A valuation-based analysis of conflict-free Petri nets

We propose a novel valuation-based approach for analyzing conflict-free Petri nets. The basic idea is to associate a natural number, called the valuation, to each marking in the Petri net. If the set of markings of zero valuation is forward closed, then the valuation along any Petri net computation is nonincreasing, and in many cases, has the tendency to move towards zero valuation. Using the valuation-based method, we demonstrate a number of problems for conflict-free Petri nets to be decidable.     

Modular state space exploration for timed petri nets

This paper extends modular state space construction for concurrent systems to cater for timed systems. It identifies different forms of timed state space and presents algorithms for computing them. These include uniprocessor algorithms inspired by conservative and optimistic approaches to discrete event simulation, and also a distributed algorithm. The paper discusses implementation issues and performance results for a simple case study.     

A synthesis technique of general petri nets

The general Petri net (GPN) is useful for modeling flexible manufacturing systems with multiple robots and workstations [15] and for parallel programs [8]. A problem of using reachability analysis for analyzing Petri nets (PN) is the large number of states generated. Most of the existing synthesis techniques do not deal with GPN. Koh et al.[15] invented a synthesis technique for GPN. We propose to improve their achievement by adding the simple Arc-ratio rules to Yaw's knitting technique [37, 38, 39] based on the notion of structure relationship together with new path generations, which mark the most distinct feature compared with other approaches. The synthesis rules and procedures of how to update the temporal matrix and structure synchronic distance are presented. The Arc-ratio rules for GPN are also presented. One can successfully synthesize complicated Petri nets using these rules. An example to synthesize a Petri net in [15] is illustrated. The correctness of each synthesis rule with an appropriate Arc-ratio rule for GPN is proved.     

Verification of causal models using petri nets

Many different approaches, mainly based on logical formalisms, have been proposed for modeling causal knowledge and the inferential mechanisms based on this type of knowledge. In this article we present an alternative approach to this problem in which the semantics of a causal model is provided by adopting Petri nets. We show how this scheme of modeling is powerful enough to capture all crucial aspects of the corresponding causal model, without resorting to very complex structures; indeed, the model is obtained using a particular type of deterministic Petri net. Moreover, a complete formalization of the aspects concerning the correctness of the represented causal model is provided in terms of reachability in the Petri net. We believe that this aspect is very important in the knowledge acquisition phase when precise correctness criteria should be defined and respected in the construction of the model. We analyze some of these criteria and we discuss an algorithm (based on a backward simulation of the net) capable of discovering incorrectness by exploiting analysis tools available for Petri nets and the explicit parallelism of the model. © 1992 John Wiley & Sons, Inc.     

Specification of software pipelining using petri nets

This paper presents a flexible model for software pipelining using the petri nets. Our technique, called the Petri Net Pacemaker (PNP), can create near optimal pipelines with less algorithmic effort than other techniques. The pacemaker is a novel idea which exploits the cyclic behavior of petri nets to model the problem of scheduling operations of a loop body for software pipelining. A way of improving the performance of loops containing predicates is given. The PNP technique also shows how nested loops can be pipelined. A comparison with some of the other techniques is presented. THis work was partially supported by the National Science Foundation under grants CDA-9100788 and CDA-9200371.     

Analysis of multi-agent activity using petri nets

This paper presents the use of place/transition petri nets (PNs) for the recognition and evaluation of complex multi-agent activities. The PNs were built automatically from the activity templates that are routinely used by experts to encode domain-specific knowledge. The PNs were built in such a way that they encoded the complex temporal relations between the individual activity actions. We extended the original PN formalism to handle the propagation of evidence using net tokens. The evaluation of the spatial and temporal properties of the actions was carried out using trajectory-based action detectors and probabilistic models of the action durations. The presented approach was evaluated using several examples of real basketball activities. The obtained experimental results suggest that this approach can be used to determine the type of activity that a team has performed as well as the stage at which the activity ended.     

Modelling automated manufacturing systems using a modification of coloured petri nets

Automated manufacturing systems (AMS) are a class of systems exhibiting concurrency, asynchronicity and distributedness, and can be modelled using Petri nets. The advantage of using Petri nets is that they provide graphical models, with formal methods of analysis. However, graphical representation of Petri net models becomes difficult even for medium-sized systems since such graphs tend to become inconveniently large. Coloured Petri nets (CPN) are a variant which enables a more concise representation with the same modelling power. This paper develops a model for simulation of AMS whose correctness can be formally established, and which can be graphically represented and visually understood. It presents a modelling approach for AMS, based on a modified version of CPN, with enhanced modelling power. The proposed modifications result in highly compact graphical representations, and also render the model dynamic, i.e. capable of changing dynamically to reflect currently selected system parameters. These features make the proposed model ideally suited for discrete event simulation.     

