Petri Nets at Modelling and Control of Discrete-Event Systems Containing Nondeterminism - Part 1

Discrete-Event Systems are discrete in nature, driven by discrete events. Petri Nets are one of the mostly used tools for their modelling and control synthesis. Place/Transitions Petri Nets, Timed Petri Nets, Controlled Petri Nets are suitable when a modelled object is deterministic. When the system model contains uncontrollable/unobservable transitions and unobservable/unmeasurable places or other failures, such kinds of Petri Nets are insufficient for the purpose. In such a case Labelled Petri Nets and/or Interpreted Petri Nets have to be used. Particularities and mutual differences of individual kinds of Petri Nets are pointed out and their applicability to modelling and control of Discrete-Event Systems are described and tested

Optimal Supervisory Control Synthesis

The place invariant method is well known as an elegant way to construct a Petri net controller. It is possible to use the constraint for preventing forbidden states. But in general case, the number forbidden states can be very large giving a great number of control places. In this paper is presented a systematic method to reduce the size and the number of constraints. This method is applicable for safe and conservative Petri nets giving a maximally permissive controller.Comment: Journ\'ee sur l'Instrumentation Industrielle J2I, ORAN : Alg\'erie (2009

VERIFICATION AND APPLICATION OF DETECTABILITY BASED ON PETRI NETS

In many real-world systems, due to limitations of sensors or constraints of the environment, the system dynamics is usually not perfectly known. However, the state information of the system is usually crucial for the purpose of decision making. The state of the system needs to be determined in many applications. Due to its importance, the state estimation problem has received considerable attention in the discrete event system (DES) community. Recently, the state estimation problem has been studied systematically in the framework of detectability. The detectability properties characterize the possibility to determine the current and the subsequent states of a system after the observation of a finite number of events generated by the system. To model and analyze practical systems, powerful DES models are needed to describe the different observation behaviors of the system. Secondly, due to the state explosion problem, analysis methods that rely on exhaustively enumerating all possible states are not applicable for practical systems. It is necessary to develop more efficient and achievable verification methods for detectability. Furthermore, in this thesis, efficient detectability verification methods using Petri nets are investigated, then detectability is extended to a more general definition (C-detectability) that only requires that a given set of crucial states can be distinguished from other states. Formal definitions and efficient verification methods for C-detectability properties are proposed. Finally, C-detectability is applied to the railway signal system to verify the feasibility of this property: 1. Four types of detectability are extended from finite automata to labeled Petri nets. In particular, strong detectability, weak detectability, periodically strong detectability, and periodically weak detectability are formally defined in labeled Petri nets. 2. Based on the notion of basis reachability graph (BRG), a practically efficient approach (the BRG-observer method) to verify the four detectability properties in bounded labeled Petri nets is proposed. Using basis markings, there is no need to enumerate all the markings that are consistent with an observation. It has been shown by other researchers that the size of the BRG is usually much smaller than the size of the reachability graph (RG). Thus, the method improves the analysis efficiency and avoids the state space explosion problem. 3. Three novel approaches for the verification of the strong detectability and periodically strong detectability are proposed, which use three different structures whose construction has a polynomial complexity. Moreover, rather than computing all cycles of the structure at hand, which is NP-hard, it is shown that strong detectability can be verified looking at the strongly connected components whose computation also has a polynomial complexity. As a result, they have lower computational complexity than other methods in the literature. 4. Detectability could be too restrictive in real applications. Thus, detectability is extended to C-detectability that only requires that a given set of crucial states can be distinguished from other states. Four types of C-detectability are defined in the framework of labeled Petri nets. Moreover, efficient approaches are proposed to verify such properties in the case of bounded labeled Petri net systems based on the BRG. 5. Finally, a general modeling framework of railway systems is presented for the states estimation using labeled Petri nets. Then, C-detectability is applied to railway signal systems to verify its feasibility in the real-world system. Taking the RBC handover procedure in the Chinese train control system level 3 (CTCS-3) as an example, the RBC handover procedure is modeled using labeled Petri nets. Then based on the proposed approaches, it is shown that that the RBC handover procedure satisfies strongly C-detectability

Ninth Workshop and Tutorial on Practical Use of Coloured Petri Nets and the CPN Tools, Aarhus, Denmark, October 20-22, 2008

This booklet contains the proceedings of the Ninth Workshop on Practical Use of Coloured Petri Nets and the CPN Tools, October 20-22, 2008. The workshop is organised by the CPN group at the Department of Computer Science, University of Aarhus, Denmark. The papers are also available in electronic form via the web pages: http://www.daimi.au.dk/CPnets/workshop0

