Coverability Tree Research Articles

A modification of Petri nets with anticipation on a position

We propose a modification of Petri nets with strong anticipation on a position. The extension modifies a transition rule by adding a new term that contains an integer function of the new marking in the position. The differences from classic Petri nets are found; for example, the set of markings that are reachable from a current marking by firing the enabled transition can either be empty or contain more than one marking. We consider the construction of a reachability graph and a coverability tree. We give the conditions for the existence of the coverability tree and propose the algorithm for constructing the coverability tree that generalizes the well-known classic algorithm. The main ideas and constructions are illustrated in the examples.

Cassava Chips Production System in Max-Plus Algebra

The research discussed here relates to the cassava chips production system. The production system was analyzed using petri net and algebra of maxplus. The goal is to obtain information on the completion time for each process and to know the estimated time of completion of production each day. Based on the data obtained, it can be described the flow of the production process and then formed a graph so that it can be formed a petri net using the Woped 3.1.0 tool. From the results of the petri net then analyzed and can be built coverability tree. So that, the completion time for each process and the estimated time for completion of production each day can be known.

A Study on Flexible Manufacturing Systems using Petri Net Reduction

Petrinets are the suitable tool for modeling and analysis of discrete event systems. The effective methods of analyzing the discrete event systems (DES) are exhibited by Petri nets. The entire structure of the system is mathematically expressed using Petrinets and also all the properties are analysed by different methods. The properties of Petrinets are different in various systems, a Flexible Manufacturing System (FMS) requires production activities in which raw materials, energy, labour, and equipment are combined together in the modification process for the production of good quality goods.” The word “flexible” explains the capability of the system to relate productively to make changes in the system. These changes can be internal failure of the system or classification problems such as a sample or external changes in the structure of the model as well as demand for the process. The inherent limitations such as undecidable properties, complexity in checking, automatic verification of the modeled system are existing in FMS. This paper explains a study on FMS using Petri net reduction. A PN underlies event structures with casuality and compatibility relations. Partial order methods and reduction methods reduce the complexity of constructing the reachability graph. The determination of PN system through reduction methods in recent years focused by many researchers. The significance of reduction methods are highlighted to execute the faster analysis of a system. Instead of coverability trees and the graphical representation the incidence matrix of the PNs are used for the reduction methods. Reduction methods are used to simplify large scale PNs into “equivalent” smaller nets. Boundedness, liveness, simplification of implicit places, shared resources and elimination of self-loops are checked though equivalent smaller nets. The structure of FMS is preserved.

Petri Net Model and Max-Plus Algebra in Outpatient Care at Solo Peduli Clinic, Surakarta

Patients come to SoloPeduli Clinic to get medical treatment. Medical treatment at SoloPeduli Clinic is divided into two parts namely outpatient and inpatient health services. Patients generally do not know how long it will take for service from arrival to discharge at the clinic. The queue flow is called a system, while the patients queuing at each service are called states, the number of states cannot be limited as health services must be available 24 hours a day. This issue includes a Discrete Event System which can be modeled with a Petri Net. Petri Net is a mathematical model that can be used to describe certain events in a Discrete Event System. In this research, service flow is modeled using Petri Net which is then represented in the form of a matrix. Coverability Tree was created to define life and deadlock. Scheduling is modeled using Max-Plus Algebra. Service times will be randomly selected to facilitate scheduling and length of service time.

Petri Net Model and Max-Plus Algebra on Queue in Clinic UNS Medical Center

Patients come to the clinic UNS (Universitas Sebelas Maret) Medical Center to get a medical treatment. The clinic provides two health services include dental polyclinics and general polyclinics. Majority of patients do not know exactly how long the process of service from patient registration to getting medicine. Moving queues to each service is an event and people who queue up at each service are state. It is clear that the sum of all possible states is finite. This problem includes a Discrete Event System (DES). One of the uses of petri net is to model a DES. In this research, service flow was built in the clinic using Petri Net and service scheduling was modeled using Max-Plus Algebra. Furthermore, a coverability tree was built to determine the liveness and deadlock of the patient service queue and analyze the petri net flow. The selection of service start time can be chosen randomly to simulate the scheduling and length of service time.

Petri Net Based Modeling and Property Analysis of Distributed Discrete Event System

PetriNet is an imperative and handy language used for modeling and analysis of discrete event system (DES) i.e. a dynamic system that progress according to unexpected occurrence of events at probably unknown, asymmetrical interval of time. This concept provides an interface for analysis of behavioral and structural properties like liveness, boundedness and cover-ability tree of discrete event systems. These properties are not only necessary for proving the correctness of system model but also helpful in checking the deadlock conditions in a system. As a graph Petri Net is used for modeling and mathematically, it can be used for analysis of the system. In this paper, we have first modeled various DES like computation model and communication model using Petri Nets and then analyzed their properties using MATLAB. These DES models have applications in almost every domain of science and engineering.