A new methodology for analyzing distributed systems modeled by petri nets

Distributed computing systems can be modeled adequately by Petri nets. The computation of invariants of Petri nets becomes necessary for proving the properties of modeled systems. This paper presents a two-phase, bottom-up approach for invariant computation and analysis of Petri nets. In the first phase, a newly defined subnet, called the RP-subnet, with an invariant is chosen. In the second phase, the selected RP-subnet is analyzed. Our methodology is illustrated with two examples viz., the dining philosophers' problem and the connection-disconnection phase of a transport protocol. We believe that this new method, which is computationally no worse than the existing techniques, would simplify the analysis of many practical distributed systems.     

Verification of problem-based learning systems using modified petri nets

In this paper, we intend to verify a web-based system on problem-based learning (PBL). To consider the design flow of the web-based PBL system, it is essential to avoid the potential hazard introduced by a logically incorrect system design. In order to eliminate the potential hazard, we define a new class of Petri net, namely, an Activity Flow (AF) net, which is suitable to be converted from a UML (Unified Modeling Language) activity diagram. Through the siphon-based deadlock detection of the AF net, we can find whether there is a process hazard in the UML activity diagram or not. This is helpful to implement the PBL system and to ensure the correct activities and the right control flow. In addition, we attempt to enhance the quality of the system verification by using a questionnaire. Thus we can interpret the user’s level of satisfaction with the designed PBL system. These two verification approaches bring us to achieve an adequately positive response to the web-based PBL system.     

Using transition set sequences to partition behaviors of petri nets

The transition set semantics (Wang and Jiao, LNCS 6128:84–103, 2010) partitions the Petri net behaviors in a canonical way such that behaviors in an equivalence class have the same canonical transition set sequence. This article extends the semantics in two ways: firstly, the semantics is parameterized by the basic relation on the structural transitions to define different variants; secondly, the semantics for the infinite firing sequences of the net is defined. We prove that these extensions still preserve the well-definedness, soundness and completeness of the semantics. Furthermore, we show how to recognize some infinite sequences called back-loops in the view of this new semantics.     

Identification and control algorithms of functioning for neighborhood systems based on petri nets

We present identification and control algorithms for Petri nets from the neighborhood systems point of view.     

Timed petri nets in modeling and analysis of simple schedules for manufacturing cells

It is shown that a large class of flexible manufacturing cells can be modeled using timed Petri nets. Net models of simple schedules (i.e., schedules in which exactly one part enters and one leaves the cell during each cycle) are conflict-free nets. Two complementary approaches to analysis of such models are presented: invariant analysis and throughput analysis. Invariant analysis provides analytic (or symbolic) solutions for the cycle time of a cell analyzing (invariant) subnets of the original net. Throughput analysis performs a series of performance-preserving net reductions to simplify the original model. Several directions for further research are indicated.     

Error recovery framework for integrated navigation system based on generalized stochastic petri nets

A mobile robot usually works in dynamic environments with many uncertainties caused by either humans or various obstacles. Such uncertainties may cause unexpected error situations that often lead to navigation failure. Therefore, the robot should be able to recover from these unexpected error situations. This paper proposes an error recovery framework based on generalized stochastic Petri nets (GSPN). The approach can provide several advantages. The proposed framework can model various error situations occurring in real environments, thereby enabling a robot to recover from error situations autonomously. The modeling, analysis, and performance evaluation can be also carried out using the GSPN model. Experimental results show that the proposed error recovery framework is useful for dependable navigation of a mobile robot operating autonomously.     

Specification and performance analysis of embedded systems with coloured petri nets

To analyze synchronization, concurrency, communication protocols and system performance, a system level specification is modelled in a coloured Petri net. A toolbox collects information for the implementation, e.g., processing times, waiting times, idle times, data accesses, processing requests. This is illustrated with a data-link protocol system, where the disturbance on the communication channels is modelled, too.     

State equation, controllability, and maximal matchings of petri nets

Petri nets are a versatile modeling device for studying the structure and control of concurrent systems. Petri nets and related graph models have been used for modeling a wide variety of systems from computers to social systems. In order to introduce this interesting modeling device to the researcher in control theory, this paper discusses Petri nets in the context of the state equation for a linear discrete-time system. The controllability concept of dynamic systems is applied to Petri nets for the first time. It is also shown that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.