy Petri Net into Equivalent Sub-FPNs using Reachability Tree

2020 ◽  
Vol 864 ◽  
pp. 012062
Author(s):  
Bi-Yu Liu ◽  
Kai-Qing Zhou ◽  
Sharifah Zarith Rahmah Syed Ahmad
Keyword(s):  
Petri Net ◽  
Large Scale ◽  
Fuzzy Petri Net ◽  
Reachability Tree

SPECIFYING AND VERIFYING TEMPORAL BEHAVIOR OF HIGH ASSURANCE SYSTEMS USING REACHABILITY TREE LOGIC

1999 ◽  
Vol 09 (02) ◽  
pp. 233-249
Author(s):  
STEPHEN J. H. YANG ◽  
WILLIAM CHU ◽  
JONATHAN LEE
Keyword(s):  
Model Checking ◽  
Petri Nets ◽  
Petri Net ◽  
System Modeling ◽  
Model System ◽  
Temporal Behavior ◽  
Time Petri Net ◽  
High Assurance ◽  
System Requirements ◽  
Reachability Tree

This paper presents our reachability tree logic (RTL) and its integration with time Petri nets to specify and verify the temporal behavior of high assurance systems. The specification phase begins with a system modeling to model system requirements into a time Petri net N and construct a reachability tree RT of N. We then use RTL to specify the desired temporal behavior as formula F. The verification phase uses a model-checking algorithm to check whether RT can satisfy F, that is to find firing sequences to satisfy F. If F is not satisfied, we then modify N into N′ and obtain a RT′ of the modified N′. The modification (refinement) continues until the modified RT′ can satisfy F. In addition, we will demonstrate how to reduce the complexity of model-checking by using our RTL-based algorithm. We have implemented a specification and verification toolkit called NCUPN (National Central University Petri Nets toolkit) using Java. NCUPN is now available on the Internet via

Petri Net Recommender System for Generating of Perfect Binary Tree

2019 ◽  
Vol 10 (2) ◽  
pp. 1-12 ◽  
Author(s):  
Gajendra Pratap Singh ◽  
Sujit Kumar Singh
Keyword(s):  
Collaborative Filtering ◽  
Recommender Systems ◽  
Petri Net ◽  
Recommender System ◽  
Binary Tree ◽  
Discrete Event ◽  
Hybrid Approach ◽  
Driven System ◽  
Output Information ◽  
Reachability Tree

In modeling a discrete event driven system, Petri net recommender systems can play a very important role in describing the structural and behavioral properties of complex and tricky networks. The finite and infinite perfect binary tree forms a predictive model which can map the input information to output information based on the inputs' attributes. A perfect binary tree can be used for three types of recommender systems such as: collaborative filtering, a content-based approach, and a hybrid approach. In this article, the authors show the existence of a Petri net whose reachability tree is a Perfect Infinite Binary Tree (PIBT).

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