Petri Net and Max-Plus Algebra Model in Bank Queue with Two Servers in Each Service

Bank is one of the business entity used by most of the people in the world including Indonesia and play an important role of nancial institutions in the economy of society. There are some of the bank services that are given to us such as customer service, teller, loan service, etc. The main services provided by every bank are customer services and tellers. Queuing problem that happened in bank services can be modeled using mathematics. Mathematics model used in this research is timed petri net. Petri net models the queue in the services system into a discrete form where in this research is used two main services in the bank with two counters in each service. Furthermore, from the ow of petri net that has been made is built the coverability tree to nd out the liveness and deadlocks of each groove petri net. Next, the petri net model is constructed using max-plus algebra.

Limitations of Coverability Trees for Context-Free Parallel Communicating Grammar Systems and Why these Grammar Systems are not Linear Space

Coverability trees offer a finite characterization of all the derivations of a context-free parallel grammar system (CF-PCGS). Their finite nature implies that they necessarily omit some information about these derivations. We demonstrate that the omitted information is most if not all of the time too much, and so coverability trees are not useful as an analysis tool except for their limited use already considered in the paper that introduces them (namely, determining the decidability of certain decision problems over PCGS). We establish this result by invalidating an existing proof that synchronized CF-PCGS are less expressive than context-sensitive grammars. Indeed, we discover that this proof relies on coverability trees for CF-PCGS, but that such coverability trees do not in fact contain enough information to support the proof.

A Solution of Synchronic Distance in Fair Petri Nets

This paper gives a solution of the synchronic distance between any two transitions in a fair Petri net. In order to describe the synchronic distance between two transitions more accurately, the concept of weighted synchronic distance is adopted. The solution method is firstly to add a weighted observe-place between two transitions, and a net system with a weighted observe-place is constructed by assigning a suitable weight function for an arc between a transition and an observe-place. Then the initial tokens of a weighted observeplace are obtained by constructing an augumented coverability tree of a net system with a weighted observe-place. The synchronic distance between two transitions is finally yielded by constructing a coverability tree of a net system with a weighted observe-place, and the corresponding solution algorithms are also given.

Optimization of VARICOL SMB processes using hybrid modeling and nonlinear programming

The Varicol process exhibits continuous and discrete-time dynamics and can be represented by a hybrid model, where the continuous-time dynamics is described by mass-balance partial differential equations, whereas the discrete-time dynamics is described by a timed transition Petri net (TTPN). This hybrid model allows to simplify the solution of a normally difficult Mixed-Integer Non-Linear Programming problem for maximizing the productivity of a Varicol process subject to constraints on the desired purities of the extract and the raffinate components. Indeed, the coverability tree of the TTPN can be constructed to generate a set of candidate integer parameters, and the corresponding nonlinear problems are solved for a subset of candidates selected on the basis of an approximate evaluation using the (true moving bed) triangle theory. The optimal solution is the Varicol configuration (column sequence) for which the productivity is maximal. A repeatability and a robustness analysis show the feasibility of this approach.

Modeling and analysis of departure routine in air traffic control based on Petri nets

Departure routine is essential part in the air traffic control and must be formally designed to avoid potential hazards and to verify proper functioning of the underlying processes. This paper addresses the Petri net approach to formally model the departure routine of the aircraft which ensures the organized flow of air traffic during departure. First, the high-level design of the system is presented by identifying key objects involved in departure routine, and then, its detailed model is presented. Moreover, the verification of the underlying methodology has been made using coverability tree. The proposed model is verified to be safe (bounded), potentially reversible and deadlock free which ensures reliability of the system and guarantees the efficient and controlled communication between the aircraft and local and ground controllers.

A Public-Key Cryptosystem Based On Stochastic Petri Net

In this paper, we present a new method to build public-key Cryptosystem. The method is based on the state explosion problem occurred in the computing of average number of tokens in the places of Stochastic Petri Net (SPN). The reachable markings in the coverability tree of SPN are used as the encryption keys. Accordingly, multiple encryption keys can be generated, thus we can perform multiple encryption to get as strong security as we expect. The decryption is realized through solving a group of ordinary differential equations from Continuous Petri Net (CPN), which has the same underlying Petri net as that of SPN. The decipherment difficulty for attackers is in exponential order. The contribution of this paper is that we can use continuous mathematics to design cryptosystems besides discrete mathematics.

A Petri Net Based Public-Key Cryptosystem

In this paper, we present a new method to build public-key Cryptosystem. The method is based on the state explosion problem occurred in the computing of average number of tokens in the places of Stochastic Petri Net (SPN). The reachable markings in the coverability tree of SPN are used as the encryption keys. Accordingly, multiple encryption keys can be generated, thus we can perform multiple encryption to get as strong security as we expect. The decryption is realized through solving a group of ordinary differential equations from Continuous Petri Net (CPN), which has the same underlying Petri net as that of SPN. The decipherment difficulty for attackers is in exponential order. The contribution of this paper is that we can use continuous mathematics to design cryptosystems instead of discrete mathematics.