Proceedings of the First NASA Formal Methods Symposium

Topics covered include: Model Checking - My 27-Year Quest to Overcome the State Explosion Problem; Applying Formal Methods to NASA Projects: Transition from Research to Practice; TLA+: Whence, Wherefore, and Whither; Formal Methods Applications in Air Transportation; Theorem Proving in Intel Hardware Design; Building a Formal Model of a Human-Interactive System: Insights into the Integration of Formal Methods and Human Factors Engineering; Model Checking for Autonomic Systems Specified with ASSL; A Game-Theoretic Approach to Branching Time Abstract-Check-Refine Process; Software Model Checking Without Source Code; Generalized Abstract Symbolic Summaries; A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing; Component-Oriented Behavior Extraction for Autonomic System Design; Automated Verification of Design Patterns with LePUS3; A Module Language for Typing by Contracts; From Goal-Oriented Requirements to Event-B Specifications; Introduction of Virtualization Technology to Multi-Process Model Checking; Comparing Techniques for Certified Static Analysis; Towards a Framework for Generating Tests to Satisfy Complex Code Coverage in Java Pathfinder; jFuzz: A Concolic Whitebox Fuzzer for Java; Machine-Checkable Timed CSP; Stochastic Formal Correctness of Numerical Algorithms; Deductive Verification of Cryptographic Software; Coloured Petri Net Refinement Specification and Correctness Proof with Coq; Modeling Guidelines for Code Generation in the Railway Signaling Context; Tactical Synthesis Of Efficient Global Search Algorithms; Towards Co-Engineering Communicating Autonomous Cyber-Physical Systems; and Formal Methods for Automated Diagnosis of Autosub 6000

Discrete Event Systems: Models and Applications; Proceedings of an IIASA Conference, Sopron, Hungary, August 3-7, 1987

Work in discrete event systems has just begun. There is a great deal of activity now, and much enthusiasm. There is considerable diversity reflecting differences in the intellectual formation of workers in the field and in the applications that guide their effort. This diversity is manifested in a proliferation of DEM formalisms. Some of the formalisms are essentially different. Some of the "new" formalisms are reinventions of existing formalisms presented in new terms. These "duplications" reveal both the new domains of intended application as well as the difficulty in keeping up with work that is published in journals on computer science, communications, signal processing, automatic control, and mathematical systems theory - to name the main disciplines with active research programs in discrete event systems. The first eight papers deal with models at the logical level, the next four are at the temporal level and the last six are at the stochastic level. Of these eighteen papers, three focus on manufacturing, four on communication networks, one on digital signal processing, the remaining ten papers address methodological issues ranging from simulation to computational complexity of some synthesis problems. The authors have made good efforts to make their contributions self-contained and to provide a representative bibliography. The volume should therefore be both accessible and useful to those who are just getting interested in discrete event systems

Verification and synthesis of asynchronous control circuits using petri net unfoldings

PhD ThesisDesign of asynchronous control circuits has traditionally been associated with application of formal methods. Event-based models, such as Petri nets, provide a compact and easy to understand way of specifying asynchronous behaviour. However, analysis of their behavioural properties is often hindered by the problem of exponential growth of reachable state space. This work proposes a new method for analysis of asynchronous circuit models based on Petri nets. The new approach is called PN-unfolding segment. It extends and improves existing Petri nets unfolding approaches. In addition, this thesis proposes a new analysis technique for Signal Transition Graphs along with an efficient verification technique which is also based on the Petri net unfolding. The former is called Full State Graph, the latter - STG-unfolding segment. The boolean logic synthesis is an integral part of the asynchronous circuit design process. In many cases, even if the verification of an asynchronous circuit specification has been performed successfully, it is impossible to obtain its implementation using existing methods because they are based on the reachability analysis. A new approach is proposed here for automated synthesis of speed-independent circuits based on the STG-unfolding segment constructed during the verification of the circuit's specification. Finally, this work presents experimental results showing the need for the new Petri net unfolding techniques and confirming the advantages of application of partial order approach to analysis, verification and synthesis of asynchronous circuits.The Research Committee, Newcastle University: Overseas Research Studentship Award

On the Equivalence of Observation Structures for Petri Net Generators

Observation structures considered for Petri net generators usually assume that the firing of transitions may be observed through a static mask and that the marking of some places may be measurable. These observation structures, however, are rather limited, namely they do not cover all cases of practical interest where complex observations are possible. We consider in this paper more general ones, by correspondingly defining two new classes of Petri net generators: labeled Petri nets with outputs (LPNOs) and adaptive labeled Petri nets (ALPNs). To compare the modeling power of different Petri net generators, the notion of observation equivalence is proposed. ALPNs are shown to be the class of bounded generators possessing the highest modeling power. Looking for bridges between the different formalisms, we first present a general procedure to convert a bounded LPNO into an equivalent ALPN or even into an equivalent labeled Petri net (if any exists). Finally, we discuss the possibility of converting an unbounded LPNO into an equivalent ALPN

Formal Techniques for Component-based Design of Embedded Systems

Embedded systems have become ubiquitous - from avionics and automotive over consumer electronics to medical devices. Failures may entailmaterial damage or compromise safety of human beings. At the same time, shorter product cycles, together with fast growing complexity of the systems to be designed, create a tremendous need for rigorous design techniques. The goal of component-based construction is to build complex systems from simpler components that are well understood and can be (re)used so as to accelerate the design process. This document presents a summary of the formal techniques for component-based design of embedded systems I have (co-)developed