Hierarchical reachability graph of bounded Petri nets forconcurrent-software analysis

Petri nets have been proposed as a promising tool for modeling and analyzing concurrent-software systems such as Ada programs and communication protocol software. Among analysis techniques available for Petri nets, the most general approach is to generate all possible states (markings) of the system in a form of a so-called reachability graph. However, this conventional reachability graph approach is inefficient or intractable, even for a bounded Petri net, due to state explosion in many practical applications. To cope with this problem, this paper proposes a method for constructing a hierarchically organized state space called the hierarchical reachability graph (HRG). Using the HRG, we obtain necessary and sufficient conditions for reachability and deadlock, as well as algorithms to test whether a given state or marking is reachable from the initial state and whether there is a deadlock state (a state with no successor states)     

On‐the‐Fly and Incremental Technique for Fault Diagnosis of Discrete Event Systems Modeled by Labeled Petri Nets

In this paper, we develop an on‐the‐fly and incremental technique for fault diagnosis of discrete event systems modeled by labeled Petri nets, in order to tackle the combinatorial explosion problem. K‐diagnosability, diagnosability, K_min (the minimum K ensuring diagnosability) and on‐line diagnosis are solved on the basis of the on‐the‐fly and incremental building of two structures, called respectively fault marking graph and fault marking set graph, in parallel. We build on existing results, namely those establishing necessary and sufficient conditions for diagnosability, but we bring mechanisms to make the checking of such conditions potentially more efficient. We show that, in general, analyzing or even building the whole reachability graph is unnecessary to analyze diagnosability and build an on‐line diagnoser. Our technique was implemented in a prototype tool called OF‐PENDA, and a railway level crossing benchmark is used to make a comparative discussion pertaining to efficiency in terms of time and memory relative to some existing approaches.     

Diagnosability of Petri nets with observation graphs

This paper addresses the problem of diagnosability for dynamic discrete event systems modeled with bounded or unbounded Petri nets that are deadlock-free and monitored with sensor configurations with marking and event measurements. The proposed method gives necessary and sufficient conditions for diagnosability. It is based on the transformation of the coverability graph into an observation graph that encodes all observation sequences of measured markings and events with respect to the sensor configuration. This graph also encodes all sequences of transitions that may fire from any reachable marking of the Petri net. Diagnosability is determined by analyzing the paths and circuits in the observation graph. The method is illustrated with several examples of bounded or unbounded Petri nets.     

Hierarchical Reachability Graph Generation for Petri Nets

Reachability analysis is the most general approach to the analysis of Petri nets. Due to the well-known problem of state-space explosion, generation of the reachability set and reachability graph with the known approaches often becomes intractable even for moderately sized nets. This paper presents a new method to generate and represent the reachability set and reachability graph of large Petri nets in a compositional and hierarchical way. The representation is related to previously known Kronecker-based representations, and contains the complete information about reachable markings and possible transitions. Consequently, all properties that it is possible for the reachability graph to decide can be decided using the Kronecker representation. The central idea of the new technique is a divide and conquer approach. Based on net-level results, nets are decomposed, and reachability graphs for parts are generated and combined. The whole approach can be realized in a completely automated way and has been integrated in a Petri net-based analysis tool.     

On reachability graphs of Petri nets

Petri net is a powerful tool for system analysis and design. Several techniques have been developed for the analysis of Petri nets, such as reachability trees, matrix equations and reachability graphs. This article presents a novel approach to constructing a reachability graph, and discusses the application of the reachability graph to Petri nets analysis.     

基于行为表达式的任意随机Petri网的品质分析

提出一种基于行为表达式的品质分析方法,可以做任意分布的有界或无界随机 Petri网的品质分析.该方法不仅拓广了分析范围,解决了文献[4]中没有解决的问题,而且 不必画出Petri网的可达标识图,使分析过程更为简洁.     

