colored petri nets
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2022 ◽  
Author(s):  
Vijay Gehlot ◽  
Elliot Sloane ◽  
Michael Kirk ◽  
Eric Miller ◽  
Jonathan Schaffer ◽  
...  

2021 ◽  
Author(s):  
Dmitry A. Zaitsev ◽  
Peyman Ghaffari ◽  
Virginia Sanz Sanchez

We develop techniques to translate deterministic cellular automata models into colored Petri nets based on an example of known cellular automata for modeling and mimicking Ebola virus dynamics. Cellular automata for Ebola virus dynamics use parametric specifications of rules that is peculiarity of the present study. The simulation results completely coincide with known results obtained via dedicated simulator. Having uniform language for models specification brings in advantages for models mutual transformations and simulation.


Author(s):  
Goharik Petrosyan ◽  
Armen Gaboutchian ◽  
Vladimir Knyaz

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.


2021 ◽  
Author(s):  
Matheus Dias Gama ◽  
Stéphane Julia ◽  
Rita Maria Silva Julia

Frequentemente, a complexidade da política de distribuição dos algoritmos distribuídos os tornam extremamente hostis a consagradas abordagens matemáticas de análise de desempenho, tais como análise assintótica, técnicas de recorrências e análise probabilística. Isso se deve ao fato de que tais métodos não provêm recursos adequados que lhes permitam avaliar o quão o gradual aumento do número de processadores impacta no tempo de execução do algoritmo. Diante disso, este artigo propõe uma abordagem visual e formal, baseada em simulações automáticas de modelos de Redes de Petri Coloridas Hierárquicas no ambiente gráfico Colored Petri Nets Tools (CPN Tools), para avaliar o speedup e o ponto de saturação de processadores de algoritmos distribuídos usados em Inteligência Artificial. Será usado como estudo de caso o algoritmo de treinamento dos Perceptrons de Múltiplas Camadas baseado na retro-propagação do erro.


Author(s):  
John David S. Belém ◽  
Hidalyn Theodory C. M. Souza ◽  
Álvaro Sobrinho ◽  
Lenardo Chaves E. Silva ◽  
Helder Fernando De Araujo Oliveira

People who live in low-income and hard-to-reach regions are usually the most affected ones by high incidences of arboviral diseases, increasing morbidity and mortality rates, and public health costs. We present the modeling of hardware and software components of an unmanned aerial vehicle (UAV) system by mathematical tools, focusing on monitoring foci of arboviral diseases transmitted by Aedes aegypti mosquito, e.g., Zika, Chikungunya, and Dengue. We used restriction equations and the colored Petri nets formal modeling language to represent the flight dynamics and the software components of the system, respectively. We evaluated the specification of desired behaviors of the monitoring system using simulations and the model checking technique. The results showed the completeness and correctness of the specification. The design of such a system is challenging due to the potential risks to people and the environment. Therefore, this study provides insights into the development of an UAV system for such an application scenario. The monitoring system has the potential of improving the efficiency in identifying foci of arboviral diseases.


Author(s):  
Aleksandr Gozhyj ◽  
Irina Kalinina ◽  
Vladyslav Nechakhin ◽  
Victor Gozhyj ◽  
Victoria Vysotska

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