Minimal Coverability Set for Petri Nets: Karp and Miller Algorithm with Pruning

This paper presents the Monotone-Pruning algorithm (MP) for computing the minimal coverability set of Petri nets. The original Karp and Miller algorithm (K&M) unfolds the reachability graph of a Petri net and uses acceleration on branches to ensure termination. The MP algorithm improves the K&M algorithm by adding pruning between branches of the K&M tree. This idea was first introduced in the Minimal Coverability Tree algorithm (MCT), however it was recently shown to be incomplete. The MP algorithm can be viewed as the MCT algorithm with a slightly more aggressive pruning strategy which ensures completeness. Experimental results show that this algorithm is a strong improvement over the K&M algorithm.

Specification and verification of safety properties along a crossing region in a railway network control

Modeling the controller of the railway network, having resource sharing based on mutual exclusion constraints, is an important problem. This paper firstly addresses the specification of safety properties for the model of a complex railway crossing. The operations, i.e., occupied, free and block, are formalized to describe the safety properties along railway crossing. Second, to develop the control model of the crossing system we construct the subnet representing the train flow along the tracks in the crossing region and the set of monitors or supervisors are also modeled as subnets. Arc-constant colored Petri net (ac-CPN) is used to construct the train flow subnet while the monitors are modeled using the place/transition-net. Arc-constant colored Petri net enforces the specification of not to shift the train from a track to another one. Bottom-up approach is adopted to model the control for railway crossing as a synchronous synthesis of the subnets is applied to build the final model. Finally, to verify the safety properties in the developed controller, the coverability tree method is used for the analysis of the final model.

APLIKASI PETRI NET PADA SISTEM PEMBAYARAN TAGIHAN LISTRIK PT. PLN (Persero) RAYON AMBON TIMUR

Petri Net is a model of Mathematics used in the system event discrit to illustrate certain event. One application of Petri Nets is to sketch the entrance occurs in a place like the public service system. This reserce will simply describe the use of Petri Net to sketch the entrance occurs in electricity bill payment system of PT.PLN (Persero) Rayon Ambon Timur by the number of place is 7 and the transition is 8, and to determine the matrix representation and the coverability tree of the model.

A Petri-net and QoS Based Model for Automatic Web Service Composition

Web services are widely used because of their features of interoperability, loose-coupled and platform independent. Web services composition is one of the most popular topics in service computing area. In this paper a method based on Petri net coverability problem and utility of Web services is proposed to handle automatic service composition. The former is for satisfying functional requirements of service composition while the latter corresponds to non-functional properties. For a set of given services, each service is translated into component of Petri net and the input/output places with same semantics are merged. According to user’s input and desired output, the initial marking and target marking can be obtained. Then the coverability tree and coverability graph can be constructed. Next, the nodes on the coverability graph which can cover the target marking should be find out. If there are more than one coverability paths, we determine the smallest weight denoted as “SW” on each path. The weight is defined as the utility calculated according to the QoS. At last, services on the path with largest SW are selected as service executing sequence to reach the goal of automatic service composition.

Reachability Analysis of Concurrent Boolean Programs with Symbolic Counter Abstraction

A basic problem in software model checking is the choice of a model for software. Boolean program is the most popular representation and is amenable to model checking. We show how to apply counter abstraction to real world concurrent Boolean programs to eliminate state redundancy. We present a model checking algorithm for thread-state reachability analysis of concurrent Boolean programs, constructing Karp-Miller coverability tree directly on a Boolean program. And finally evaluate the performance of the approach using a substantial set of Boolean program benchmarks.

Checking system boundedness using ordinary differential equations

Boundedness is one of the most important properties of discrete Petri nets. Determining the boundedness of a Petri net is usually done through building coverability graph or coverability tree. However, the computation is infeasible for complex applications because the size of the coverability graph may increase faster than any primitive recursive functions. This paper proposes a new technique to check the boundedness without causing this problem. Let a concurrent system be represented by a (discrete) Petri net. By relaxing the (discrete) Petri net to a continuous Petri net, we can model the concurrent system by a family of ordinary differential equations. It has been shown that the boundedness of the discrete Petri net is equivalent to the boundedness of the solutions of the corresponding ordinary differential equations. Hence, we can check the boundedness of a (discrete) Petri net by analyzing the solutions of a family of ordinary differential equations. A case study demonstrates the benefits of our technique.

Petri net based formal analysis for multimedia conferencing services orchestration

Development of services that span over the Internet and Telecom networks is driving significant efforts towards the integrated of services offered by Telecom operators. Service-oriented communication (SOC) is a new trend in the industry to enable communication through a service-oriented architecture (SOA) and thereby package communications as services. In this paper, we firstly introduce the design and implementation for business process execution language (BPEL) based multimedia conferencing communication services orchestration, and mainly focus on the issue of guaranteeing the correctness of such applications, we presents a Petri net-based approach to analyzing the BPEL based multimedian conferencing communication services orchestration correctness and also a set of translation rules is proposed to transform BPEL processes into Petri nets. Especially, we define the correctness of multimedia conferencing services orchestration and address the verification method based on Petri nets. The algorithms and corresponding reliable issues have been proposed, such as the coverability tree for detecting flow safeness, the incidence matrix & state equation for finding reachable issues, and a transitive matrix for detecting a deadlock problem. With the Petri Net Markup Language (PNML) are introduced to transform a orchestrated services into a Petri net model, and providing an automated support for the formal analysis of their behavior. Finally, we give the conclusions.