A polynomial algorithm for testing diagnosability of discrete-eventsystems

Failure diagnosis in large and complex systems is a critical task. In the realm of discrete-event systems, Sampath et al. (1995) proposed a language based failure diagnosis approach. They introduced the diagnosability for discrete-event systems and gave a method for testing the diagnosability by first constructing a diagnoser for the system. The complexity of this method of testing diagnosability is exponential in the number of states of the system and doubly exponential in the number of failure types. We give an algorithm for testing diagnosability that does not construct a diagnoser for the system, and its complexity is of fourth order in the number of states of the system and linear in the number of the failure types     

一种基于扩展时间Petri网的工作流时间性能评价方法

时间性能分析是工作流模型分析和评价的重要方面．首先介绍了业务过程的一般Petri网模型,然后建立了工作流网的扩展时间模型,在可达图的基础上提出了简单路径图和可变换子网的概念,利用保持网响应时间和分配概率不变的网变换方法对扩展时间工作流网进行化简,给出了找出可变换子网的算法和计算工作流模型时间性能指标的方法．     

Verifying time Petri nets by linear programming

The paper proposes an approach to solving some verification problems of time petri nets using linear programming.The approach is based on the observation that for loop-closed time Ptri nets,it is only necessary to investigate a finite prefix of an untimed run of the underlying Petri net.Using the technique the paper gives solutions to reachabiltiy and bounded delay timing analysis problems.For both problems algorithms are given,that are decision procedures for loop-closed time Petri nets.and semi-decision procedures for general time Petri nets.     

Fault detection for discrete event systems using Petri nets with unobservable transitions

In this paper we present a fault detection approach for discrete event systems using Petri nets. We assume that some of the transitions of the net are unobservable, including all those transitions that model faulty behaviors. Our diagnosis approach is based on the notions of basis marking and justification, that allow us to characterize the set of markings that are consistent with the actual observation, and the set of unobservable transitions whose firing enable it. This approach applies to all net systems whose unobservable subnet is acyclic. If the net system is also bounded the proposed approach may be significantly simplified by moving the most burdensome part of the procedure off-line, thanks to the construction of a graph, called the basis reachability graph.     

Discrete event diagnosis using labeled Petri nets. An application to manufacturing systems

In this paper an approach to on-line diagnosis of discrete event systems based on labeled Petri nets is presented. The approach is based on the notion of basis markings and justifications and it can be applied both to bounded and unbounded Petri nets whose unobservable subnet is acyclic. Moreover it is shown that, in the case of bounded Petri nets, the most burdensome part of the procedure may be moved off-line, computing a particular graph called Basis Reachability Graph.Finally, the effectiveness of the proposed procedure is analyzed applying a MATLAB diagnosis toolbox we developed to a manufacturing example taken from the literature.     

A Reduced Reachability Tree for a Class of Unbounded Petri Nets

As a powerful analysis tool of Petri nets, reachability trees are fundamental for systematically investigating many characteristics such as boundedness, liveness and reversibility. This work proposes a method to generate a reachability tree, called ωRT for short, for a class of unbounded generalized nets called ω-independent nets based on new modified reachability trees (NMRTs). ωRT can effectively decrease the number of nodes by removing duplicate and ω-duplicate nodes in the tree, and verify properties such as reachability, liveness and deadlocks. Two examples are provided to show its superiority over NMRTs in terms of tree size.      

Reachability determination in acyclic Petri nets by cell enumeration approach

Reachability is one of the most important behavioral properties of Petri nets. We propose in this paper a novel approach for solving the fundamental equation in the reachability analysis of acyclic Petri nets, which has been known to be NP-complete. More specifically, by adopting a revised version of the cell enumeration method for an arrangement of hyperplanes in discrete geometry, we develop an efficient solution scheme to identify firing count vector solution(s) to the fundamental equation on a bounded integer set, with a complexity bound of O((nu)^n−m), where n is the number of transitions, m is the number of places and u is the upper bound of the number of firings for all individual transitions.     

