On the Expressive Power of Non-deterministic and Unambiguous Petri Nets over Infinite Words

We prove that ω-languages of (non-deterministic) Petri nets and ω-languages of (nondeterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Turing machines. We also show that it is highly undecidable to determine the topological complexity of a Petri net ω-language. Moreover, we infer from the proofs of the above results that the equivalence and the inclusion problems for ω-languages of Petri nets are ∏21-complete, hence also highly undecidable. Additionally, we show that the situation is quite the opposite when considering unambiguous Petri nets, which have the semantic property that at most one accepting run exists on every input. We provide a procedure of determinising them into deterministic Muller counter machines with counter copying. As a consequence, we entail that the ω-languages recognisable by unambiguous Petri nets are △30 sets.

Articulations and Products of Transition Systems and their Applications to Petri Net Synthesis

In order to speed up the synthesis of Petri nets from labelled transition systems, a divide and conquer strategy consists in defining decompositions of labelled transition systems, such that each component is synthesisable iff so is the original system. Then corresponding Petri Net composition operators are searched to combine the solutions of the various components into a solution of the original system. The paper presents two such techniques, which may be combined: products and articulations. They may also be used to structure transition systems, and to analyse the performance of synthesis techniques when applied to such structures.

Railway Infrastructure Asset Management Modelling

Railway infrastructure comprises a large collection of diverse and complex systems and structures. Many of them are aging assets and require a significant budget to deliver the maintenance to ensure the required safety and service performance standards. With such a large amount of money spent each year to maintain and renew the network assets, small percentage savings can amount to substantial sums of money. There is therefore a huge incentive to better understand the degradation that assets experience and how these can be effectively managed through the implementation of efficient maintenance strategies. Track and bridges are the most expensive assets to keep in the required condition, and this chapter provides a method to analyse their degradation and build Petri net models to predict the future state of the asset, the number of each maintenance activity which are expected to be undertaken, and their costs experienced by following a particular strategy. Utilising these models enables the quality of the asset management decisions made to be improved and optimised.

A modular framework for optimal scheduling of industrial processes

This paper proposes an extended Petri net formalism as a suitable language for composing optimal scheduling problems of industrial production processes with real and binary decision variables. The proposed approach is modular and scalable, as the overall process dynamics and constraints can be collected by parsing of all atomic elements of the net graph. To conclude, we demonstrate the use of this framework for modeling the moulding sand preparation process of a real foundry plant.

Model Petri Net Sistem Pembayaran Pajak Kendaraan Bermotor Jenis 5 Tahun

Paying taxes is an example of public service. In the process of serving, the service is often synonymous with the queuing process. Queuing is a condition in which several people or objects from a waiting line to be served are generally caused by the need for services to exceed the service capacity or service facilities so that users of arriving facilities cannot immediately receive service. Therefore, overcoming many complaints due to queues can be done by improving services and maximizing time efficiency using the Petri net model. In this study, a Petri net model of the 5-year tax payment service system for a motor vehicle at SAMSAT Oku Timur 1 was made as many as 17 places, 15 transitions, two operators, and 30 arcs using WOPED 3.2.0 software.

Machine-Learning-Based White-Hat Worm Launcher in Botnet Defense System

This article proposes a white-hat worm launcher based on machine learning (ML) adaptable to large-scale IoT network for Botnet Defense System (BDS). BDS is a cyber-security system that uses white-hat worms to exterminate malicious botnets. White-hat worms defend an IoT system against malicious bots, the BDS decides the number of white-hat worms, but there is no discussion on the white-hat worms' deployment in IoT network. Therefore, the authors propose a machine-learning-based launcher to launch the white-hat worms effectively along with a divide and conquer algorithm to deploy the launcher to large-scale IoT networks. Then the authors modeled BDS and the launcher with agent-oriented Petri net and confirmed the effect through the simulation of the PN2 model. The result showed that the proposed launcher can reduce the number of infected devices by about 30-40%.