Property analysis of logic Petri nets by marking reachability graphs

Logic Petri nets (LPNs) are suitable to describe and analyze batch processing functions and passing value indeterminacy in cooperative systems. To investigate the dynamic properties of LPNs directly, a new method for analyzing LPNs is proposed based on marking reachability graphs in this paper. Enabled conditions of transitions are obtained and a marking reachability graph is constructed. All reachable markings can be obtained based on the graph; the fairness and reversibility of LPNs are analyzed. Moreover, the computing complexity of the enabled conditions and reachable markings can be reduced by this method. The advantages of the proposed method are illustrated by examples and analysis.     

Verification of robust diagnosability for partially observed discrete event systems

In this paper, we study robust failure diagnosis of discrete event systems. Given a set of possible models, each of which has its own nonfailure specification, we consider the existence of a single diagnoser such that, for all possible models, it detects any occurrence of a failure within a uniformly bounded number of steps. We call such a diagnoser a robust diagnoser. We introduce a notion of robust diagnosability, and prove that it serves as a necessary and sufficient condition for the existence of a robust diagnoser. We then present an algorithm for verifying the robust diagnosability condition.     

Compositional schedulability analysis of real-time systems using time Petri nets

This paper presents an approach to the schedulability analysis of real-time systems modeled in time Petri nets by separating timing properties from other behavioral properties. The analysis of behavioral properties is conducted based on the reachability graph of the underlying Petri net, whereas timing constraints are checked in terms of absolute and relative firing domains. If a specific task execution is schedulable, we calculate the time span of the task execution, and pinpoint nonschedulable transitions to help adjust timing constraints. A technique for compositional timing analysis is also proposed to deal with complex task sequences, which not only improves efficiency but also facilitates the discussion of the reachability issue with regard to schedulability. We identified a class of well-structured time Petri nets such that their reachability can be easily analyzed.     

Comments on “An Iterative Synthesis Approach to Petri Net Based Deadlock Prevention Policy for Flexible Manufacturing Systems”

In the above paper, it proposes a deadlock prevention policy for a flexible manufacturing system (FMS), which needs the complete state enumeration of the FMS that is modeled with Petri nets. The reachability graph of a Petri-net model is divided into two parts: the live zone (LZ) and the deadlock zone (DZ). The states in the LZ of the reachability graph of a Petri net constitute the legal behavior of the net from the viewpoint of deadlock prevention. The concept of first-met bad markings is proposed. A first-met bad marking is a node in DZ, whose father nodes are in LZ. The deadlock prevention policy is used in an iterative way. At each iteration, a first-met bad marking is identified from the reachability graph of a Petri net to be controlled. The reachability of a first-met bad marking is prohibited by adding a monitor, establishing a marking invariance relationship between the additional monitor and the activity places that are marked under the first-met bad marking. To achieve this, without a formal proof, [Lemma 1] is developed as shown in this article.     

Detection of Ada static deadlocks using Petri net invariants

A method is presented for detecting deadlocks in Ada tasking programs using structural; and dynamic analysis of Petri nets. Algorithmic translation of the Ada programs into Petri nets which preserve control-flow and message-flow properties is described. Properties of these Petri nets are discussed, and algorithms are given to analyze the nets to obtain information about static deadlocks that can occur in the original programs. Petri net invariants are used by the algorithms to reduce the time and space complexities associated with dynamic Petri net analysis (i.e. reachability graph generation)     

Liveness-enforcing supervision of bounded ordinary Petri nets usingpartial order methods

This paper combines and refines recent results into a systematic way to verify and enforce the liveness of bounded ordinary Petri nets. The approach we propose is based on a partial-order method called network unfolding. Network unfolding maps the original Petri net to an acyclic occurrence net. A finite prefix of the occurrence net is defined to give a compact representation of the original net reachability graph while preserving the causality between net transitions. A set of transition invariants denoted as base configurations is identified in the finite prefix. These base configurations capture all of the fundamental executions of the net system, thereby providing a modular way to verify and synthesize supervisory net systems. This paper proves necessary and sufficient conditions that characterize the original net liveness and the existence of maximally permissive supervisory policies that enforce liveness